TA 347 F5 K829 2005 WENDT
Engineering Analysis with COSMOSWorks Professional Finite Element Analysis with COSMOSWorks 2005
Paul M. Kurowski Ph.D., PEng.
SolidWorks
^ PUBLICATIONS
Design Generator, Inc.
Schroff Development Corporation
www.schroff.com www.schroff-europe.com
Engineering Analysis with COSMOSWorks Professional Finite Element Analysis with COSMOSWorks 2005
Paul M. Kurowski Ph.D., PEng.
ISBN: 1-58503-249-2
SDC PUBLICATIONS
Schroff Development Corporation www.schroff.com www.schroff-curope.com
General Library System University of Wisconsin - Madison 728 State Street Madison, Wl 53706-1494 U.S.A.
IrabematKs and/Disclaimer SolidWorks and its family of products are registered trademarks of Dassault Systemes. COSMOS Works is registered trademarks of Structural Research & Analysis Corporation. Microsoft Windows and its family products are registered trademarks of the Microsoft Corporation. Every effort has been made to provide an accurate text. The author and the manufacturers shall not be held liable for any parts developed with this book or held responsible for any inaccuracies or errors that appear in the book.
Copyright © 2005 by Paul M. Kurowski All rights reserved. This document may not be copied, photocopied, reproduced, transmitted, or translated in any form or for any purpose without trie express written consent ot the publisher, Schroff Development Corporation.
General Library System University of Wisconsin - Madison 728 State Street Madison, Wl 53706-1494 U.S.A.
Trademarks and Disclaimer SolidWorks and its family of products are registered trademarks of Dassault Systemes. COSMOS Works is registered trademarks of Structural Research & Analysis Corporation. Microsoft Windows and its family products are registered trademarks of the Microsoft Corporation. Every effort has been made to provide an accurate text. The author and the manufacturers shall not be held liable for any parts developed with this book or held responsible for any inaccuracies or errors that appear in the book.
Copyright © 2005 by Paul M. Kurowski All rights reserved. This document may not be copied, photocopied, reproduced, transmitted, or translated in any form or for any purpose without the express written consent of the publisher, Schroff Development Corporation.
TA o ,,—
KM 7m
Engineering Analysis with COSMOSWorks
Acknowledgements Writing this book was a substantial effort that would not have been possible without the help and support of my professional colleagues and friends. 1 would like to thank: •
SolidWorks Corporation
Suchit Jain
•
Mathseed Expeditions Tutoring
Maciej P. Kurowski
•
Javelin Technologies, Inc.
John Carlan, Ted Lee, Bill McEachern, Joseph Vera, Karen Zapata
I would like to thank the students attending my training courses in Finite Element Analysis, for their questions and comments that helped to shape the unique approach this book takes. I thank my wife Elzbieta for her support and encouragement that made it possible to write this book.
About the Author Dr. Paul Kurowski obtained his M.Sc. and Ph.D. in Applied Mechanics from Warsaw Technical University. He completed postdoctoral work at Kyoto University, and the University of Western Ontario. Paul is the President of Design Generator Inc., a consulting firm with expertise in Product Development, Design Analysis, and training in Computer Aided Engineering methods. His teaching experience includes Finite Element Analysis, Machine Design, Mechanics of Materials, Dynamics of Machines and Solid Modeling for universities, professional organizations, and industries. He has published many technical papers and taught professional development seminars for the Society of Automotive Engineers, the American Society of Mechanical Engineers, the Association of Professional Engineers of Ontario, the Parametric Technology Corporation (PTC), Rand Worldwide, SolidWorks Corporation, and Javelin Technologies. Paul is a member of the Association of Professional Engineers of Ontario and the Society of Automotive Engineers. His professional interests focus on Computer Aided Engineering methods used as design tools for faster and more effective product development processes where numerical models replace physical prototypes. Paul Kurowski can be contacted at www.designgenerator.com or
[email protected]
i
Finite Element Analysis with COSMOSWorks
About the cover The image on the cover presents heal flux results in the microchip heat sink. Sec chapter 8 for details.
u
Engineering Analysis with COSMOSWorks
Table of contents Before You Start
1
Notes on hands-on exercises Prerequisites Windows XP terminology
1: Introduction
3
What is Finite Element Analysis? Who should use Finite Element Analysis? Objectives of FEA for Design Engineers What is COSMOSWorks? Fundamental steps in an FEA project Errors in FEA A closer look at finite elements What is calculated in FEA? How to interpret FEA results Units of measurements Using on-line help Limitations of COSMOSWorks Professional
2: Static analysis of a plate
25
Using COSMOSWorks interface Linear static analysis with solid elements The influence of mesh density on displacement and stress results Controlling discretization errors by the convergence process Presenting FEA results in desired format Finding reaction forces
in
Finite Element Analysis with COSMOSWorks
3: Static analysis of an L-bracket
61
Stress singularities Differences between modeling errors and discretization errors Using mesh controls Analysis in different SolidWorks configurations
4: Frequency analysis of a thin plate with shell elements
75
Use of shell elements for analysis of thin walled structures Frequency analysis
5: Static analysis of a link
91
Symmetry boundary conditions Defining restraints in a local coordinate system Preventing rigid body motions Limitations of small displacements theory
6: Frequency analysis of a tuning fork
99
Frequency analysis with and without supports Rigid body modes The role of supports in frequency analysis
7: Thermal analysis of a pipeline component
105
Steady state thermal analysis Analogies between structural and thermal analysis Analysis of temperature distribution and heat flux
8: Thermal analysis of a heat sink Analysis of an assembly Global and local Contact/Gaps conditions Steady state thermal analysis Transient thermal analysis Thermal resistance layer Use of section views in results plots
IV
113
Finite Element Analysis with COSMOSWorks
3: Static analysis of an L-bracket Stress singularities Differences between modeling errors and discretization errors Using mesh controls Analysis in different SolidWorks configurations
4: Frequency analysis of a thin plate with shell elements Use of shell elements for analysis of thin walled structures Frequency analysis
5: Static analysis of a link Symmetry boundary conditions Defining restraints in a local coordinate system Preventing rigid body motions Limitations of small displacements theory
6: Frequency analysis of a tuning fork Frequency analysis with and without supports Rigid body modes The role of supports in frequency analysis
7: Thermal analysis of a pipeline component Steady state thermal analysis Analogies between structural and thermal analysis Analysis of temperature distribution and heat flux
8: Thermal analysis of a heat sink Analysis of an assembly Global and local Contact/Gaps conditions Steady state thermal analysis Transient thermal analysis Thermal resistance layer Use of section views in results plots
IV
Engineering Analysis with COSMOSWorks 9: Static analysis of a hanger
127
Analysis of assembly Global and local Contact/Gaps conditions Hierarchy of Contact/Gaps conditions
10: Analysis of contact stress between two plates
139
Assembly analysis with surface contact conditions Contact stress analysis Avoiding rigid body modes
11: Thermal stress analysis of a bi-metal beam
145
Thermal stress analysis of an assembly Use of various techniques in defining restraints Shear stress analysis
12: Buckling analysis of an L-beam
153
Buckling analysis Buckling load safety factor Stress safety factor
13: Design optimization of a plate in bending
157
Structural optimization analysis Optimization goal Optimization constraints Design variables
14: Static analysis of a bracket using p-elcments P-elements P-adaptive solution method Comparison between h-elements and p-elements
v
169
Finite Element Analysis with COSMOSWorks 15: Design sensitivity analysis
179
Design sensitivity analysis using Design Scenario
16: Drop test of a coffee mug
1S7
Drop test analysis Stress wave propagation Direct time integration solution
17: Miscellaneous topics
195
Selecting the automesher Solvers and solvers options Displaying mesh in result plots Automatic reports E drawings Non uniform loads Bearing load Frequency analysis with pre-stress Large deformation analysis Shrink fit analysis Rigid connector Pin connector Bolt connector
18: Implementation of FEA into the design process
219
FEA driven design process FEA project management FEA project checkpoints FEA report
19: Glossary of terms
227
20: Resources available to FEA User
235
VI
Engineering Analysis with COSMOSWorks
Before You Start Notes on hands-on
exercises
This book goes beyond a standard software manual because its unique approach concurrently introduces you to COSMOSWorks software and the fundamentals of Finite Element Analysis through hands-on exercises. We recommend that you study the exercises in the order presented in the text. As you go through the exercises, you will notice that explanations and steps described in detail in earlier exercises are not repeated later. Each subsequent exercise assumes familiarity with software functions discussed in previous exercises. Every exercise builds on the skills, experience and understanding gained from problems in the previous exercises. An exception to the above is chapter 18, Implementation ofFEA into the design process, which is the only chapter without hands-on exercises. The functionality of COSMOS Works2005 depends on which software bundle is used. In this book we cover the functionality of COSMOSWorks Professional 2005. Functionality of different bundles is explained in the following table: COSMOSWorks Designer
COSMOSWorks Professional
COSMOSWorks Advanced Professional
Linear static analysis of parts and assemblies with gap/contact
The features of COSMOSWorks Designer plus:
The features of COSMOSWorks Professional plus:
Frequency analysis
Nonlinear analysis
Buckling analysis
Fatigue analysis
Drop test analysis
Dynamic analysis
Thermal analysis
Composite analysis
All exercises use SolidWorks models of parts or assemblies, which you can download from http://www.schroffl.coiu/. For your reference, we also provide exercises in ready-to-mesh form. However, these should be treated as a "last resort" as we encourage you to complete exercises without this help. This book is not intended to replace regular software manuals. While you are guided through the specific exercises, not all of the software functions are explained. We encourage you to explore each exercise beyond its description by investigating other options, other menu choices, and other ways to present results. You will soon discover that the same simple logic applies to all functions in COSMOSWorks software.
1
Finite Element Analysis with COSMOSWorks
Prerequisites We assume that you have the following prerequisites: a
An understanding of Mechanics of Materials
•
Experience with parametric, solid modeling using SolidWorks software
a
Familiarity with the Windows Operating System
Windows XP terminology The mouse pointer plays a very important role in executing various commands and providing user feedback. The mouse pointer is used to execute commands, select geometry, and invoke pop-up menus. We will use Windows terminology when referring to mouse-pointer actions.
Item
Description
Click
Self explanatory
Double-click
Self explanatory
Click-inside
Click the left mouse button. Wait a second, and then click the left mouse button inside the pop-up menu or text box. Use this technique to modify the names of folders and icons in COSMOSWorks Manager.
Drag
Use the mouse to point to an object. Press and hold the left mouse button down. Move the mouse pointer to a new location. Release the left mouse button.
Right-click
Click the right mouse button. A pop-up menu is displayed. Use the left mouse button to select a menu command.
All SolidWorks files names appear in CAPITAL letters, even though the actual file name may use a combination of small and capital letters. Selected menu items and COSMOSWorks commands appear in bold, and folder and icon names appear in italics except in illustrations captions, which use only italics.
2
Engineering Analysis with COSMOSWorks
1: Introduction What is Finite Element
Analysis?
Finite Element Analysis, commonly called FEA, is a method of numerical analysis. FEA is used for solving problems in many engineering disciplines such as machine design, acoustics, electromagnetism, soil mechanics, fluid dynamics, and many others. In mathematical terms, FEA is a numerical technique used for solving field problems described by a set of partial differential equations. In mechanical engineering, FEA is widely used for solving structural, vibration, and thermal problems. However, FEA is not the only available tool of numerical analysis. Other numerical methods include the Finite Difference Method, the Boundary Element Method, and the Finite Volumes Method to mention just a few. However, due to its versatility and high numerical efficiency, FEA has come to dominate the engineering analysis software market, while other methods have been relegated to niche applications. You can use FEA to analyze any shape; FEA works with different levels of geometry idealization and provides results with the desired accuracy. When implemented into modern commercial software, both FEA theory and numerical problem formulation become completely transparent to users.
Who should use Finite Element
Analysis?
As a powerful tool for engineering analysis, FEA is used to solve problems ranging from very simple to very complex. Design engineers use FEA during the product development process to analyze the design-in-progress. Time constraints and limited availability of product data call for many simplifications of the analysis models. At the other end of scale, specialized analysts implement FEA to solve very advanced problems, such as vehicle crash dynamics, hydro forming, or air bag deployment. This book focuses on how design engineers use FEA as a design tool. Therefore, we first need to explain what exactly distinguishes FEA performed by design engineers from "regular" FEA. We will then highlight the most essential FEA characteristics for design engineers as opposed to those for analysts. FEA for Design Engineers: another design tool For design engineers, FEA is one of many design tools among CAD, prototypes, spreadsheets, catalogs, data bases, hand calculations, text books, etc. that are all used in the design process.
3
Finite Element Analysis with COSMOSWorks
FEA for Design Engineers: based on CAD models Modern design is conducted using CAD tools, so a CAD model is the starting point for analysis. Since CAD models are used for describing geometric information for FEA, it is essential to understand how to design in CAD in order to produce reliable FEA results, and how a CAD model is different from FEA model. This will be discussed in later chapters. FEA for Design Engineers: concurrent with the design process Since FEA is a design tool, it should be used concurrently with the design process. It should keep up with, or better yet, drive the design process. Analysis iterations must be performed fast, and since these results are used to make design decisions, the results must be reliable even when limited input is available. Limitations of FEA for Design Engineers As you can see, FEA used in the design environment must meet high requirements. An obvious question arises: would it be better to have a dedicated specialist perform FEA and let design engineers do what they do best - design new products? The answer depends on the size of the business, type of products, company organization and culture, and many other tangible and intangible factors. A general consensus is that design engineers should handle relatively simple types of analysis, but do it quickly and of course reliably. Analyses that are very complex and time consuming cannot be executed concurrently with the design process, and are usually better handled either by a dedicated analyst or contracted out to specialized consultants.
4
Engineering Analysis with COSMOSWorks
Objectives ofFEA for Design
Engineers
The ultimate objective of using the FEA as a design tool is to change the design process from repetitive cycles of "design, prototype, test" into a streamlined process where prototypes are not used as design tools and are only needed for final design verification. With the use of FEA, design iterations are moved from the physical space of prototyping and testing into the virtual space of computer simulations (figure 1-1).
TRADITIONAL PRODUCT DESIGN PROCESS
FEA-DRIVEN PRODUCT DESIGN PROCESS
DESIGN
It PROTOTYPING
PROTOTYPING
TESTING
TESTING
it PRODUCTION
PRODUCTION
Figure 1-1: Traditional and. FEA-drivcn product development Traditional product development needs prototypes to support design in progress. The process in FEA-driven product development uses numerical models, rather than physical prototypes to drive development. In an FEAdriven product, the prototype is no longer a part of the iterative design loop.
5
Finite Element Analysis with COSMOSWorks
What is
COSMOSWorks? COSMOSWorks is a commercial implementation of FEA, capable of solving problems commonly found in design engineering, such as the analysis of deformations, stresses, natural frequencies, heat flow, etc. COSMOSWorks addresses the needs of design engineers. It belongs to the family of engineering analysis software products developed by the Structural Research & Analysis Corporation (SRAC). SRAC was established in 1982 and since its inception has contributed to innovations that have had a significant impact on the evolution of FEA. In 1995 SRAC partnered with the SolidWorks Corporation and created COSMOSWorks, one of the first SolidWorks Gold Products, which became the top-selling analysis solution for SolidWorks Corporation. The commercial success of COSMOSWorks integrated with SolidWorks CAD software resulted in the acquisition of SRAC in 2001 by Dassault Systemes, parent of SolidWorks Corporation. In 2003, SRAC operations merged with SolidWorks Corporation. COSMOSWorks is tightly integrated with SolidWorks CAD software and uses SolidWorks for creating and editing model geometry. SolidWorks is a solid, parametric, feature-driven CAD system. As opposed to many other CAD systems that were originally developed in a UNIX environment and only later ported to Windows, SolidWorks CAD was developed specifically for the Windows Operating System from the very beginning. In summary, although the history of the family of COSMOS FEA products dates back to 1982, COSMOSWorks has been specifically developed for Windows and takes full advantage this of deep integration between SolidWorks and Windows, representing the state-of-the-art in the engineering analysis software.
Fundamental steps in an FEA project The starting point for any COSMOSWorks project is a SolidWorks model, which can be one part or an assembly. At this stage, material properties, loads and restraints are defined. Next, as is always the case with using any FEAbased analysis tool, we split the geometry into relatively small and simply shaped entities, called finite elements. The elements are called "finite" to emphasize the fact that they are not infinitesimally small, but only reasonably small in comparison to the overall model size. Creating finite elements is commonly called meshing. When working with finite elements, the COSMOSWorks solver approximates the solution being sought (for example, deformations or stresses) by assembling the solutions for individual elements.
6
Engineering Analysis with COSMOSWorks
From the perspective of FEA software, each application of FEA requires three steps: •
Preprocessing of the FEA model, which involves defining the model and then splitting it into finite elements
U Solution for computing wanted results J
Post-processing for results analysis
We will follow the above three steps every time we use COSMOSWorks. From the perspective of FEA methodology, we can list the following FEA steps: •
Building the mathematical model
a
Building the finite element model
•
Solving the finite element model
•
Analyzing the results
The following subsections discuss these four steps.
Building the mathematical model The starting point to analysis with COSMOSWorks is a SolidWorks model. Geometry of the model needs to be meshable into a correct and reasonably small element mesh. This requirement of meshability has very important implications. We need to ensure that the CAD geometry will indeed mesh and that the produced mesh will provide the correct solution of the data of interest, such as displacements, stresses, temperature distribution, etc. This necessity often requires modifications to the CAD geometry, which can take the form of defeaturing, idealization and/or clean-up, described below:
Description
Term Defeaturing
The process of removing geometry features deemed insignificant for analysis, such as external fillets, chamfers, logos, etc.
Idealization
A more aggressive exercise that may depart from solid CAD geometry by for example, representing thin walls with surfaces
Clean-up
Sometimes needed because for geometry to be meshable, it must satisfy much higher quality demands than those required for Solid Modeling. To cleanup, we can use CAD quality-control tools to check for problems like sliver faces, multiple entities, etc. that could be tolerated in the CAD model, but would make subsequent meshing difficult or impossible
7
Finite Element Analysis with COSMOSWorks
It is important to mention that we do not always simplify the CAD model with the sole objective of making it meshable. Often, we must simplify a model even though It would mesh, correctly "as is", but the resulting mesh would be too large and consequently, the analysis would take too much time. Geometry modifications allow for a simpler mesh and shorter computing times. Also, geometry preparation may not be required at all; successful meshing depends as much on the quality of geometry submitted for meshing as it does on the sophistication of the meshing tools implemented in the FEA software. WaVvrvo rserjareA am^aVAe^utuoYNe\me%\\e& °eometxv ,vvenovg teime material properties (these can also be imported from a SolidWorks model), loads and restraints, and provide information on the type of analysis that we wish to perform. This procedure completes the creation of the mathematical model (figure 1-2). Notice that the process of creating the mathematical model is not FEA-specific. FEA has not yet entered the picture.
Modification ot seometn.... . -,, (ir required)
. . Loads
*
.
. . . Restraints
I! t t Material properties
CAD geometry
Type of analysis
FEA geometry
Figure 1-2: Building the mathematical model The process of creating a mathematical model consists of the modification of CAD geometry (here removing external fillets), definition of loads, restraints material properties, and definition of the type of analysis (e.g., static) that we wish to perform.
Finite Element Analysis with COSMOSWorks
It is important to mention that we do not always simplify the CAD model with (he sole objective of making it meshable. Often, we must simplify a model even though it would mesh correctly "as is", but the resulting mesh would be too large and consequently, the analysis would take too much time. Geometry modifications allow for a simpler mesh and shorter computing times. Also, geometry preparation may not be required at all; successful meshing depends as much on the quality of geometry submitted for meshing as it does on the sophistication of the meshing tools implemented in the FEA software. Having prepared a meshable, but not yet meshed geometry, we now define material properties (these can also be imported from a SolidWorks model), loads and restraints, and provide information on the type of analysis that we wish to perform. This procedure completes the creation of the mathematical model (figure 1-2). Notice that the process of creating the mathematical model is not FEA-specific. FEA has not yet entered the picture.
Modification of geometry
*M
Loads
k
Restraints
* "
MATHEI ATTCAL MOBEL "M:
t t Material Type of 1 roperties analysis geometry
FEA geometry
Figure 1-2: Building the mathematical model The process of creating a mathematical model consists of the modification of CAD geometry (here removing external fillets), definition of loads, restraints, material properties, and definition of the type of analysis (e.g., static) that we wish to perform.
Engineering Analysis with COSMOSWorks
Building the finite element model The mathematical model now needs to be split into finite elements through a process of discretization, more commonly known as meshing (figure 1-3). I ,oads and restraints are also discretized and once the model has been meshed, the discretized loads and restraints are applied to the nodes of the finite element mesh.
Discretization
Numerical solver
I
I MATHEMATICAL MODEL
:-;iiliS!"'
FEA model
FEA results
Figure 1-3: Building the finite element model The mathematical model is discretized into a finite element model. This completes the pre-processing phase. The FEA model is then solved with one of the numerical solvers available in COSMOSWorks.
Solving the finite element model Having created the finite element model, we now use a solver provided in COSMOSWorks to produce the desired data of interest (figure 1-3). Analyzing the results Often the most difficult step of FEA is analyzing the results. Proper interpretation of results requires that we understand all simplifications (and errors they introduce) in the first three steps: defining the mathematical model, meshing its geometry, and solving.
9
Finite Element Analysis with COSMOSWorks
Errors in FEA The process illustrated in figures 1-2 and 1-3 introduces unavoidable errors. Formulation of a mathematical model introduces modeling errors (also called idealization errors), discretization of the mathematical model introduces discretization errors, and solving introduces numerical errors. Of these three types of errors, only discretization errors are specific to FEA. Modeling errors affecting the mathematical model are introduced before FEA is utilized and can only be controlled by using correct modeling techniques. Solution errors caused by the accumulation of round-off errors are difficult to control, but are usually very low.
A closer look at finite
elements
Meshing splits continuous mathematical models into finite elements. The type of elements created by this process depends on the type of geometry meshed, the type of analysis, and sometimes on our own preferences. COSMOSWorks offers two types of elements: tetrahedral solid elements (for meshing solid geometry) and shell elements (for meshing surface geometry). Before proceeding we need to clarify an important terminology issue. In CAD terminology "solid" denotes the type of geometry: solid geometry (as opposed to surface or wire frame geometry), in FEA tenninology it denotes the type of element. Solid elements The type of geometry that is most often used for analysis with COSMOSWorks is solid CAD geometry. Meshing of this geometry is accomplished with tetrahedral solid elements, commonly called "tets" in FEA jargon. The tetrahedral solid elements in COSMOSWorks can either be first order elements (draft quality), or second order elements (high quality). The user decides whether to use draft quality or high quality elements for meshing. However, as we will soon prove, only high quality elements should be used for an analysis of any importance. The difference between first and second order tetrahedral elements is illustrated in figure 1-4.
10
Engineering Analysis with COSMOSWorks
Alter deformation
Before deformation
After deformation
Before deformation 2m order tetrahedral element
1* order tetrahedral element
Figure 1 -4: Differences between first and second order tetrahedral elements First and the second order tetrahedral elements are shown before and after deformation. Note that the deformed faces of the second order element may assume curvilinear shape while deformed faces of the first order element must remain fiat. First order tetrahedral elements have four nodes, straight edges, and flat faces. These edges and faces remain straight and flat after the element has experienced deformation under the applied load. First order tetrahedral elements model the linear field of displacement inside their volume, on faces, and along edges. The linear (or first order) displacement field gives these elements their name: first order elements. If you recall from the Mechanics of Materials, strain is the first derivative of displacement. Therefore, strain and consequently stress, are both constant in first order tetrahedral elements. This situation imposes a very severe limitation on the capability of a mesh constructed with first order elements to model stress distribution of any real complexity. To make matters worse, straight edges and flat faces can not map properly to curvilinear geometry, as illustrated in figure 1-5.
11
Finite Element Analysis with COSMOSWorks
Figure 1-5: Failure of straight edges and flat faces to map to curvilinear geometry A detail of a mesh created with first order tetrahedral elements. Notice the imprecise element mapping to the hole; flat faces approximate the face of the cylindrical hole. Second order tetrahedral elements have ten nodes and model the second order (parabolic) displacement field and first order (linear) stress field in their volume, along laces, and edges. The edges and faces of second order tetrahedral elements before and after deformation can be curvilinear. Therefore, these elements can map precisely to curved surfaces, as illustrated in figure I -6. Even though these elements are more computationally demanding than first order elements, second order tetrahedral elements are used for the vast majority of analyses with COSMOSWorks.
Figure 1-6: Mapping curved surfaces A detail is shown of a mesh created with second order tetrahedral Second order elements map well to curvilinear geometry.
12
elements.
Engineering Analysis with COSMOSWorks
Shell elements Besides solid elements, COSMOSWorks also offers shell elements. While solid elements are created by meshing solid geometry, shell elements are created by meshing surfaces. Shell elements are primarily used for analyzing thin-walled structures. Since surface geometry does not carry information about thickness, the user must provide this information. Similar to solid elements, shell elements also come in draft and high quality with analogous consequences with respect to their ability to map to curvilinear geometry, as shown in figure 1-7 and figure 1-8. As demonstrated with solid elements, first order shell elements model the linear displacement field with constant strain and stress while second order shell elements model the second order (parabolic) displacement field and the first order strain and stress field.
1
- ^ " '
A
%
\
X 1
/A
r k
1
Figure 1-7: First order shell element This shell element mesh was created with first order elements. Notice the imprecise mapping of the mesh to curvilinear geometry.
13
Finite Element Analysis with COSMOSWorks
Figure 1-8: Second order shell element Shell element mesh created with second order elements, which map correctly to curvilinear geometry. Certain classes of shapes can be modeled using either solid or shell elements, such as the plate shown in figure 1-9. The type of elements used depends then on the objective of the analysis. Often the nature of the geometry dictates what type of element should be used for meshing. For example, parts produced by casting are meshed with solid elements, while a sheet metal structure is best meshed with shell elements.
Figure 1-9: Plate modeled with solid elements (left) and shell elements The plate shown can be modeled with either solid elements (left) or shell elements (right). The actual choice depends on the particular requirements of analysis and sometimes on personal preferences.
14
Engineering Analysis with COSMOSWorks
Figure 1-10, below, presents the basic library of elements in COSMOSWorks. Elements like a hexahedral solid, quadrilateral shell or other shapes are not available in COSMOSWorks
Triangular shell element
Tetrahedral solid element
6 Degrees of Freedom per node
3 Degrees of Freedom per node
First order element Linear displacement field Constant stress field
Second order element Parabolic (second order) displacement field Linear stress field
I
/
/
A \
/ \ 2 /
\ "••••
'.
/A
^3
"-*-4
Most commonly used element
Figure 1-10: COSMOSWorks element library Four element types are available in the COSMOSWorks element library. The vast majority of analyses use the second order tetrahedral element. Both solid and shell first order elements should be avoided.
The degrees of freedom (DOF) of a node in a finite element mesh define the ability of the node to perform translation or rotation. The number of degrees of freedom that a node possesses depends on the type of element that the node belongs to. In COSMOSWorks, nodes of solid elements have three degrees of freedom, while nodes of shell elements have six degrees of freedom. This means that in order to describe transformation of a solid element from the original to the deformed shape, we only need to know three translational components of nodal displacement, most often the x, y, z displacements. In
15
Finite Element Analysis with COSMOSWorks the case of shell elements, we need to know not only the translational components of nodal displacements, but also the rotational displacement components.
What is calculated in FEA ? Each degree of freedom of every node in a finite element mesh constitutes an unknown. In structural analysis, where we look at deformations and stresses, nodal displacements are the primary unknowns. If solid elements are used, there are three displacement components (or 3 degrees of freedom) per node that must be calculated. With shell elements, six displacement components (or 6 degrees of freedom) must be calculated. Everything else, such as strains and stresses, are calculated based on the nodal displacements. Consequently, rigid restraints applied to solid elements require only three degrees of freedom to be constrained. Rigid restraints applied to shell elements require that all six degrees of freedom be constrained. In a thermal analysis, which finds temperatures and heat flow, the primary unknowns are nodal temperatures. Since temperature is a scalar value (unlike the vector nature of displacements), then regardless of what type of element is used, there is only one unknown (temperature) to be found for each node. All other results available in the thermal analysis are calculated based on temperature results. The fact that there is only one unknown to be found for each node; rather than three or six, makes thermal analysis less computationally intensive than structural analysis.
How to interpret FEA results Results of structural FEA are provided in the form of displacements and stresses. But how do we decide if a design "passes" or "fails" and what does it take for alarms to go off? What exactly constitutes a failure? To answer these questions, we need to establish some criteria to interpret FEA results, which may include maximum acceptable deformation, maximum stress, or lowest acceptable natural frequency. While displacement and frequency criteria are quite obvious and easy to establish, stress criteria are not. Let's assume that we need to conduct a stress analysis in order to ensure that stresses are within an acceptable range. To judge stress results, we need to understand the mechanism of potential failure, [fa part breaks, what stress measure best describes that failure? Is it von Mises stress, maximum principal stress, shear stress, or something else? COSMOSWorks can present stress results in any form we want. It is up to us to decide which stress measure to use for issuing a "pass" or "fail" verdict. Discussion of various failure criteria would be out of the scope of this book. Any textbook on the Mechanics of Materials provides information on this topic. Interested readers can also refer to books listed in chapter 20. Here we will limit our discussion to outlining the differences between two commonly used stress measures: von Mises stress and the principal stress.
16
Engineering Analysis with COSMOSWorks
Von Mises stress Von Mises stress, also known as Huber stress, is a stress measure that accounts for all six stress components of a general 3-D state of stress (figure 1-11).
>;
Figure 1-11: General state of stress represented by three normal stresses: o\. a^,, a z and six shear stresses TVV = TVY, TV7 = T7V, TX7 = T7X Two components of shear stress and one component of normal stress act on each side of an elementary cube. Due to equilibrium requirements, the general 3-D state of stress is characterized by six stress components: ax, av, a- and rTV = rVA, rv-
Von Mises stress oeq, can be expressed either by six stress components as:
(Jeq
= A J O . 5 * [((Jx
- (Jy)
+ (0"v - (7z)2
+ (CT= - (Jx)2
] + 3 * (jxy2
+ Ty~2
+ T-J
or by three principal stresses (see the next paragraph) as:
(Jeq = y 0 . 5 * [ ( C r , -G2)
+ « T 2 -
Note that von Mises stress is a non-negative, scalar value. Von Mises stress is commonly used to present results because structural safety for many engineering materials showing elasto-plastic properties (for example, steel) can be evaluated using von Mises stress. The magnitude of von Mises stress can be compared to material yield or to ultimate strength to calculate the yield strength or the ultimate strength safety factor.
17
)
Finite Element Analysis with COSMOSWorks Principal stresses By properly adjusting the angular orientation of the stress cube in figure 1-11, shear stresses disappear and the state of stress is represented only by three principal stresses: o : , o2, and 03, as shown in figure 1-12. In COSMOSWorks, principal stresses are denoted as PI, P2, and P3.
$* O ,
Figure 1-12: General state of stress represented bv three principal stresses: a-,, a;. o-, PI stress is used for evaluating stress results in parts made of brittle material whose safety is better related to PI than to von Mises stress
18
Engineering Analysis with COSMOSWorks
Units of
measurements Internally, COSMOSWorks uses the International System of Units (SI). However, for the user's convenience, the unit manager allows data entry in three different systems of units: SI, Metric, and English. Results can be displayed using any of the three unit systems. Figure 1-13 summarizes the available systems of units. International System (SI)
Metric (MKS)
Mass Length
kg
kg
lb.
m
cm
in.
Time
s
s
s
Force
N
Kgf
lb.
kg/cm
lb./in.3
°C
°F
Mass density
kg/m
Temperature
°K
J
English (IPS)
Figure 1-13: Unit systems available in COSMOSWorks SI, Metric, and English systems of units can be interchanged when entering data or analyzing results in COSMOSWorks. Experience indicates that units of mass density are often confused with units of specific gravity. The distinction between these two is quite clear in SI units: Mass density is expressed in [kg/m3], while specific gravity in [N/m3]. However, in the English system, both specific mass and specific gravity are . expressed in [lb/in.3], where [lb] denotes either pound mass or pound force. As COSMOSWorks users, we are spared much confusion and trouble with systems of units. However, we may be asked to prepare data or interpret the results of other FEA software where we do not have the convenience of the unit manager. Therefore, we will make some general comments about the use of different systems of units in the preparation of input data for FEA models. We can use any consistent system of units for FEA models, but in practice, the choice of the system of units is dictated by what units are used in the CAD model. The system of units in CAD models is not always consistent; length can be expressed in [mm], while mass density can be expressed in [kg/m3]. Contrary to CAD models, in FEA all units must be consistent. Inconsistencies are easy to overlook, especially when defining mass and mass density, and they can lead to very serious errors.
19
Finite Element Analysis with COSMOSWorks
In the SI system, which is based on meters [m] for length, kilograms [kg] for mass and seconds [s] for time, all other units are easily derived from these basic units. In mechanical engineering, length is commonly expressed in millimeters [mm], force in Newtons [N], and time in seconds [s]. All other units must then be derived from these basic units: [mm], [N], and [s]. Consequently, the unit of mass is defined as a mass which, when subjected to a unit force equal to IN, will accelerate with a unit acceleration of 1 mm/s2. Therefore, the unit of mass in a system using [mm] for length and [N] for force, is equivalent to 1,000 kg or one metric ton. Consequently, mass density is expressed in metric tonnes [tonne/mm3]. This is critically important to remember when defining material properties in FEA software without a unit manager. Notice in figure 1-14 that an erroneous definition of mass density in [kg/m3] rather than in [tonne/mm3] results in mass density being one trillion (1012) times higher (figure 1-14).
System SI
[m], [N], [s]
Unit of mass
kg
Unit of mass density
kg/m
Density for aluminum
2794 kg/m3
System of units derived from SI
[mm], [N], [s]
Unit of mass
tonne
Unit of mass density
tonne/mm3
Density of aluminum
2.794 x 10"9 tonne/mm3
English system (IPS)
[in], [LB], [s]
Unit of mass
LB = slug/12
Unit of mass density
slug/12/in.3
Density of aluminum
2.614 xl0' 4 slug/12/in. 3
Figure 1-14: Mass densities of aluminum in the three systems of units Comparison of numerical values of mass densities of aluminum defined in the SI system of units with the system of units derivedfrom SI, and with the English (IPS) system of units.
20
Engineering Analysis with COSMOSWorks
Using on-line help COSMOSWorks features very extensive on-line Help and Tutorial functions, which can be accessed from the Help menu in the main COSMOSWorks tool bar (figure 1-15). COSMOSWorks Help Topics
t <^
I
COSMOSWorks Online Tutorial COSMOSWorks Service Facte.,, f'
<•
SolidWorks Help Topics Quick Tips COSMOSWorks QuickTips SolidWorks API and Add-Ins Help Topics Moving from AutoCAD Introducing SoiidWorks Online Tutorial What's New Manual Interactive What's U&M Service Packs,,, SolidWorks Release Notes About. SolidWor
Customise Menu
Figure 1-15: Accessing the on-line Help and Tutorial On-line Help and Tutorial can be accessed from the main COSMOSWorks toolbar.
21
Finite Element Analysis with COSMOSWorks
Limitations of COSMOSWorks Professional We need to appreciate some important limitations of COSMOSWorks Professional: material is assumed as linear, deformations are small, and loads are static. Linear material Whatever material we assign to the analyzed parts or assemblies, this material will be assumed as linear, meaning that stress is proportional to strain (figure 1-16).
STRESS
Linear material model used by COSMOSWorks Professional
Linear ranee
Non-linear material model available in COSMOSWorks Advanced Professional STRAIN
Figure 1-16: Linear material model assumed in COSMOSWorks In all materials used by COSMOSWorks Professional stress is linearly proportional to strain. Using a linear material model, the maximum stress magnitude is not limited to yield or to ultimate stress as it is in real life. For example, in a linear model, if stress reaches 800 MPa under a load of 1,000 N, then stress will reach 8,000 MPa under a load of 10,000 N. 8,000 MPa is of course, an absurdly high stress value. Material yielding is not modeled, and whether or not yield may in fact be taking place can only be established based on the stress magnitudes reported in results. Most analyzed structures experience stresses below the yield stress, and the factor of safety is most often related to the yield stress. Therefore, the analysis limitations imposed by linear material seldom impede COSMOSWorks Professional users.
22
Finite Element Analysis with COSMOSWorks
Limitations of COSMOSWorks Professional We need to appreciate some important limitations of COSMOSWorks Professional: material is assumed as linear, deformations are small, and loads are static. Linear material Whatever material we assign to the analyzed parts or assemblies, this material will be assumed as linear, meaning that stress is proportional to strain (figure 1-16).
STRESS
Linear material model used by COSMOSWorks Professional
Linear ranae
Non-linear material model available in COSMOSWorks Advanced Professional STRAIN
.
Figure 1-16: Linear material model assumed in COSMOSWorks In all materials used by COSMOSWorks Professional, stress is linearly proportional to strain. Using a linear material model, the maximum stress magnitude is not limited to yield or to ultimate stress as it is in real life. For example, in a linear model, if stress reaches 800 MPa under a load of 1,000 N, then stress will reach 8,000 MPa under a load of 10,000 N. 8,000 MPa is of course, an absurdly high stress value. Material yielding is not modeled, and whether or not yield may in fact be taking place can only be established based on the stress magnitudes reported in results. Most analyzed structures experience stresses below the yield stress, and the factor of safety is most often related to the yield stress. Therefore, the analysis limitations imposed by linear material seldom impede COSMOSWorks Professional users.
72
Engineering Analysis with COSMOSWorks
Small deformations Any structure experiences deformation under load. The Small Deformations assumption requires that these deformations be "small". What exactly is a small defonnation? Often it is explained as a deformation that is small in relation to the overall size of the structure. For example, large deformations of a beam are shown in figure 1-17.
\ Shape before deformation
Shape after deformation
Figure 1-17: Beam experiencing large deformations in bending COSMOSWorks Professional assumes that deformations are small. If deformations are large, as shown in this illustration, these assumptions do not apply. Other COSMOS analysis tools, such as COSMOSWorks Advanced Professional must be used to analyze this structure. However, the magnitude of defonnation is not the deciding factor when classifying defonnation as "small" or "large". What really matters is whether or not the defonnation changes structural stiffness in a significant way. An analysis run with the assumption of small defonnations assumes that the structural stiffness remains the same throughout the deformation process. Large deformation analysis accounts for changes of stiffness caused by deformations. While the distinction between small and large deformations is quite obvious for the beam in figure 1 -17, it is not at all obvious for a flat membrane under pressure in figure 1-18.
23
Finite Element Analysis with COSMOSWorks
Figure 1-18: Flat membrane under pressure load. Bottom illustrations shows model in a radial cross section. Here is a classic case where the assumption of small deformation leads to erroneous results. Analysis of a flat membrane under pressure requires a large deformation analysis even though deformations are small in comparison to the size of membrane. For a Hat membrane, initially the only mechanism resisting the pressure load is bending stiffness. During the deformation process, the membrane additionally acquires membrane stiffness. In effect, the resultant stiffness changes significantly during deformation. This change in stiffness requires a large deformation analysis, using tools like COSMOSWorks Advanced Professional or COSMOSDesignSTAR.
Static loads All loads, as well as restraints, are assumed not to change with time, meaning that dynamic loading conditions cannot be analyzed with COSMOSWorks Professional (the only exception is Drop Test analysis). This limitation implies that loads are applied slowly enough to ignore inertial effects. Dynamic analysis can be performed with COSMOSWorks Advanced Professional
24
Engineering Analysis with COSMOSWorks
2: Static analysis of a plate Topics covered a
Using COSMOSWorks interface
•
Linear static analysis with solid elements
•
The influence of mesh density on displacement and stress results
•
Controlling discretization errors by the convergence process
•
Presenting FEA results in desired format
•
Finding reaction forces
Project description A steel plate is supported and loaded, as shown in figure 2-1. We assume that the support is rigid (this is also called built-in support or fixed support) and that the 100,000 N tensile load is uniformly distributed along the end face, opposite to the supported face.
S*N,j :--...
Fixed restraint applied to this face
:imS^:V:i?N.
:
M:>..
100,000 N tensile load uniformly distributed on this face
Figure 2-1: SolidWorks model of a rectangular plate with a hole We will perform displacement and stress analysis using meshes with different element sizes. Note that repetitive analysis with different meshes does not represent standard practice in FEA. We will repeat the analysis using different meshes only as a learning tool to gain more insight into how FEA works.
25
Finite Element Analysis with COSMOSWorks
Procedure In SolidWorks, open the model file called HOLLOW PLATE. Verify that COSMOSWorks is selected in the Add-lns list. To start COSMOSWorks, select the COSMOSWorks Manager tab, as shown in figure 2-2.
V
] eOfawings 2005 I Fe-stunsWorks j PhotoWorks J Save As PDF J SolidWorks 2D Emulate
%a hollow plate
IcosMOSV-iwisl^!^}:
; j Parameters
"OSMOSVorte ''005 design Anaiysis program by SoSdWorks Z:\COSMOS 2005 beta 2\cosworks.dll
Figure 2-2: Add-lns list and COSMOSWorks Manager tab Verify that COSMOSWorks is selected in the list of Add-lns (left), and then select the COSMOSWorks Manager tab (right). To create an FEA model, solve it, and analyze the results, we will use a graphical interface. You can also do this by making the appropriate choices in the COSMOSWorks menu. To call up the menu, select COSMOSWorks from the main tool bar of SolidWorks (figure 2-3).
26
Engineering Analysis with COSMOSWorks
Study...
Loads/Restraint
•
Shell-;
>
Mesh
•
Plot Results
•
List Results
•
Result Tools
•
Design Scenario
Optimization Fatigue Parameters...
Export,,. Import Motion Loads... Launch COSMQSDesignSTAR
See Figure 2-4.
Options,,,
$ Help About COSMOSWorks Customize Menu
Figure 2-3: COSMOSWorks menu All functions used for creating, solving, and analyzing a model can be executed either from this menu or from the graphical interface in the COSMOSWorks Manager window. We will use the second method. Before we create the FEA model, let's review the Options window in COSMOSWorks (figure 2-4). This window can be accessed from the COSMOSWorks main menu (figure 2-3).
27
Finite Element Analysis with COSMOSWorks
Plot
Results Genets!
j
Urite
teieiiel
Export Load/Reslraint
Mesh
System of unite: tetigih unic: i Kek
Tempeiatufe units. Angulai velocity unite
lad/sec
Help
Fjgure 2-4: COSMOSWorks Options window; shown is Units tab 77?e COSMOSWorks Preferences window has several tabs. Selecting the Units tab, displayed above, allows selection of units of measurement. We will use the SI system. Please review other tabs before proceeding with the exercise. Creation of an FEA model always starts with the definition of a study. To define a study, right-click the mouse on the Part icon in the COSMOSWorks Manager window and select Study... from the pop-up menu. In this exercise, the Part icon is called hollow plate, as it is in the Solid Works Manager. Figure 2-5 shows the required selections in the study definition window: the analysis type is Static, the mesh type is Solid mesh. The study name is tensile load 01.
28
Engineering Analysis with COSMOSWorks
hollow pi< !» Parameter*: «>? ornpare Test Data.
Part icon
Define Function Curves
Right-click
Options,.,
K y name tensile bad 01
\ Analysis type Static .
Cancel
Figure 2-5: Study window To display the Study window (bottom), right-click the Part icon in the COSMOSWorks Manager window (top left), and then from the pop-up menu (top right), select Study.... When a study is defined, COSMOSWorks automatically creates a study folder (named in this case tensile load 01) and places several sub-folders in it (some of these sub-folders are empty because their contents must by defined by the user), as shown in figure 2-6. Not all folders are used in each analysis. In this exercise, we will use the Solids folder to define and assign material properties, the Load/Restraint folder to define loads and restraints, and the Mesh folder to create the finite element mesh.
29
Finite Element Analysis with COSMOSWorks
t hollow plate J | ! | Parameters • ^ f tensile load 01 (-Default-) -
^Solids :
^
hollow plate
l"-43 Load/Restraint • §§§ Design Scenario • ^
Mesh
EbJReport
Figure 2-6: Study folders COSMOSWorks automatically creates a study folder, called tensile load 01, with the following sab folders: Solids, Load/Restraint, Design Scenario, Mesh and Report folder. The Design Scenario and Report folders will not be used in this exercise, nor will the Parameters folder, which is automatically created prior to study definition. We are now ready to define the mathematical model. This process generally consists of the following steps: •
Geometry preparation
•
Material properties assignment
•
Restraints application
u
Load application
In this case, the model geometry does not need any preparation (it is already very simple), so we can start by assigning material properties. You can assign material properties to the model either by: LI
Right-clicking the mouse on the Solids folder, or
•
Right-clicking the mouse on the hollow plate icon, which is located in the Solids folder.
The first method assigns the same material properties to all components in the model, while the second method assigns material properties to one particular component (in this exercise, hollow plate). In this example there is no difference between the two methods, because we are working with a single part and not with an assembly. Therefore, there is only one component in the Solids folder.
30
Engineering Analysis with COSMOSWorks
Right-click on the Solids folder and select Apply Material to All. This action opens the Material window shown in figure 2-7.
cbo! matsrisi source
Properties ; Tables S, Curves
O Use Sofciwaks material CjOMom
defined
O Getito! fbtaty <*r From library fifes : cosmos materials
Model Type.
; Linear Elastic Isotropic
Units:
I SI
l&nch
Category:
:|
B B :- B I S © -S
AISI4130Steel,?: AISI 4340 Steel," AISI 4340 Steel, AISI Type 316L AISI Type A2 Tc ASTMA38Stee;:
a a S E3
CastA!!qy Steel -: Cast Carbon Ste Cast Stainless Si Chrome StsWes;|
Name; Property
:
NlKr" SHY DENS SIGXT SiSXC SIGYLD AlPX KX C
i**f : Description Value Elastic modulus :zi<*timm\,r±; iSM'S:iPoksort's ratio Shea? modulus 3:IS98aS8s
! ! "r'..
iUnits t i ' n " ; "" MA N/nT~2 kq/rn~3 N/nT\s NAr)A2 M/nT\2 /Kelvin W/jm.KJ J/ll-gM
mmmmms' •mmmmz v:mm -»^ ,
»
;
,
,
•
•
:
•
&
\ Temp Dependency :
Ite8ter>r:™:i|itiii . v ,t,l i
.EonsSi-fs. .:>':.:.'. Snsfenj;y :
r'.i.
. --,.
.
.Constant -::. C n> • &:#t«r*:.
•
\.;i
Help
Figure 2-7: Material window Select From library files in the Select material source area, then Select Alloy Steel. Select SI units under Properties tab (other units could be used as well). Notice that the Solids folder now shows a check mark and the name of the selected material to indicate that a material has successfully been assigned. If needed, you could define your own material by selecting Custom Defined material. Note that material assignment actually consists of two steps: •
Material selection (or material definition if custom material is used)
•
Material assignment to either all solids in the model or to selected components (this makes a difference only if the assembly is analyzed)
We should also notice that if a material has been defined for a SolidWorks part model, material definition is automatically transferred to the COSMOSWorks model. Assigning a material to the SolidWorks model is actually a preferred modeling technique, especially when working with an assembly consisting of parts with many different materials. We will do this in later exercises.
31
Finite Element Analysis with COSMOSWorks
To display the pop-up menu that lists the options available for defining loads and restraints, right-click the Load/Restraint folder in tensile load 01 study (figure 2-8).
j hollow plate * | Parameters
q* tensile load 01 (-Default-) -
^Solids
i hollow plate (-Alloy Steel*-)
Restraints.,, Pressure... Force.. Gravity..,
Centrifugal,,. Remote Load,.. Bearing Load,..
Connectors,.. Temperature... Option;., Copy
Figure 2-8: Pop-up menu for the Load/Restraint folder The arrows indicate the selections used in this exercise. To define the restraints, select Restraints... from the pop-up menu displayed in figure 2-8. This action opens the Restraint window shown in figure 2-9.
32
Engineering Analysis with COSMOSWorks
F«ed
f.Shw,
v
fSV&w
:* * •:•:•••• • • . . . . .
Nil C£for,
t t f •<»
V
Fixed support applied to this face
Figure 2-9: Restraint window face
You can rotate the model in order to selert tin P fo
u
COSMOSWorks work the same as in SolidWorks. In the Restraint window, select Fixed as the w chart r „,e W S „'ther c h ^ ^ ^
fo..ow,„g
33
«f * S S ^
S
^
^
Finite Element Analysis with COSMOSWorks
Definition
Restraint Type Fixed
Also called built-in or rigid support, all translational and all rotational degrees of freedom are restrained. Note that Fixed restraints do not require any information on the direction along which restraints are applied.
Immovable (No translations)
Only translational degrees of freedom are constrained, while rotational degrees of freedom remain unconstrained. If solid elements are used (like in this exercise), Fixed and Immovable restraints have the same effect because solid elements do not have rotational degrees of freedom.
Reference plane or axis
This option restrains a face, edge, or vertex only in a certain direction, while leaving the other directions free to move. You can specify the desired direction of restraint in relation to the selected reference plane or reference axis.
On flat face
This option provides restraints in selected directions, which are defined by the three principal directions of the flat face where restraints are being applied.
On cylindrical face
This option is similar to On flat face, except that the three principal directions of a cylindrical face define the directions of restraints.
On spherical face
Similar to On flat face and On cylindrical face. The three principal directions of a spherical face define the directions of applied restraints.
Symmetry
This option is similar to On flat face. It applies symmetry boundaiy conditions automatically to a flat face. Translation in the direction normal to the face is restrained and rotations about axes aligned with the face are restrained.
When a model is fully supported (as it is in our case), we say that the model does not have any rigid body motions (term "rigid body modes" is also used), meaning it cannot move without experiencing deformation. Note that the presence of supports in the model is manifested by both the restraint symbols (showing on the restrained face) and by the automatically created icon, Restraint-1, in the Load/Restraint folder. The display of the restraint and load symbols can be turned on and off by either: •
Using the Hide All and Show All commands in the pop-up menu shown in figure 2-8, or
•
Right-clicking the restraint or load icon individually to display a pop-up menu and then selecting Hide from the pop-up menu.
34
Engineering Analysis with COSMOSWorks
We now define the load by selecting Force from the pop-up menu shown in figure 2-8. This action opens the Force window, (figure 2-10).
«i
(•;•) Apply rsi-ffoi forcr;
l i : : : : : : : : : ; (Per: entity)
JJ-IGGOQO L.J
M j
''•toriLirfiffflTffCiJstrJbutiij
i i i l ! EdtcoiGf
t!f
IW
IT'|
-
Symbol s&ttsrQs
;I:J
*
Figure 2-10: Force window TVze Force window displays the selectedface where tensile force is applied. This illustration also shows symbols of applied restraint and load. In the Type area, select the Apply normal force button in order to load the model with 100,000 N of tensile force uniformly distributed over the end face, as shown in figure 2-10. Note that tensile force requires that the load magnitude be defined with a minus sign.
35
Finite Element Analysis with COSMOSWorks
Generally, forces can be applied to faces, edges, and vertexes using different methods, which are reviewed below: Force Type Apply force/moment
Definition This option applies force or moment to a face, edge, or vertex in the direction defined by selected reference geometry (plane or axis). Note that moment can be applied only if shell elements are used. Shell elements have all six degrees of freedom (three translations and three rotations) per node and can take moment load. Solid elements have only three degrees of freedom (translations) per node and, therefore, cannot take moment load directly. If you need to apply moment to solid elements, it must be represented with appropriately applied forces.
Apply normal force
Available for flat faces only, this option applies load in the direction normal to the selected face.
Apply torque
Used for cylindrical faces, this option applies torque about a reference axis using the Right-hand Rule.
The presence of load(s) is visualized by arrows symbolizing the load and by automatically created icons Force-1 in the Load/Restraint folder. Try using the click-inside technique to rename Restraint-1 and Force-1 icons. Note that renaming using the click-inside technique works on all icons in the COSMOSWorks Manager. The mathematical model is now complete. Before creating the Finite Element model, let's make a few observations about defining: •
Geometry
•
Material properties
•
Loads
a
Restraints
Geometry preparation is a well-defined step with few uncertainties. Geometry that is simplified for analysis can be checked visually by comparing it with the original CAD model. Material properties are most often selected from the material library and do not account for local defects, surface conditions, etc. Therefore, definition of material properties usually has more uncertainties than geometry preparation. The definition of loads is done in a few quick menu selections, but involves many assumptions. Factors such as load magnitude and distribution are often known only approximately and must be assumed. Therefore, significant idealization errors can be made when defining loads.
36
Engineering Analysis with COSMOSWorks Defining restraints is where severe errors are most often made. For example, it is easy enough to apply a fixed restraint without giving too much thought to the fact that a fixed restraint means a rigid support - a mathematical abstract. A common error is over-constraining the model, which results in an overly stiff structure that will underestimate deformations and stresses. The relative level of uncertainties in defining geometry, material, loads and restraints is qualitatively shown in figure 2-11.
Geometry
Material
Loads
Restraints
Figure 2-11: Qualitative comparison of uncertainty in defining: geometry, material, loads, and restraints
The level of uncertainty (or the risk or error) has no relation to time required for each step, so the message in figure 2-11 may be counterintuitive. In fact, preparing CAD geometry for FEA may take hours, while applying restraints takes onlv a few mouse clicks.
37
Finite Element Analysis with COSMOS Works
In all of the examples presented in this book, we will assume that material properties, loads, and supports are known with certainty and that the way they are defined in the model represents an acceptable idealization of real conditions. However, we need to point out that it is the responsibility of user of the FEA software to determine if all those idealized assumptions made during the creation of the mathematical model are indeed acceptable. We are now ready to mesh the model but first, verify under study Options, Mesh tab (figure 2-12) that High mesh quality is selected.
Jacobian check: i 4 Points Q Automate transition O Smooth surface Automafc looping D Enable automatic looping foi solids No. of loops:
\3
Slobal element see factor for each loop:
jpg
Tolerance facte!foreach loop:
| p.g
!
eS ¥3
OK
Jj
Cancel
j
Help
Figure 2-12: Mesh tab in the Preferences window We use this window to verify that the choice of mesh quality is set to High. The difference between High and Draft mesh quality is that: •
Draft quality mesh uses first order elements
•
High quality mesh uses second order elements
Differences between first and second order elements were discussed in chapter 1.
38
Engineering Analysis with COSMOSWorks
Now, right-click the Mesh folder to display the pop-up menu (Figure 2-13).
i hollow plate %li Parameters • ^ fcensSSe toad 0 1 ( - D e f a u l t - )
- % Solids :
^ h o l b w plate (-Alloy Steel*-)
S~4§ Load/Restraint i - ^ f Restraint-1 ;
J ^ Foree-2
• B Design Scenario i^y
Hide Mesh • Show Mesh Hide Ail Control Symbols Show All Control Symbols
Print.., Save A s , , . Apply Control,.. Create,,,
<:
List Selected Probe
Failure Diagnostics,,. Options,,, Copy
Figure 2-13: Mesh pop-up menu In the pop-up menu, select Create... to open the Mesh window. This window offers a choice of element size and element size tolerance. In this exercise, we will study the impact of mesh size on results. We will solve the same problem using three different meshes: coarse, medium (default), and fine. Figure 2-14 shows the respective selection of meshing parameters to create the three meshes.
39
Finite Element Analysis with COSMOSWorks
u'J X... Mesh Parameters:
Coarse j ^
A
"
1J.449066
c
ine
Coarse
*s
Fine
Fine
Coarse
i mm
H y j 2,8622666
mm
! mm
tt
mm
'x
mm
fir °EE^EZ3 mm
: ,^
Mesh Parameters:
Mesh Parameters:
"lis j 0.28622666
0.H3U333
[Reset to default sizej
(Reset to default sizes
Sfieset to default size:
j—>Run analysis after L J fogsJTJng
i—.Run an^ysfe after *—-* meshing
-sRun analysis after L "^meshing
I Options,,, j
| Options.,.
j Options,,. J „,^ „„,
J
Figure 2-14: Three choices for mesh density from left to right: coarse, medium (default) and fine The medium mesh density, shown in the middle window in figure 2-14, is the default that COSMOSWorks proposes for meshing our model. The element size of 5.72 mm and the element size tolerance of 0.286 are established automatically based on the geometric features of the SolidWorks model. The 5.72-mm size is the characteristic element size in the mesh, as explained in figure 2-15. The element size tolerance is the allowable variance of the actual element sizes in the mesh.
40
Finite Element Analysis with COSMOSWorks
V
zJ zJ
Coarse
•"•
JITI Mesh Parameters;
Mesh Parameters:
Mesh Parameters:
Fine
\ 11.449066
I mm
0.5724533
i mm
Coarse
W
*•
\ 0.28622666
Fine
Coarse
*»
F ne
| 2.8622666
: mm
fig
! mm |
H I0.H311333
(Reset to default s »|
[Reset to dtfai it size
|
[Reset to default sfeej
t—i Run analysis -af et '—' meshing
r~-sRunanalysfe after ! —' meshing
1
p-s Ron analysis after '--' meshing
j Options.,,
\ Options,
mm mm
| Options... ~^ w~~,.„...
Figure 2-14: Three choices for mesh density from left to right: coarse, medium (default) and fine The medium mesh density, shown in the middle window in figure 2-14, is the default that COSMOSWorks proposes for meshing our model. The element size of 5.72 mm and the element size tolerance of 0.286 are established automatically based on the geometric features of the Solid Works model. The 5.72-mm size is the characteristic element size in the mesh, as explained in figure 2-15. The element size tolerance is the allowable variance of the actual element sizes in the mesh.
40
Engineering Analysis with COSMOSWorks
Mesh density has a direct impact on the accuracy of results. The smaller the elements, the lower the discretization errors, but the meshing and solving time take longer. In the majority of analyses with COSMOSWorks, the default mesh settings produce meshes that provide acceptable discretization errors, while keeping solution times reasonably short.
Figure 2-15: Characteristic element size for a tetrahedral element The characteristic element size of a tetrahedral element is the diameter h of a circumscribed sphere (left). This is easier to illustrate with the 2-D analogy of a circle circumscribed on a triangle (right).
41
Finite Element Analysis with COSMOSWorks
Right-click the Mesh icon again and select Create... to open Mesh window. With the Mesh window open, set the slider all the way to the left (as illustrated in figure 2-14 left) to create a coarse mesh, and click the green check mark button. The mesh will be displayed as shown in figure 2-16.
Figure 2-16: Coarse mesh created with second order, solid tetrahedral elements You can control the mesh visibility by selecting Hide Mesh or Show Mesh from the pop-up menu shown in figure 2-12. To start the solution, right-click the tensile load 01 study folder. This action displays a pop-up menu (figure 2-17).
5 hollow plate §!« Parameters
Run Design Scenario
»*llsj i 1
Export.,. Convergence Graph,,. Delete
•o
Details...
%n
Properties.,.
Jb!
F
Copy Save all plots as JPEG files
Figure 2-1 7: Pop-up menu for the Study icon Start the solution by right-clicking the tensile load 01 icon to display a pop-up menu. Select Run to start the solution. 42
Engineering Analysis with COSMOS Works The solution can be executed with different properties, which will be investigated in later chapters. You can monitor the solution progress while the solution is running (figure 2-18). The exact appearance of this window depends on what solver is being used as selected in Options under General tab (figure 2-4).
.. i ;-
M«fes ,;•:;•2083;,
• :::?
'.:-,.
:
v :•
j I •
i"> ' : •": .(MB
; ^ '-,--,.... ;/. :...8S8' ' f
,.- •
',•-<
x:^-'BBZm0AM-\ •
:\-\
v.
"is..
!'!,':'• '-;
Figure 2-18: Solution Progress window The Solver reports solution progress while the solution is running. This window is specific to FFEPlns solver. A successful or failed solution is reported (figure 2-19) and must be acknowledged before proceeding to analysis of results.
Figure 2-lc->: Solution outcome: completed or tailed
43
Finite Element Analysis with COSMOSWorks
With the solution completed, COSMOSWorks automatically creates several new folders in the COSMOSWorks Manager window: •
Stress
u
Displacement
•
Strain
•
Deformation
•
Design Check
F.ach folder holds an automatically created plot with its respective type of result (figure 2-20). If desired, you can add more plots to each folder.
hollow piate ~| Parameters
f tensile load 01 (-Default-) - ^Solids fl|| hoiiow plate (-Alloy Steel*-}
~ IS load/Restrain): 4
Force-2
Igjf Restraint-2 Design Scenario Mesh Report Stress
* Jftai Displacement Strain Deformation Design Check
H3
Figure 2-20: Automatically created Results folders One default plot of respective results is contained in each of the automatically created Results folders: Stress, Displacement, Strain, Deformation and Design Check. Fo display stress results, double-click on Plotl icon in the Stress folder or right-click it and select Show from a little pop-up menu. Default stress plot is shown in figure 2-21.
44
Engineering Analysis with COSMOSWorks
von Mises (,Ulm*2) ^ ^
3.4736+008 SSe+008 . 2.3438+008 . 2.679e+008 . 2.4146+008 .2.1498+008 388+008 i .8208+008 i .3558+008 .1,0818+003
. 8 25.3e+007 •.5.6136+007
"•Yield strength: 6,2048+008
Figure 2-21: Stress plot displayed using default stress plot settings Von Mises stress results are shown by default in stress phi window. Notice that results are shown in (Pa.) and the highest stress 347.3e8 Pa is below the material yield strength 620.4e8 Pa. Once stress plot is showing, right-click plot icon to display pop-up menu featuring different plot display options (figure 2-22). -
th Stress
|
Hide
iA SJiSjrj
Edit Definition.,,
Animate... Sectiorv Clipping. Iso Clipping... Chart Options... Settings... Axes.,. Probe List Selected
Figure 2-22: Pop-up menu with plot display options Any type ofplot can be modified using selections from this pop-up menu. We will now examine how to modify the stress plot using Edit Definition, Chart Options and Settings, which are all selectable from the pop-up menu in figure 2-22.
45
Finite Element Analysis with COSMOSWorks Select Edit Definition to open Stress Plot window, change units to MPa then close the window. In the Chart Options window, change the range of displayed stress results from Automatic to Defined, and define the range as from 0 to 300 MPa. In Settings, select Discrete in Fringe options and JVlesh in Boundary options. All these selections are shown in figure 2-23.
V
zs Display >&••
*J JL
Legend Options
'
ZJ ^k
•j*3 Display legend
;
l b \TON:von Mises stres
V:
P
ZZi
N/mro >{MPa'
IMesh
Deformed plot options
-i o
i
:
•*•
r~| Superimpose mode! on LJ the deformed shape
1 | 300
..*
[ j S h o w min annotation
'
0 Show max annotation
Q Defined:
J7j Display plot details
169.902 Chart Options
Property
*
C : Dsfirted:
©Automatic;
if]
»1
••
I
0 Element values
fln "
1 Discrete Boundary options
{*) Node value*
13 Deformed Shape
A
0 Automatic:
\^'Z
3*T Fringe
Fringe options
•w
•y
Color Options
Figure 2-23: Stress Plot (invoked by Edit Definition...), Chart Options and Settings windows we use in this exercise to modify stress plot display.
46
Engineering Analysis with COSMOSWorks
von Mises (N;tnm"2 (MPaTi 3.0006+002
lli;
, 2.50O6+0O2 2.2508+002 "$fMilfii
ijil
?•$#'£
m filf-
%Mkim^h
M'p^-
iHllll
%s§* . :*•.lil^f v i'^l^l;
J i t s&mg^*
If
~i£&p
v
#.
V.
iip^U
*M fsl|| 1• 'fff ft ., ip: Siiil 4f fljlf i t ||f •IIIL
•?;:;;>
ll&ft::
ilii^Sx
r
-•-,
. 2O0Oe+OO2
Itpiilfl
. 1 SOe+002
ll|l|i| S;S^M*v.
v ^ # 4&p%!;:j
life y t l Ifcl-%#'-' ..
IS
i l l -IS*! fSsi§gf ^ilf pj^ilS 111Ifitiij
. 1 SOOe+002
ilia
. 1.2308+002 1 UOOe+002
v
. ?.500e+001
• 5.0006+001
^•W
H . 2.5008+001 !
i 0 0008+000
•Yisto strength: 8.204e+Q02
Figure 2-24: Modified stress plot results The modified stress plot using selections shown in windows infigure2-23. Stress plots in figure 2-21 and 2-24 are both presented as node values, also called averaged stresses. Element values (or non-averaged stresses) can also be displayed by proper selection in the Stress Plot window. Node values are most often used to present stress results. See chapter 3 and the glossary of terms at the end of this book for more comments on node and element values of stress results. Before you proceed, please investigate other selections available from the pop-up menu in figure 2-22 We will now review the displacement, strain, and deformation results. All of these plots are created and modified in the same way. Sample results are shown in: •
Figure 2-25 (displacement)
•
Figure 2-26 (strain)
•
Figure 2-27 (deformation)
47
Finite Element Analysis with COSMOSWorks
URES (mm)
Figure 2-25: Displacement results using Continuous fringe options Also try Discrete fringe option selectable in Settings from plot pop up menu. This plot shows the deformed shape in an exaggerated scale. You can change the display .from undeformed to deformed and modify the scale of deformation in the Displacement Plot window activated by right-click plot icon, Edit Definition.
48
Engineering Analysis with COSMOSWorks
SllPi
Figure 2-26: Strain results Strain results are shown using element values. Notice that strain is dimensionless.
Figure 2-27: Deformation results Note that deformed plots can also be created in all previous types of display if the deformed shape display is selected.
The last folder, called Design Check holds the Plotl, which by default displays the distribution of the factor of safety based on von Mises stress. We will modify this plot to display areas where the factor of safety falls below 2.
49
Finite Element Analysis with COSMOSWorks
Right-click Plotl icon and select Edit Definition... from the pop-up menu to display the first of three Design Check windows. Follow step 1, step 2 and step 3 as shown in figure 2-28.
V Stop 1 of 3
; *. j
%
Step 2 of 3 f]
:
<1
j N/mm'NS (MPs)
Factor of safety *** distribution
@ t o Yield strength
[
O to Ultimate strength
Limit > to:
M/mrn'*-;
i Material: i Alloy Steel* i Yield strength; !S20,422 Hfmor-2 (MPa) iUltimate strength: i?23.326iy/mmA2(MPa>
Property
Step 3 of 3 f-,
Set stress limit:
I Max von Mises stress y I PVOKM&JS
*•
f-'~,
Non-dimensional stress - ' distribution
,<e. Areas below factor of •'-'safety
Safety result Based on the maximum Factor of safety; i .78662
iMax stress result ivonMises stress: 1347.3 N/mm'x2 (MPa)
«-
«•
Figure 2-28: Three windows show three steps in the Design Check plot definition Step one selects the failure criterion, step 2 selects display units and sets the stress limit, step three selects what will he displayed in the plot (here we select areas below the factor of safety 2).
50
Engineering Analysis with COSMOSWorks
Figure 2-29: Red color (shown as light gray in this grayscale illustration) displays the areas where the factor of safety falls below 2
We have completed the analysis with a coarse mesh and now wish to see how a change in mesh density will affect the results. Therefore, we will repeat the analysis two more times using medium and fine density meshes respectively. We will use the settings shown in figure 2-13. All three meshes used in this exercise (coarse, medium, and fine) are shown in figure 2-30.
51
Finite Element Analysis with COSMOSWorks
Figure 2-30: Coarse, medium, and fine meshes We use the three meshes to study the effects of mesh density on the results. To compare the results produced by different meshes, we need more information than is available in the plots. Along with the maximum displacement and the maximum von Mises stress, for each study we need to know: •
The number of nodes in the mesh
•
The number of elements in the mesh
a
The number of degrees of freedom in the mesh
The information on the number of nodes and number of elements can be found in Mesh Details (figure 2-31).
%r — ~ ;
ii
;.*;1 Si iE &l
\is
1 1
., ,
Hide Mesh Show Mesh
Hide All Control Symbols Show All Control Symbols Print.. Save A s . . . Apply Control,,. Create,,,
list Selected
Failure Diagnostics, Details.,. Options...
C
i Sfcjdj1 n<s« tensile load 01 {-Default...*-! \ Element: sfee 11.4431 ram ol:sr-i,~ 0.572453 mm I Mesh quality High Hotei nodes ••<•> _ - j 208S l o t * -"emenls 359 ? Mearom Aspect Ratio 3,6074 I Petcentags of elements >) - L i Ratio < 3 i Percentage of elements
j
93,8 A
copy
Figure 2-31: Meshing details window Right click on Mesh, Details... to activate Mesh Details window.
52
*"*
Engineering Analysis with COSMOSWorks The number of degrees of freedom can be found in one of COSMOS data base files located in Work directory folder specified in Options window under Results tab (figure 2-32).
Detail!; soket ;ot sialic s:uC!s;
©FFEPIu:
Woik director
C sCOSMOS lesults
Report dnectoiy
C:\C0SM0S reports
A change rmde to the weak directory will teke efiect only on closing the model Current work directory:
C:\C0SMQS tesute
f~l Keep temporary database iiie-s
Help
Figure 2-31: COSMOSWorks database is located in Work directory specified under Results tab in Options window Any folder can be used for storing COSMOSWorks results files. Using Windows Explorer, find thefilenamed hollow plate-tensile load 01 .OUT. Open it with a text editor (e.g. Notepad) and verify that the number of degrees of freedom for tensile load 01 study equals 6267. Note that the OUT file is available only while the model is opened in COSMOSWorks. Upon exiting from COSMOSWorks by deselecting COSMOSWorks from the list of add-ins or by closing SolidWorks model, all data base files are compressed into one file with the extension CWR. In our case, the file is named hollow plate-tensile load 01.CWR. If more than one study has been executed, then there is one CWR file for each study. Compressing the entire data base into one file allows for a convenient backup of COSMOS results.
53
Finite Element Analysis with COSMOSWorks
Now create and run two more studies: tensile load 02 with medium (default) element size and tensile load 03 with fine element size as shown in figure 213. To create a new study we could just repeat the same steps as before but an easier way is to copy a study. To copy a study, right-click the study folder and select Copy. Next, right-click the model icon (hollow plate) and select Paste to invoke Define Study Name window, where the name of new study is defined in (figure 2-32).
5|Sl!li!ii!Sli!ffiiillllllI
Study,,. Run Design 5 :er •afio
Compare Test Oat
Export,, Convergence Sr a p b . . .
Define Function C
Oefete
Options, w
SMyName;; i tensile k » d 0 2
4=>
Defcafe... Properties...
§81
:
So&Nwfks eorifsgurafentouse; \ Dsla.it
••
Copy I
OK
J |
Cancel
j
Help
j
Save all pfots as JPEG f
Figure 2-32:.A study can be copied into another study in three steps as shown An alternative way to copy a study is to use Copy (Ctrl-C) and Paste (Ctrl-V) technique of the Windows operating system. Yet another way is to drop study folder tensile load 01 into hollow plate folder. Note that all definitions in a study (material, restraints, loads, mesh) can also be copied individually from one study to another. A study is copied complete with results and plot definitions. Before remeshing study tensile load 02 with the default element size mesh, you must acknowledge the warning message shown in figure 2-33.
Retneshsig wili dstete the resute for study; fcensfe load 02.
OK
Cancel
Figure 2-33: Remeshing deletes any existing results in the study
54
Engineering Analysis with COSMOSWorks
The summary of results produced by the three models is shown in figure 2-34.
mesh density
max. dispi, magnitude [mm]
max. von j Mises stress «umber of DOF [MPs]
coarse
0.1177
347
medium (default)
0.1180
fine
0.1181
number of elements
number of nodes
6096
953
2089
368
23601
3916
8052
378
239748
52329
80419
Figure 2- 34: Summary of results produced bv the three meshes
Note that these results are based on the same problem. Differences in the results arise from the different mesh densities used. Figures 2-35 and 2-36 show the maximum displacement and the maximum von Mises stress as functions of the number of degrees of freedom. The number of degrees of freedom is in turn a function of mesh density.
v
0.1182
T5 3 +^
'c
0.1181
S) CO
E c
0.1180
I?
0.1179
° p Q. to T3
0.1178 0.1177
X
£
0.1176 1000
10000
100000
1000000
number of degrees of freedom
Figure 2-35: Maximum displacement magnitude Maximum displacement magnitude is plotted as a function of the number of degrees of freedom in the mode. The three points on the curve correspond to the three models solved. Straight lines connect the three points only to visually enhance the graph.
55
Finite Element Analysis with COSMOSWorks
- , 380 T as
a. s a 370 V)
•2 360 o > 350 E 3
£ x (0
340 1000
10000
100000
1000000
number of degrees of freedom
Figure 2-36: Maximum von Mises stress Maximum von Mises stress is plotted as a function of the number of degrees of freedom in the model. The three points on the curve correspond to the three models solved. Straight lines connect the three points only to visually enhance the graph. Having noticed that the maximum displacement increases with mesh refinement, we can conclude that the model becomes "softer" when smaller elements are used. This effect stems from the artificial constraints imposed by element definition, which become less influential with mesh refinement. In our case, because we selected second order elements, the displacement field of each element was described by the second order polynomial function. With mesh refinement, while the displacement field in each element remains a second order, and larger number of elements make it possible to approximate the real displacement and stress field more accurately. Therefore, we can say that the artificial constraints imposed by element definition become less imposing with mesh refinement. Displacements are always the primary unknowns in FEA, and stresses are calculated based on displacement results. Therefore, stresses also increase with mesh refinement. If we continued with mesh refinement, we would see that both the displacement and stress results converge to a finite value. This would be the solution of the mathematical model. Differences between the solution of the FEA model and the mathematical model are due to discretization errors, which diminish with mesh refinement. We will now repeat our analysis of the hollow plate by using prescribed displacements in place of a load. Rather than loading it with a 100,000 N force that has caused a 0.118 mm displacement of the loaded face, we will apply a prescribed displacement of 0.118 mm to this face to see what stresses this causes. For this exercise, we will use only one mesh with default (medium) mesh density.
56
Engineering Analysis with COSMOSWorks Define the fourth study, called prescribed displ. The easiest way is to copy the definitions from the tensile load 02 study. The definition of material properties, the built-fixed restraint to the left-side end-face and mesh are all identical to the previous design study. What we need to do is delete the load (right-click load icon and select Delete) and apply in its place prescribed displacement. To apply the prescribed displacement to the right-side end-face, select this face and define the displacement as shown in figure 2-37. The minus sign is necessary to obtain displacement in the tensile direction.
V 1 On flat fac
I Show preview
Iran stations
*
j
mm 1
\ mm |
-f^;
| mm j
11!
-0.118
' mm f
Symbol settings
Figure 2-37: Restraint definition window The prescribed displacement of 0.118 mm is applied to the same face where the tensile load of 100,000 N had been applied. Note that once prescribed displacement is defined to the end face, it overrides any load, which have been earlier applied to the same end face. While it is better to delete the load in order to keep the model clean, the load has no effect if prescribed displacement is applied to the same entity and in the same direction.
57
Finite Element Analysis with COSMOSWorks
Figures 2-38 and 2-39 compare displacement and stress results for both studies.
0.11813 10.10829 10.098441 10.080597 i 0.078753
n
10.068909 10.059065 1.0.049221 I0,039377 10.029532
Figure 2-38: Comparison of displacement results Displacement results in the model with the force load are displayed on the left, and displacement results in the model with the prescribed displacement load are displayed on the right.
von Mises (Nj'mjriA2 (MPa))
iir
Figure 2-39: Von Mises stress results Von Mises stress results with load applied as force are displayed on the left and Von Mises stress results with load applied as prescribed displacement are displayed on the right. Note the numerical format of results. You can change the fonnat in the Chart Options window (figure 2-23).
58
Engineering Analysis with COSMOSWorks
Results produced by applying a force load and by applying a prescribed displacement load are very similar, but not identical. The reason for this discrepancy is that in the force load model, the loaded face is allowed to deform. In the prescribed displacement model, this face remains flat, even though it experiences displacement as a whole. Also, while the prescribed displacement of 0.118 mm applies to the entire face in the prescribed displacement model, it is only seen as a maximum displacement on one point in the force load model. We conclude our analysis of the hollow plate by examining the reaction forces. If any result plot is still displayed, hide it now (right-click the Plot icon and select Hide from pop-up window). Before accessing the reaction force results, please select the face for which we wish to obtain the reaction force results. In this case, it is the face where the fixed support was applied. 1 laving selected the face, right-click the Displacement folder. A pop-up menu appears (figure 2-40). Select Reaction Force....
-j; fte
Reaction Force.,. Remote Load Interface Force... Options.,, Copy
Figure 2-40: Pop-up menu associated with the Displacement folder Right-click the Displacement folder to display a pop-up menu, which allows yon to open the Reaction Force window.
59
Finite Element Analysis with COSMOSWorks
Figure 2-41 shows the Reaction Force results for both studies: with force load (left) and with prescribed displacement load (right).
lected reference aeorristry
Unite:
;-U USIcSCi
Units:
j Newton
Selected items 1 Face:
Selected items •• 1 Faces
Component SurnX: Sum Y: Sum 2: Resultant:
Selection -99993 3.0286 5.2344 99993
Update
i Newton
Component SumX: SumY: SumZ: Resultant:
Entire lodel -99993 3.0286 5.2344 99993
Help
; Selection -1.0118E+005 -0.28217 -0.19102 1.0118E+005
Zlose
J
Update
|
Entire Model -0.54321 -0.50385 1.9164 2.0546
Help
Figure 2-41: Comparison of reaction force results Reaction forces are shown on the face where the built-in support is defined for the model with force loud (left) and for the model with prescribed displacement load (right).
60
Engineering Analysis with COSMOSWorks
3: Static analysis of an L-bracket Topics covered
Project
•
Stress singularities
•
Differences between modeling errors and discretization errors
•
Using mesh controls
•
Analysis in different SolidWorks configurations
description An L-shaped bracket (in'a file called L BRACKET in SolidWorks) is supported and loaded as shown in figure 3-1. We wish to find the displacements and stresses caused by a 1,000 N bending load. In particular, we are interested in stresses in the corner where the 2-mm round edge (fillet) is located. Since the radius of the fillet is small compared to the overall size of the model, we decide to suppress it. As we will soon prove, suppressing the fillet is a bad mistake!
Fixed support to the top
Round edge
1,000 N load uniformly distributed over the end face
Figure 3-1: Loads and supports applied to the L-BRACKET model The geometry features an edge rounded by a fillet .This fillet will be mistakenly suppressed leaving in its place a sharp re-entrant corner. The L BRACKET model has two configurations: round corner and sharp corner. Please change to sharp corner configuration. Material (Alloy steel) is 61
Finite Element Analysis with COSMOSWorks applied to the SolidWorks model and is automatically transferred to COSMOSWorks
Procedure Following the same steps as those described in chapter 2, please define the study called mesh 1. Next, mesh the model with second order tetrahedral elements, accepting the default element size. The finite element mesh is shown in figure 3-2.
Figure 3-2: Finite element mesh created using the default setting of the automesher In this mesh, the global element size is 4.76 mm.
62
Engineering Analysis with COSMOSWorks
The displacement and stress results obtained in mesh I study are shown in figure 3-3. von Mises (IVmm"?. (wf'iv)) ^ ^ 6.797e*GQ1 • I 6 2318*001 .5.6S5e*G01 . 51399e+0Q1 1-
rfliOl
l l i ^367e*00; I e*001 l:lpS35e*001
|(:,2.269e*001 7038*0131 1 H . 1 1376*00! | | l S.?14e+0Q0
^Yieid strength: 8::>04e+003
Figure 3-3: Displacements and von Mises stresses results produced using mesh 1 The maximum displacement is 0.247 mm and the maximum von Mises stress is 68.MPa. Now we will investigate how using smaller elements affects the results. In chapter 2, we did this by refining the mesh uniformly so that the entire model was meshed with elements of smaller size. In this exercise, we will use a different technique. Having noticed that the stress concentration is near the sharp re-entrant corner, we will refine the mesh locally in that area by applying mesh controls. Element size everywhere else will remain the same as it was before: 4.76mm. Copy the meshl study into the mesh2 study. Notice that the name of active study is always shown in bold. Select the edge where mesh controls will be applied, then right-click the Mesh folder in mesh2 study (the folder is empty at this moment) to display the pop-up menu shown in figure 3-4.
Finite Element Analysis with COSMOSWorks
Hide Mesh Show Mesh Hide Ail Control Symbols Show All Control Symbols Print,.. Save As ,.. Apply Control. Create.., list Selected Probe
Failure Diagnostics... Details... Options.,. Copy
Figure 3-4: Mesh pop-up menu Select Apply Control..., which opens the Mesh Control window (figure 3-5). Note that it is also possible to open the Mesh Control window first and then select the desired entity or entities (here the re-entrant edge) where mesh controls are to be applied.
64
Engineering Analysis with COSMOSWorks
Selected .11 i - -
13 Show preview Control Parameters
•*•
Element size along the selected edge
Low A
: 2.3818266 ' I mm
Relative element size in adjacent layers of elements
1.5 J||| Number of element layers affected by the applied control
Figure 3-5: Mesh Control window Mesh controls allow you to define the local element size on selected entities. Please accept the default values of Mesh Control window. The element size along the selected edge is now controlled independently of the global element size. Mesh control can also be applied to vertexes, faces, or entire components of assemblies. Having defined mesh control we can create a mesh with the same global element size as before (4.76 mm), but elements created along the selected edge will be 2.38 mm. The added mesh controls shows as Control-1 icon in Mesh folder and can be edited using a pop-up menu displayed by right-clicking the control icon (figure 3-6).
65
Finite Element Analysis with COSMOSWorks j Mesh Hide
Suppress Edit Definition. Delete Details... Copy
Figure 3-6: Pop-up menu for the Mesh icon
The mesh with applied control (also called mesh bias) is shown in figure 3-7.
Figure 3-7: Mesh with applied controls (mesh bias) Mesh 2 is refined along the selected edge. The effect of mesh bias extends for three layers of elements adjacent to the edge as specified in Mesh Control definition window (figure3-5).
66
Engineering Analysis with COSMOS Works
Maximum displacements and stress results obtained in study mesh 2 are 2.47697 mm and 74.1 MPa respectively. The number of digits shown in result plot is controlled using Chart Options (right-click plot and select Chart Options). Now we will repeat the same exercise three more times using progressively smaller elements along the sharp re-entrant edge (figure 3-8): •
Study mesh 3: element size 1.19mm
•
Study mesh 4: element size 0.60mm
•
Study mesh 5: element size 0.30mm
Selected Entit
Selected Entities
Selected Entities 1
ill
O Shew preview
tJShow preview
Contra! Parameters
Control Parameters
Low
[ J Show preview
High
tow
• 1.19
-1 0,5
J i.S
. I l.S
Control Parameters
High
low
K
i.s
Figure 3-8: Mesh Control windows in studies mesh 3, mesh 4 and mesh 5
67
High
Finite Element Analysis with COSMOSWorks
The summary of results of all five studies is shown in figures 3-9 and 3-10.
MAXIMUM DISPLACEMENT
mesh 1
mesh 2
mesh 3
mesh 4
mesh 5
Figure 3-9: Summary of maximum displacement results While each mesh refinement brings about an increase in the maximum displacement, the difference between consecutive results decreases.
MAXIMUM VON MISES STRESS
mesh 1
mesh 2
mesh 3
mesh 4
mesh 5
Fieure 3-10: Summary of maximum stress results Each mesh refinement brings about an increase in the maximum stress. The difference between consecutive results increases proving that maximum stress result is divergent.
68
Engineering Analysis with COSMOSWorks We could continue with this exercise of progressive mesh refinement, either: •
Locally, near the sharp re-entrant, as we have done here by means of mesh controls, or
•
Globally, by reducing the global element size, as we did in chapter 2.
If so, we would notice that displacement results converge to a finite value and that even the first mesh is good enough if we are looking only for displacements. Stress results behave quite differently than displacement results. Each subsequent mesh refinement produces higher stress results. Instead of converging to a finite value, the maximum stress magnitude diverges. Given enough time and patience, we can produce results showing any stress magnitude we want. All that is necessary is to make the element size small enough! The reason for divergent stress results is not that the finite element model is incorrect, but that the finite element model is based on the wrong mathematical model. According to the theory of elasticity, stress in the sharp re-entrant corner is infinite. A mathematician would say that stress in the sharp re-entrant corner is singular. Stress results in a sharp re-entrant corner are completely dependent on mesh size: the smaller the element, the higher the stress. Therefore, we must repeat this exercise after un-suppressing the fillet, which is done in by changing to round corner configuration in SolidWorks Configuration Manager.
69
Finite Element Analysis with COSMOSWorks
Notice that after we return from the Configuration Manager window to the COSMOSWorks window, all studies pertaining to the model in sharp corner configuration are not accessible. They can be accessed only if model configuration is changed back to sharp corner.
%lhrarM i- | l ! | Parameters + '/' mesh t (-sharp edge-)
+ -^mesh4(-srwj + " mesh S (-sharl
De|ete
Copy
"I Figure 3-11: Studies become inaccessible when the model configuration is changed to a configuration other than that corresponding to now greyed-out studies. The SolidWorks model can he changed to a configuration corresponding to given study by right-click study icon and selecting Activate SW configuration. Since the fillet is a small feature compared to the overall size of the model, meshing with the default mesh settings will produce an abrupt change in element size between the fillet and the adjacent faces. To avoid this problem, we must select the Automatic transition option in the Options window under the Mesh tab (figure 3-12). Using the model of the L bracket in round edge configuration, create and run two more studies: round corner no transition and round corner auto transition. Both studies should be identical except that Automatic transition option is not checked in round corner no transition study.
70
Engineering Analysis with COSMOSWorks
Ptci
Result; Genera! ljrit<
Export
> Standard
0H,gr, ^Bcobfan check
4 Points
v
£3 Automatic iKrs&bn
^ >
r. § Smooth suiface
f j Eriabie automatic fcops-ig fw scSds
Gtoba! element : 2& factor fot esc;-: loop:
i 0.8
T oletance factoi iof each foop
: 0.8
Help
J
Figure 3-12: Meshing preferences with Automatic transition selected
71
Finite Element Analysis with COSMOSWorks
Figure 3-13 shows von Mises stress results superimposed on the plot of the finite element mesh, without and with the Automatic transition option applied as obtained in studies round corner no transition and round corner auto transition.
Figure 3-13: Von Mises stress results in a model with a fillet using different meshes: no automatic transition (left) and automatic transition (right) Compare meshes and stress results created without (left) and with (right) the Automatic transition option .The reason for slightly different results is that meshing with Automatic transition option selected produces smaller elements in the bend area.
A similar effect to that of refining the mesh by using Automatic transition option could be achieved by applying mesh control to the fillet face. Please try this after completing this exercise. The L-BRACKET example is a good place to review the different ways of displaying stress results. Figure 3-14 shows the node values and element values of von Mises results produced in the study round corner auto transition. To select either node values or element values, right click the plot icon and select Edit Definition. This will open the Stress Plot window.
72
Engineering Analysis with COSMOS Works
IllSt 1IIHI
Figure 3-14: Von Mises stresses displayed as node values (left) and element values (right) As we explained in chapter 1, nodal displacements are computed first. Strains and then stresses are calculated from the displacements' results. Stresses are first calculated inside the element at certain locations, called Gauss points. Next, stress results are extrapolated to all of the elements' nodes. If one node belongs to more than one element (which is always the case unless it is a vertex node), then the stress results from all those elements sharing a given node are averaged and one stress value, called a node value, is reported for each node. An alternate procedure to present stress results can also be used. Having obtained stresses in Gauss points, those stresses are averaged in-between themselves. This means that one stress value is calculated for the element. This stress value is called an element value. Node values are used more often because they offer smoothed out, continuous stress results. However, examination of element values provides important feedback on the quality of the results. If element values in two adjacent elements differ too much it indicates that the element size at this location is too large to properly model the stress gradient. By examining the element values, we can locate mesh deficiencies without running a convergence analysis. To decide how much is "too much" of a difference requires some experience. As a general guideline, we can say that if the element values of stress in adjacent elements are apart by several colors on the color chart, then a more refined mesh should be used.
Engineering Analysis with COSMOSWorks
4: Frequency analysis of a thin plate with shell elements Topics covered _l
Use of shell elements for analysis of thin walled structures
•
Frequency analysis
Project description We will analyze a support bracket, shown in figure 4-1, with the objective of finding stresses and the first few modes of vibration. This will require running both static and frequency analyses. We will use the SolidWorks model, called SUPPORT BRACKET with assigned material properties of AISI 304.
Fixed restraint 20N load uniformly distributed over the face defined by split
Figure 4-1: Support bracket Note that CAD model con la ins split line used by COSMOSWorks for load application.
Procedure Before defining the study, consider that thin wall geometry would be difficult to mesh with solid elements. Generally it is recommended that two layers of second order tetrahedral elements be used across the thickness of a wall undergoing bending, in our case of a flat model, one layer of solid elements might suffice but this would still require a rather large number of small solid elements. Instead of using solid elements, we will use shell elements to mesh the surface located mid-plane in the bracket thickness. The study definition with the
75
Finite Element Analysis with COSMOSWorks meshing option selected for the mid-plane shell elements is shown in figure 4-2.
OH Carnoel Help
j
Active * . # name: Ho study defined
COSMOSWorks 1
»\ _J j
This option works only for simple thin parts. SolsdWorks is woriang to improve Shell Meshing for future updates, |
OK
|
Figure 4-2: Study window and COSMOSWorks message The study support bracket defines the Mesh type as a Shell mesh using midsurfaces. Also shown is a notification that this option works only for simple geometries. Having created the study we notice that Solids folder does not exist in a study with shell elements.
support bracket x~£ Parameters
fl{f support bracket (-Default-) - |jjP Mid-surface Shell •• 0 support bracket (-[SWJAISI304-}
Figure 4-3: Assignment of material properties Material properties are applied to shells if the shell elements are used in the study. There is no Solids folder, instead there is Mid-surface Shell folder. To apply loads, we select the face adjacent to the hole (figure 4-1) and apply a 20N normal force (figure 4-4).
76
Engineering Analysis with COSMOSWorks
» / TfpB ;
, : Apply force/momerrt •, Apply normal force O Apply torqye
| Show preview *.
lints
PI SI
-V
Norma! Force/Torque (Per entity}
JL 20 L_ ?*> <
H m Distribution •
Symbol settings
Figure 4-4: Force window Support is applied to the end face, as shown in figure 4-1. Since shell elements have six degrees of freedom, there is now a difference between applying fixed supports and immovable supports. In our case, we need a fixed support to eliminate all six degrees of freedom because immovable support would only eliminate 3 degrees of freedom (translational), leaving rotational degrees of freedom unsupported. This would cause an unintentional hinge in place of the intended rigid support.
77
Finite Element Analysis with COSMOSWorks
he Restraint window is shown in figure 4-5.
V *Type I Fixed
EjShow preview Symbol setthas
Figure 4-5: Restraint window Note that fixed support rather than immovable support is selected. We do not explicitly define the shell thickness. COSMOSWorks assigns shell thickness automatically, based on the corresponding dimension of the solid CAD model, which in this case is 5mm. The model is now ready for meshing (right-click Mesh folder, Create).
78
Engineering Analysis with COSMOSWorks
} Atl«B19t«
:
[ J Smooth* f.:.;i:ace
Enable »jfc^a&-bopw-S f>
actor fc! <
11
; Tfifewnce*,
£*
I
Figure 4-6: Shell element mesh In the shell element mesh, elements have been placed mid surface between the faces thai define the thin wall. Different colors distinguish between the top and bottom of the shell elements. The bottom face color is specified in Options window under Mesh tab.
79
Finite Element Analysis with COSMOSWorks
COSMOSWorks creates the mid-surface where shell elements are placed. In a SolidWorks model this surface is an imported feature and is visible in the Feature Manager (figure 4-7).
^
support bracket j y Annotations + ^ Design Binder L | = AISI304 •«- M Lighting + m '• Solid Bodiesi 1) \ ^ plane 2 \. - ^ plane 3 k + ||| + {|!| ||
Origin 8ase~Extmde-Thin Cut-Extrude2 Cut-ExtrudeS
23 Split Unel dot MidSurfacei
<
Figure 4-7: Mid-surface is an imported feature in the SolidWorks Manager 77ze surface that has been meshed with shell elements is automatically created and appears as an importedfeature in SolidWorks Manager. Review the mesh colors to ensure that the shell elements are properly aligned, meaning that there are no elements on the same side showing tops and bottoms facing the same way. Try reversing the shell element orientation: select the face where you want to reverse the orientation, right-click the Mesh folder to display a pop-up menu and select Flip shell elements (figure 4-8). Misaligned shell elements lead to the creation of erroneous plots like one shown in figure 4-9, which shows a rectangular plate undergoing bending.
80
Engineering Analysis with COSMOSWorks
Figure 4-8: Pop-up menu for modifying shell element orientation Reverse shell element orientation with this menu choice.
von Mises (N/mmA2 CMPa) 4.3403e+002 l i t 4,44526+002
bottom
" 1e+G02 . t5£Qe+D02 |||3.2599e+002 | | | . 2.S64ae+002 |f|
2 4697e+002 U7468+002 " " 5e+002 4e+0D2
* J | 8 3933e+001 W 4
9423e+00l
§K9.9'I37e+000
Figure 4-9: Misaligned shell elements and erroneous von Mises Stress plot resulting from this misalignment The misaligned shell element mesh (left) and erroneous von Mises Stress plot are the residt of shell element misalignment. This model is unrelated to our exercise. The difference between stress results on the top and bottom sides of shell elements in our exercise model is illustrated in figures 4-10 and 4-11.
81
Finite Element Analysis with COSMOSWorks Mode! name support bracket Stuey rams, support bracket Piot type: Static nodal stress (Bottom) Plot! Deformation scale: 61,801 P1 CWfamA2 (MPa)) ^ ^ 1,347e+Q01 i 235e+001 .1.1238*001
,:x
; f l i . 1.0l0e*00i
":iW
. 8.982e+000 . ?.8S9e*000
Ha j P i : 1st principal stres v •
I I I 6 7378*000
n W " -Fringe
t4e*000
Ilx
v
£*>f
,4 491e+000 3.3698+000
(,) Oemem value?
. 2.246e+000 j|jj.1.123e+000
y k 6.975e-004
Figure 4-10: Maximum principle stress (PI) results for the bottom sides of the shell elements which is on the tensile side of the model Model name: support bracket Study name: support bracket Plot type: Static nodal stress (Top) P3 top Deformation scale: 81.801 P3 CWmrrr'2 (MPs)) ^ ^ -6.97S8-004 "- . ,
1.1238+000 "'• _
i/,
JA> '?.
2 6 tOOO
~"^%5
.-3.3898+000 . -4.491 e+000
Display %V ^
..
j X.
: P3; 3rd principal Ui-
. -S,6'!4e+000 I
. r000 -?.8SSe+000
fj
fjirrin i fllPsi
&
j Fringe
.4-1-000
i-
i l l -1 ,oioe+ooi
§ } Mode vsiu.es
>0D1
O lament values 4-
tup
1.23S8+0O1
1 1 1 -1.3478*001
< ^
Figure 4-11: Minimum principle stressflP3)results for the top sides of the shell elements which is on the compressive side of the model Because of model orientation in figures 4-10 and 4-11, we are looking at the bottom faces of the shell elements (consult figure 4-6). Still, stress results in figure 4-11 are displayed for the top sides of the elements as if the shells were transparent.
82
Engineering Analysis with COSMOSWorks
Having obtained displacement and stress solutions (we have not reviewed displacement results), the structural analysis of the support bracket has been completed. We will now proceed to calculate several natural frequencies for the same bracket. This calculation requires us to set up and run a frequency analysis (figure 4-12), which among analysts is often called modal analysis.
i
) t .1 -
i » > > 1 s. <support bracket fr
-"..i «'
' 'Frequency
> .
T
* Properties
> >: ~ ">
~-~
i;
'IZHHHZ
She!! mesh using mid-surfaces
j
Delete
.
:CK3 Active s*udji name: support bracks!
Figure 4-12: Study window showing two study definitions Two studies are defined: the support bracket study is a static analysis and the support bracket fr study is a frequency analysis. You can copy the material definition from the static study to the frequency study by dropping the material definition icon into the corresponding icon in the frequency study. The same can be done with supports. Notice that although loads can be defined in a frequency study, they will have no effect because frequency analysis calculates natural frequencies and associated modes of vibration, disregarding any effects of external loads, unless special options are activated (see chapter 17). Figure 4-13 shows the COSMOSWorks Manager window with both studies after solution.
83
Finite Element Analysis with COSMOSWorks
; support bracket ^ ° | Parameters j^f support bracket (-Default-) + ($) Mid-surface Shell t 4 § Load/Restraint ••••• m Design Scenario ^BMesh Hi Report + Jbi Stress + Dpj Displacement + | y Strain + | b ! Deformation H-i 'i» Desiqn Check i^V support bracket fr (-Default-) - j | P Mid-surface Shell •• f support bracket (-[SWjAISI 304-) i • AS Load/Restraint ;••
Figure 4-13: Two design studies defined and solved in the same model: the static (support bracket) studv and the frequencv (support bracket fr) study. The name of active studv is shown in bold. Note that only Displacement frequency analysis.
and Deformation folders are created in a
Let's review the options of a frequency study (right-click study icon, Properties). The Frequency window offers the choice of how many frequencies and associated modes of vibration will be calculated (figure 4-14). Please accept the default number of five frequencies.
84
Engineering Analysis with COSMOSWorks
Options j Rsmaik \
£•3 Mumber oi
frequencies:
'?
bwn!
!
Heiiz
I! ^!sr ;; : I
' ; Direct sp/s- • :•••:.,.
II
:;
I ! ; OFFE !
I
& FFEPIus
I
OK
| :
Cancel
\
\
Heip
i
Figure 4-14: Frequency window The Options tab in the Frequency window allows selecting properties of the frequency study. By defaidt, the first five natural frequencies are calculated. When a frequency analysis is run, two results folders are automatically created: a Displacement folder and a Deformation folder. Each folder holds one plot, which by default shows results corresponding to the first mode. This can be changed by proper selection in Displacement Plot or Deformed Shape Plot window (right-click plot icon, select Edit Definition) shown in figure 4-15.
85
Finite Element Analysis with COSMOSWorks
Display
^
•*•
v
- -
(Hn UP.ES: Resultant displ <•
fc (mm Of"* Fringe
y#fl "
v
J;*:
| ^J^:. 114, t oo H2
0
Deformed Shape
V
•*
O Automatic;
\*.» Defined; f W 0.012 Property
Figure 4-15: Displacement plot window The definition of the displacement plot in the Frequency analysis requires us to specify the mode to be displayed. Here we select the first mode (frequency ]15Hzj.
86
Engineering Analysis with COSMOSWorks
Figure 4-16 shows displacement results related to the first mode of vibration.
URES (mm) 3.3986+003 .3.1158+003 . 2.832e+003 . 2.S49e+Q03 . 2.2688+003 . 1.982&+003 . 1.699e+003 . !.418e+003 . i.133e+003 . 8.49Se+002 5 36 e+002 s+002 0.000e+000
Figure 4-16: Displacements associated with Mode 1 Note that the iindeformed shape is superimposed on the deformed shape. This option is selected in the Settings of result plot. Even though the displacement plot (figure 4-16) does show displacement magnitude, the displacement results have no quantitative importance in frequency analysis. Let us repeat this: Frequency analysis does not provide any quantitative information on displacements. Displacement results are purely qualitative and can be used only for comparison of displacements within the same mode of vibration. Relative comparison of displacements between different modes is invalid. More informative and less confusing is the defonnation plot. This plot shows the shape of deformation associated with the given mode of vibration, as well as the associated frequency of vibration (figure 4-17).
87
Finite Element Analysis with COSMOSWorks Mocfst name: support bracket Study name: support bracket fr Plot type: Frequency Piotl Mode Shape: 1 Value = 114.73 Hi Deformation scale: 0.005885
Model name: support bracket Study name: support bracket fr Plot type: Frequency mode 2 Mode Shape: 2 Value 372.04 Hz Deformation scale: 0.00539242
• ';:0m:m;.
r N:;;
Figure 4-17: Deformation plot showing the shape of deformation (mode shape) and the frequency of vibration for a given mode Note that COSMOSWorks results plots can be viewed more than one at a time using split window technique.
The image in figure 4-17 on the left illustrates the first mode of vibration with frequency 115 Hz, and the image on the right shows the second mode with frequency 372 Hz. While the undeformed shape appears as a solid, the defonned shape is a surface because shell elements are used in this frequency study. The best way to analyze the results of a frequency analysis is by examining the animated deformation plots. To animate any plot, right-click a plot icon to display an associated pop-up menu, and then select Animate. To List Resonance Frequencies and List Mass Participation right-click Deformation folder and make appropriate selection (figure 4-18)
Engineering Analysis with COSMOSWorks
S'S;ii%*4'!7sf^
^
^
Study name: support bracket fr
1
:|
Define... List Resonant Frequencies... List Mass Participation..,
\
4
l Qose
riem&ucMfiidn&oW 721.18 2338.6 4198.3 6043.3
j
j
Ftequencyl'Hertsi 114.73 372.04 608.01 961.43
Save
|
FenodfSetondsl 0.0087159 0.0026373 0.001437 0.0010401
|
Help
|
Options.., <-opy Pasts Fte<} |Herte| 11473 372.04 668.01 361.43 1141.6
;< direction
as&feoaT 8.3185&020 4.41236-013 3.8153e-014 2.6833e-020 SumX =3.8154e-014
V direction 04541 4.8553s-012 0,19061 7.1289e-017 3.1671S-011 SanV =0.64472
Figure 4-1 8: The Summary of frequency analysis results for all calculated modes ol'xibration includes the list of modal frequencies and corresponding mass participation factors. Click Help button in Mass Participation window for more information about modal mass participation.
89
Engineering Analysis with COSMOSWorks
5: Static analysis of a link Topics covered •
Symmetry boundary conditions
•
Defining restraints in local coordinate system
•
Preventing rigid body motions
•
Limitations of small displacements theory
Project description We need to calculate the displacements and stresses of a steel link shown in figure 5-1. The link is pin-supported at the two end holes and is loaded with 100,000 N at the central hole. The other two holes are not loaded. Please open part file LINK. It has assigned material properties of Chrome Stainless Steel.
Pin support
Pin support Load 100,000 N
Figure 5-1: CAD model of the link Note that the supporting pins and the load pin are not present in the model. All rounded edges should be suppressed to simplify meshing.
91
Finite Element Analysis with COSMOS Works
Procedure One way to conduct this analysis would be to model both the link and all three pins, and then conduct an assembly analysis. However, we are not interested in the contact stresses that will develop between pins and the link. Our focus is on the deflections and stresses that will develop in the link, so the analysis can be simplified by NOT modeling the pins. Instead of modeling the pins, we can simulate their effects by proper definition of restraints and load. Also, notice that the link geometry, restraints and load are all symmetrical. We can take advantage of this symmetry and analyze only half of the model and replace the other half with symmetry boundary conditions. To work with half of the model, please unsuppress the cut which is the last feature in the SolidWorks Feature Manager window. Also suppress all the small fillets in the model. The fillets have negligible structural effect and would unnecessarily complicate the mesh. Removing geometry details deemed unnecessary for analysis is called defeaturing. Finally, note a split face in the middle hole that defines the area where load will be applied. Geometry in FEA-ready form is shown in figure 5-2. Figure 5-2 also explains what restraints and symmetry boundary conditions should be applied.
1! In order to model pin support, only . . £ . ; . , circumferential displacements are allowed on this cylindrical face.
'
/ / / JpP
/
^___ ^ I
. , boundary ... conditions Svmmctry
boundary conditions
Figure 5-2: Half of the link with restraints explained. Highlighted restraints are: a hole where the pin support is simulated and two faces in the plane of symmetry where symmetry boundary conditions are required The model is ready for the definition of supports - the highlight of this exercise. Please move to COSMOSWorks and define a study as static analysis with solid elements. Select the pin supported cylindrical face, as shown in figure 5-2 and open the Restraint window (figure 5-3).
92
Engineering Analysis with COSMOSWorks
Symbol settings
Figure 5-3: Restraint window The Restraint definition window specifies the restraint type as On cylindrical face because a cylindrical face was selected prior to opening the Restraint window. Notice that restraint directions are now associated with the cylindrical face directions (radial, circumferential, and axial), rather than with global directions (x, y, z). To simulate the pin support that allows the link to rotate about the pin axis, radial displacement needs to be restrained and circumferential displacement allowed. Furthermore, displacement the in axial direction needs to be restrained in order to avoid rigid body motions of the entire link along this direction. Notice that while we must restrict the rigid body motion of the link in the direction defined by the pin axis, we can do this by restraining any point of the model. It is simply convenient to apply the axial restraints to this cvlindrical face.
93
Finite Element Analysis with COSMOSWorks
To simulate the entire link, we apply symmetry boundary conditions to the two faces located in the plane of symmetry. The symmetry boundary conditions impose the requirement that these two faces remain in the plane of symmetry when the link experiences deformation. In-plane displacements are allowed, but out-of-plane displacements must be suppressed. The easiest way to define symmetry boundary conditions is to use Symmetry as a type of restraint. The definition of the symmetry boundary conditions is illustrated in figure 5-4.
Figure 5-4: Definition of symmetry boundary conditions Recall from figure 5-1 that the link is loaded with 100,000 N. Since we are modeling half of the link, we must apply a 50,000 N load to a portion of the cylindrical face, as shown in figure 5-5. The size of the area created with split line, where the load is applied is arbitrary. It should be close to what we expect the contact area to be between the pin and the link.
94
Engineering Analysis with COSMOSWorks
When defining the load (figure 5-5), take advantage of SolidWorks fly-out menu visible in COSMOSWorks window to select reference plane required in Force definition window. £ltf* • 0 Desigr,8md
• 9 Apply force/moment O Apply norma) force O Apply torque
Q.)r-^
y
y,Pn^.
* '£§ 6ase-£*ude
pes i.^aiiwri!
/: gjihowpn-A't
Figure 5-5: 50.000N force applied to the central hole The Top reference plane is used to determine the load direction. Notice that the load is distributed uniformly. We are not trying to simulate a contact stress problem. The last task of model preparation is meshing. Right-click the Mesh folder to display the related pop-up menu, and then select Create.... Verify that the mesh preferences are set on high quality, meaning that second order elements will be created, and mesh the geometry using the default clement size. For more information on the mesh, you may wish to review Mesh Details (figure 5-6).
95
Finite Element Analysis with COSMOSWorks
Figure 5-6: Mesh Details window shown over the meshed model After solving the model, we first need to check if the pin support and boundary conditions have been applied properly. This includes checking whether the link can rotate around the pin and whether it behaves as a half of the whole link. This is best done by examining the animated displacements, preferably with both undeformed and deformed shapes visible (figure 5-7).
(JRES (mm)
r
1.0306-001 19.5468-002 L 8.788e-002 . 8.0328-002 L 7.275e-002
Figure 5-7: Comparison of the deformed and undeformed shapes Comparison of the deformed and undeformed shapes verifies the correctness of the restraints definition: link rotates around the imaginary pin andfaces in the plane of symmetry remain flat and perform only in-plane translations.
96
Engineering Analysis with COSMOSWorks
To conclude this exercise, review the stress results. Examine the different stress components, including the maximum principal stresses, minimum principal stresses, etc.
P3 (N*nm"2 (MPa)) 1.4Q4e+000
•f -2.267e.t000
. -5.S38e+00Q •:•• . -3.609e+000 . -1.3288+001 -1.8958+001 -2.0628+001 2.429e+001 . -2.7888+001 -3.1838+001
.-3.5318+001 -4,265e+001
Figure 5-8: Sample of stress results In.this example, the minimum principal stress (Pi) plot is shown. Please repeat this exercise using the full model. To do this, open the SolidWorks Manager, suppress the cut, and return to COSMOSWorks. You will be prompted to acknowledge the change in the model and the boundary conditions (figure 5-9). You will need to add load to the uncut model, define support for the other pin, and then proceed with meshing, running the solution, and reviewing the analysis results.
ii|ii1pfi3iSWllll|~™a~3 #\ ''• ''
Mode! has been chanced, AS the Load/Restraints willfasupdated automatically. Current mesh and results may be invaW.
Figure 5-9: COSMOSWorks notifies the user of changes in model geometry Any change in model geometry invalidates FEA results. Changes may also require modification of restraints and loads definitions. Before finishing the analysis of LINK, we should notice that the link supported by two pins as modeled in this exercise, corresponds to the
97
Finite Element Analysis with COSMOSWorks configuration shown in figure 5-10, where one of the hinges is free to move horizontally. Since linear analysis does not account for changes in model stiffness during the deformation process, linear analysis is unable to model membrane stresses that would have developed if both pins were in fixed position. Non- linear geometry analysis would be required to model support if both hinges were in fixed position. This could be done using COSMOSWorks Advanced Professional. Refer to chapter 1 for a brief review of limitations of linear analysis.
r
r
:
Figure 5-10: Our model corresponds to the situation where one hinge is floating, symbolically shown here by rollers under the left hinge. Non-linear geometry analysis would be required if both hinges were infixed positions.
98
Engineering Analysis with COSMOSWorks
6: Frequency analysis of a tuning fork Topics covered
Project
•
Frequency analysis with and without supports
•
Rigid body modes
•
The role of supports in frequency analysis
description Structures have preferred frequencies of vibration, called resonant frequencies. When excited with a resonant frequency, a structure will vibrate in a certain way, called mode of vibration. A mode of vibration is the shape in which a structure will vibrate at a given natural frequency. The only factor controlling the amplitude of vibration resonance is damping. While any structure has an infinite number of resonant frequencies and associated modes of vibration, only a few of the lowest modes are important in their response to a dynamic loading. A frequency analysis calculates these resonant frequencies and their associated modes of vibration. Please open the part file called TUNING FORK. It has material properties already assigned (Chrome Stainless Steel). The model is shown in figure 6-1.
Fixed restraint
Figure 6-1: Tuning fork geometry Fixed restraint is applied to the surface of the ball. A quick inspection of the CAD geometry reveals a sharp re-entrant edge. This condition renders the geometry unsuitable for stress analysis, but still acceptable for frequency analysis.
99
Finite Element Analysis with COSMOSWorks
Procedure Define Frequency study as shown in figure 6-2.
111
MMiL
j OplB = ; Rema*
Number <Jbfequf ttta
's^liiilll tuning fotk.
1 KatiSolid me& J Oitec. ; sp C<st":t;e!
>FFE iJFFEPte
e;
i
Car es!
.
I
He
Figure 6-2: Frequency study definition (left) and study properties (right) The Options tab in the Frequency window allows for specifying the number of frequencies- to be calculated in the frequency study. Notice that as always, different solvers are available. We request that five frequencies be calculated using FFEPlus Solver which is the fastest of the three solvers available in COSMOSWorks.
Next, define fixed restraints to the ball surface, as shown in figure 6-1. This approximates the situation when the tuning fork is held with two fingers. Finally, mesh the model with a default element size of 1.46 mm. The meshed model is shown in figure 6-3. The automesher selects element size to satisfy the requirements of a stress analysis. A frequency analysis is less demanding on the mesh. Generally, a less refined mesh is acceptable Nevertheless, since this is a very simple model, we accept the mesh without making an attempt to simplify it.
100
Engineering Analysis with COSMOSWorks
Figure 6-3: Meshed model of the tuning fork After the solution is complete, COSMOSWorks creates two folders named Displacement and Deformation and places one plot in each folder. If desired, you can define more result plots by right-clicking the Displacement or Deformation folder, which opens an associated pop-up menu, from where you can define more result plots. We will add three more plots to the Deformation folder, corresponding to mode 2, mode 3, and mode 4. Using click-inside technique, rename these plots to model. mode2, mode3, mode4. jpaj Deformation ^model 1%) mode? imodes
) Deformation \[^ mode i U% rnodeS Show Hide
Delete,
Edit Definition,.. Animate... Settings... Axes...
Copy
Print... Save As .,. Delete Copy
Figure 6-4: ['our plots defined in Deformation
folder
The active plot (the one that is showing) can be modified using selections from the pop-up menu activated by right-click the plot icon (left). An Inactive plot can be displayed by double-clicking the appropriate plot icon, or right-clicking the plot icon to display the associated pop-up menu (right), and then clicking Show.
101
Finite Element Analysis with COSMOSWorks The deformation plot in the modal analysis shows the mode of vibration associated and corresponding natural frequency. The first four modes of vibration are presented in figure 6-5.
Figure 6-5: First four modes of vibration and their associated frequencies As any musician will tell us, the most common type of tuning fork produces a low A sound, which has a frequency of 440 Hz. However, the lower A frequency of 440 Hz, which we were expecting to be the first mode, is actually the fourth mode. Before explaining the reasons for this, let's run the frequency analysis again, this time without any restraints. We need to define a new frequency study, which we will call tuning fork no supports. The easiest way is to copy the existing timing fork study and either delete or suppress the restraint (right-click the restraint icon and make proper selection). In the Options tab of the Frequency window in the tuning fork no supports study, we again specify that five modes be calculated (no change compared to previous study). After the solution is has been completed, right-click the Deformation folder and select List Resonant Frequencies. Here, we find that the highest calculated mode is mode 11 (figure 6-6) even though we asked that only five modes be calculated.
102
Engineering Analysis with COSMOSWorks
Study name: tuning fork no supports Mode Ni |
2
1
3 4
1
1
I.
5 8 7 8 3
10 11
1-1
{Bad 0 0 0 0 0 0 2768.8 4244.1 10218 11009 17427
c • ' 0 0 0 0 0 0 440.17 675.19 1625.6 1751,4 2772.5
•
> >nd le+032 le+032 1e+032 le+032 1e+032 1<s+032 0.0022718 0.0014811 0.00081516 0.00057097 0.00036068
:.:>:
Figure 6-6: List Modes window The illustration has been modified in a graphic program to show all eleven modes without scrolling.
We also notice that the first six modes have the associated frequency 0 Hz. Why? The first six modes of vibration correspond to rigid body modes. Because the tuning fork is not supported, it has six degrees of freedom as a rigid body: three translations and three rotations. COSMOSWorks detects those rigid body modes and assigns them zero frequency (0 Hz). The first elastic mode of vibration, meaning the first mode requiring the fork to have elastic deformation is mode 7, which has a frequency of 440.2 Hz. This is close to what we were expecting to find as the fundamental mode of vibration for the tuning fork. Why did the frequency analysis with the restraint not produce the first mode with a frequency near to 440 Hz? If we closely examine the first three modes of vibration of the supported tuning fork, we notice that they all need the support in order to exist. The support is needed to sustain these modes, but vibrations do not persist because the three modes are quickly damped by the very support that sustains them. This is because the support is never rigid as we have modeled, it is elastic and there is always damping associated with elastic support that is not modeled here. After modes 1, 2 and 3 have been damped out, the tuning fork vibrates the way it was designed to: in mode 4 (calculated in the analysis with supports) or mode 7 (calculated in the analysis without supports). These two modes are identical.
103
Engineering Analysis with COSMOSWorks
7: Thermal analysis of a pipeline component Topics covered
Project
•
Steady state thermal analysis
•
Analogies between structural and thermal analysis
•
Analysis of temperature distribution and heat flux
description So far, we have performed static analyses and frequency analyses, which both belong to the class of structural analyses. Static analysis provides results in the form of displacements, strains, and stresses, while frequency analysis provides results in the form of natural frequencies and associated modes of vibration. We will now examine a themial analysis. Numerous analogies exist between thermal and structural analyses. The most direct analogies are summarized in figure 7-1.
Structural Analysis
Thermal Analysis
Displacement [m]
Temperature [K]
Strain [7]
Temperature gradient [K/m]
Stress [N/m2]
Heat flux [W/m2]
Load
Heat source 2
3
[N] [N/m] [N/m ] [N/m ]
[W] [W/m] [W/m2] [W/m3]
Prescribed displacement
Prescribed temperature
Figure 7-1: Selected analogies between structural and thermal analysis
In this exercise, we will perform a simple thermal analysis of two pipes crossing, using the model CROSSING PIPES with Brass material properties already assigned.
105
Finite Element Analysis with COSMOSWorks
Figure 7-2: CAD model of two crossing pipes Also shown are the prescribed temperatures, applied to the endfaces as temperature boundary conditions.
Procedure Temperatures to be applied to the model are shown in figure 7-2. As indicated in figure 7-1, prescribed temperatures are analogous to prescribed displacements in structural analyses. Our objective is to determine what temperature field will be established after the prescribed temperatures have been applied long enough for temperature field to stabilize itself. Since no convection coefficients are defined on any faces, heat can enter and leave the model only through the end faces with prescribed temperatures assigned. In thermodynamics jargon, we say that the model has adiabatic walls. The first step is study definition. Call this study crossing pipes and define it as shown in figure 7-3.
106
Engineering Analysis with COSMOSWorks
; Mesh t ::Sold'8>«h;::
I\
iiisiiaiaiiiii
lililllltliililllillllffl
Acwe $!.ud>i name; crossing pipe*
Figure 7-3: Definition of crossing pipes study The study definition for crossing pipes is a Thermal analysis type using a Solid mesh. To define the prescribed temperature, open the pop-up menu by right-clicking the Loads/Restraints folder and selecting Temperature....(figure 7-4), i crossing pipes ®lt Parameters ^ c r o s s i n g pipes (-Default-) fi% Solids i crossing pipes (-[SW]8rass-)
Temperature,., Convection.., Heat Flux.., Heat Power.,. Radiation.,, Options,.. Copy
Figure 7-4: Pop-up menu related to a thermal analysis The pop-up menu lists the thermal boundary conditions (Temperature, Convection, Radiation) and thermal loads (Heat Flux, Heat Power) available in a thermal analysis.
107
Finite Element Analysis with COSMOSWorks
Figure 7-5 shows the Temperature window for the face where a temperature of 100°C is applied. Since each of four faces has a different prescribed temperature, we need to assign temperatures in four separate steps.
••V £j) Temperature
[_J Show preview Temperature I I I 100
|)i
Variation with time
ll«;i: '"' Symbol settings
*r 1
Figure 7-5: Temperature window Note that the units are in degrees Celsius. The next step is meshing the model. To ensure that fillets are meshed with elements with low turn angles (it is important for heat flux calculations for a concave face of element not to cover more than a 45 degree angle), define mesh control as shown in figure 7-6. Use the default global element size to create the mesh shown in figure 7-7.
108
Finite Element Analysis with COSMOSWorks
Figure 7-5 shows the Temperature window for the face where a temperature of 100°C is applied. Since each of four faces has a different prescribed temperature, we need to assign temperatures in four separate steps.
Type
•*•
L J Show preview Temperature I t i 100
•*• ic
v
Variation with time
H Symbol settings
Fiaurc 7-5: temperature window Note that the units are in degrees Celsius. The next step is meshing the model. To ensure that fillets are meshed with elements with low turn angles (it is important for heat flux calculations for a concave face of element not to cover more than a 45 degree angle), define mesh control as shown in figure 7-6. Use the default global element size to create the mesh shown in figure 7-7.
108
Engineering Analysis with COSMOSWorks
Seeded tribes
CT3II :lilllillllllli
Corf.ro! P a s
Low
A? 2-E
High
•mm
\^i
% I'Kl %
L-:.„, ,,.
Syrfibdisevtjriss
Figure 7-6: Mesh Control window specifies element size 2.5mm on both fillets.
Figure 7-7: Finite element mesh of crossing pipes model created with the default global element size and mesh control applied to both fillets. After solving the model, we notice that only one folder called Thermal has been created (figure 7-8). This folder called Thermal, has one plot in it. By default, it shows the temperature distribution. We need to create one more plot showing heat flux.
109
Finite Element Analysis with COSMOSWorks crossing pipes J l l Parameters C%I crossing pipes (-Default-) - ^ Solids " \ ^ crossing pipes (-[SW]Brass~) B kk Load/Restraint | 100C § BfJC § 2S0C | 400C S Design Scenario - : 'lip Mesh Q Control-! j y Report -', j y Thermal (yj| temperature [fiteheat flux
Figure 7-8: COSMOSWorks Manager window and the single Thermal folder The COSMOSWorks Manager window shows only one results folder, called Thermal. Notice that we have renamed the prescribed temperature icons and plots in Thermal folder to give them more descriptive names. .
'
"
"
"
. . . . : : . . •
'
•
^•'-"•.iS.sjS***''
">:-rr:s:' (Cs-isius) ^ ^ 4.0006+002
H
2?33e+002 'w+QG2
Display
. 3.200e+Gt)2 . 2.9338+002 . 2.SS7et-G02
I TEMP: Temperature ,y\ | Celsius i Fringe
Hfflli
'•••!'•
* IMGOe+002 I 3*r+0l -
. 1 .gg?e*002 1 1 1 1 .8GGe*0£&
-
, 1 3i:'e+002
H i i S.000e+00'l
Figure 7-9: Thermal Plot window defining temperature plot and the corresponding plot
110
Engineering Analysis with COSMOSWorks
HR-J^N (W,'m'2) 5.843s*CC5 5 449&+00S •. 4.SSSe*005
Dispi
.4.4S13+0GS
5 4726*005
HFlUXM: Resultant h>: * 111
:W/m''"i ]::::::::::::::::: i Fringe
•*! I
^^IlilSilSI^Bllffi^SSfil^SlSlliSllliS (
.
'
:
S**005
||l. 2 4ftfe»ijos •: 1 .ssos*t« 1 4SS**G05 1 DO'i e*C0S
Figure 7-10: Thermal Plot window defining heat flux plot and the corresponding plot
111
Engineering Analysis with COSMOSWorks
8: Thermal analysis of a heat sink Topics covered
Project
•
Analysis of an assembly
•
Global and local Contact/Gaps conditions
•
Steady state thermal analysis
a
Transient thermal analysis
•
Thermal resistance layer
a
Use of section views in results plots
description In this exercise, we continue with thermal analysis. However, this time we will analyze an assembly rather than a single part. Please open the assembly file named HEAT SINK (figure 8-1).
Vertex for probing results
Microchip
Radiator
Figure 8-1: CAD model of a radiator assembly The CAD model of a radiator assembly consists of two components: aluminum radiator and a ceramic microchip.
113
Finite Element Analysis with COSMOSWorks
Analysis of an assembly allows assignment of different material properties to each assembly component. Notice that the Solids folder, visible in figure 8-2, contains two icons corresponding to the two assembly components with material properties already assigned. This is because material has been assigned to parts which are assembly components: Ceramic Porcelain material to the microchip and Aluminum Alloy 1060 to the radiator. The ceramic insert generates a heat power of 25 W and the aluminum radiator dissipates this heat. The ambient temperature is 27°C (300K). Heat is dissipated to the environment by convection through all exposed faces of the radiator. We assume that the microchip is isolated, meaning it can not dissipate heat to ambient air. The convection coefficient (also called the film coefficient) is assumed to be 250W/m7K in this model. This means that if the difference of temperature between the face of the radiator and the surrounding air is IK, then each square meter of the surface dissipates 250W of heat. This rather high value of convection coefficient corresponds to forced convection caused, for example, by a cooling fan. Heat flowing from the microchip to the radiator encounters thermal resistance on the boundary between microchip and radiator. Therefore, thermal resistance layer must be defined on the interface between these two components. Our first objective is to determine the temperature and heat flux of the assembly in steady state conditions, meaning after enough time has passed for temperatures to stabilize. This will require steady state thermal analysis. The second objective is to study the temperature in the assembly as a function of time in a transient process when the assembly is initially at room temperature and power is turned on at time t=0. This will require transient thermal analysis.
Procedure In COSMOSWorks and create a study called heat sink steady state. Before proceeding, we need to investigate a new icon, called Contact/Gaps, which is found in the COSMOSWorks Manager window. Right-click the Contact/Gaps icon to open the pop-up menu, shown in figure 8-2.
114
Engineering Analysis with COSMOSWorks
•jjjc! Parameters
<^S heat sink (-Default-) - <% Solids ^microchip-1 (-[S'#]Cerar«c Porcelain-) ^ r a * * o r - l ( - [ S W ] 1 0 6 0 Alloy-)
"'..'
4 J Load/Restraint
i?) 8or«ted
1 Design Scenario 1 Mesh
".'
w*!r«?«Si.
Set Global Contact,,,
I
Define Contact Set,,, Define Contact for Components,,.
I |
O Mode to rcssfe
Figure 8-2: Contact/Gaps icon in the COSMOSWorks Manager When an assembly is analyzed, the COSMOSWorks Manager window always includes a Contact/Gaps icon. Right-click Contact/Gaps icon (left) and select Set Global Contact (middle) to display Global Contact window (right)
The default setting for the Contact/Gaps conditions is Touching Faces: Bonded, meaning that assembly components are merged. Even though this is what we need, we still have to define local Contact Set for contacting faces because we need to define a thermal resistance between the contacting faces. This can only be done as local Contact/Gaps condition. Right-click Contact/Gaps folder and select Define Contact Set to open Contact Set window shown in figure 8-3. Select Surface as contact type. Note that only Surface contact condition allows the definition of thermal resistance. Referring to figure 8-3, select contacting faces and enter Distributed Thermal Resistance as 0.001Km2/W (this value is usually obtained by testing).
Finite Element Analysis with COSMOSWorks
w, V:f^-\
m
mm
O fata!
Face
A:'<§) Distributed 0.00J Friction;
:
{K-n,-^)iw ^
Face <2>
Figure 8-3: Defining thermal resistance between microchip and radiator Modeling thermal resistance between contacting faces requires that contact between these two faces is defined as Surface. This contact condition overrides the global contact condition which we left at default settings as Bonded. Next, we specify the heat power generated in the microchip. To do this select the microchip from the Solids folder and right-click the Load/Restraint folder to open the pop-up menu. Next select Heat Power... to open the Heat Power window (figure 8-4).
116
Engineering Analysis with COSMOSWorks
| heat sink
>
®il Parameters iheat sink (-Default-) 1 Solids 5 microchip-1 (-[SW]Cerarnic Porcelain-)
Selected grtlties
IJX^IIllllII *w m
imtor-1 (-[5WJ1Q6Q Alloy-) Hide All stgn ice
£j Show preview
Show All
\ Contact/^* <^g Mesh | Q Report
Temperature... Convection... Heat Flux.., Heat Power... Radiation,,,
Heal power (Per Entity) :
SI
*1i 25
Options... Copy
Thermostat (Transient) Symbol settings
Figure 8-4: Pop-up menu associated with the Load/Restraint
folder
Right-click the Load/Restraint folder to open a pop-up menu. From this menu, select Heat Power to open Heat Power definition window. Notice that microchip-1 appears in the Selected Entity filed and the heat power is applied to the entire volume of the selected component.
Finite Element Analysis with COSMOSWorks
So far we have assigned material properties to each component as well as defined the heat source and thennal resistance layer. In order for heat to flow, we must also establish a mechanism for the heat to escape the model. This is accomplished by defining convection coefficients. Right-click the Load/Restraint folder to open a pop-up menu (already shown in figure 8-4) and select Convection... to open the Convection window (figure 8-5). Select all faces of the radiator including the bottom one. Enter 250 W/nr/K as the value of convection coefficient for all selected faces and define the ambient temperature as 300K as bulk (ambient) temperature.
Selected Entities f
j
f. .
•
M^- ;~* ^ : ^ ;s;ss>~;;
O s N o w preview Units
*•
fcl SI
SBi
Convection Coefficient; fit
;S0
Bu$; Temper ature If : 3M
-'•• x
W/(ftv" 2.K5
.*. Kelvin
Symbol settings
Figure 8-5: Convection window Use this window to specify convection coefficient, and Bulk Temperature (ambient temperature).
118
Engineering Analysis with COSMOSWorks
The last step before solving is creating the mesh. For accurate heat flux results apply mesh control to all six fillets as shown in figure 8-6.
y\*j Selected Entities
ff) l l l l l l l l l ; f ~ l Show preview J*. \
Con i-el Parameters
Component signtficar ce
Low
^
12.4619062
\
High \ ;imm
"b I 1,5 7s- i 3
Figure 8-6: Mesh control applied to rounds in Radiator
Now mesh the assembly with default global element size to produce mesh as shown in figure 8-7. Also, see the book cover.
119
Finite Element Analysis with COSMOSWorks
Figure 8-7: Exploded view of the meshed assembly The exploded view of the meshed model is created using the SolidWorks Configuration Manager. Once the solution is ready, define two plots: temperature and heat flux. The required choices are shown in figure 8-8.
Display
Display
:
m
| TEMP: Temperature
g§
HFIU 't
n mi h*
I Celsius } Fringe
i Fringe
Figure 8-8: Thermal Plot definition window for temperature distribution plot (left) and heat flux plot (right)
120
Engineering Analysis with COSMOSWorks
Both temperature and heat flux result plots are much more informative if presented using section views. COSMOSWorks offers a multitude of options for sections plots which are easier to practice than to explain. Here we describe the procedure of creating a flat section result plot using one of SolidWorks default reference planes (any reference plane can be used). To show the temperature distribution plot, right-click plot icon and select Section Clipping from the pop-up menu. By default, the cutting surface is flat and aligned with the first reference plane in SolidWorks Feature Manager. To select another cutting plane, click COSMOSWorks tab to expose SolidWorks Feature Manager while still keeping Section window open. From SolidWorks Feature Manager select Right reference plane. This creates the section plot shown in figure 8-9. Note that this procedure is required because SolidWorks fly-out menu us not available for result plots. Mode; name;"'frss^sink Therms: Ploi3 "" Temp (Celsius)
•in cngm
J55555B-S;334e+0Oi
<%(f)racr»lcr :^: < p Mates in heat sink : • S B Annotations
.. 3.321 e+OC-l
:
M^,i'-- C^sign Binder
1 %
7,8t4e*G01
J
. ?.307e+001 6:SSC«*001 fa 2^ eKiGi . 5 73"*e*0Gi I 5 2S0e+DO1 „4 ??3e+0&i * _4 2?e&*00l
*£ [^ J^'"
OptfefK
Bstan section pi sns
* :j
O H o t jn section only : ;; ShowcontciyD vths : 03imtutportion^ the model :
:|
R sset
|
Section clipping on / off
Figure 8-9: Section plot of temperature distribution in the assembly The illustration has been modified in a graphics program to show the entire Section window and a portion of the exposed SolidWorks Feature Manager window. Normally this would require scrolling. Please experiment with different options in Section window, then construct section plot of heat flux. In addition to section clipping, use exploded view to produce heat flux plot similar to one shown in figure 8-10.
121
Finite Element Analysis with COSMOSWorks £f
I Study nasTie/ heat sink ste&rfy state : } Tiftre step: fi
V
\i
i
HFIuxtl C>.'«nA2)
^^20)08.06") H,1833stOC4
mm
t 6S7<M»4 , 1 .SGOe+004 1 ..->3e*00
>e*004
11 l0,«
„ 5 nnnft+004
I I I 3.333&+0C3 6.6e7e*0G3 5OOne+!.'i03 < j j - I 333e*OCC< H . 1 S676-KK3
Shew section plane
lj*Aon;s«acfi oniy Show eontewr o Yihe lifKut portion of me ^jgxofctde^ef: \
Reset
|
*m
Sppi
f
Figure 8-10: Section plot of heat flux in the assembly The legend was modified in Chart Option to show heat flux in the range 0 20000 W/m2. This completes the steady state thermal analysis of the heat sink assembly. We now proceed with transient thermal analysis. Please copy study heat sink steady state into study heat sink transient. Right-click study heat sink transient folder and select Properties to open window shown in figure 8-11. Select Transient analysis (Steady State is the default option). Our objective is to monitor the temperature changes every 60 seconds during the first 600 seconds with particular attention to the vertex location shown in figure 8-1. To accomplish that enter 600 as Total time and 60 as Time increment.
122
Engineering Analysis with COSMOSWorks
SoSdWorks model swr Conhgyf alien name Flow jtesatson no.
} bmzi sparse • FFE SFFEMus
I Advanced Options-... )
Cancel
Figure 8-11: Transient thermal analysis is specified in thermal study Options Analysis will be carried on for 600 seconds with results reported every 60 seconds.
Transient thermal analysis requires that the initial temperature of the model be specified. We assume that both components have the same initial temperature 27°C. Right-click Load/Restraint folder in heat sink transient study and select Temperature to open window shown in figure 8-12. Select Initial Temperature and enter 27°C.
123
Finite Element Analysis with COSMOSWorks
: L.-J
S heat sink
, ! |^j i^fels
fJ*J Annotations :
~4# Design Binder
i " l & Lighting " "NX Front " ^ X Top -•<$<: Right
} Initial temperature
" *+ Origin
>Teri-ipecatufe
[Jl;
'§f I
i:iiiiililli|
i^f Show preview Terisperature
11 r
c
Symbol settings
Figure 8-12: Initial Temperature specified for both assembly components Assembly components can be selectedfrom the SolidWorks fly-out menu. Now run the analysis and display the temperature distribution plot. Display the temperature plot for the last step (step number 10) by right-clicking plot icon, selecting Edit Definition and setting Plot Step to 10 (figure 8-13)
rs«*ooi
'.7878+001 ' 2SSe+001 TEMP: T e?r
17828+001 s.2S0e+OO1 i.7S7e*001
m"fringe
i .7528+001 S .2508+001 s.74?e+001 S.2468+001
Figure 8-13: Temperature distribution after 600 seconds since the heat power has been turned on.
Since we have not specified heat power as function of time, it is assumed that the full power is turned on at time t=0 when assembly is at the initial
124
Engineering Analysis with COSMOSWorks temperature 27°C. Figure 8-13 shows temperature distribution after 600 seconds. Notice that this result is very close to the result of steady state thermal analysis meaning that after 600 seconds, the temperature of assembly has almost stabilized. To see the temperature history in selected locations of the model, we proceed as follows: make sure the plot in figure 8-13 is still showing, and right-click its icon in COSMOSWorks Manager and select Probe. To probe temperature in the location shown in figure 8-1, select (left-click) this location with the cursor. For the exact location where we want to probe results, display the mesh, then probe the node that has been placed coincidently with the vertex created by the spilt lines. Probing opens the window shown in figure 8-14.
Figure 8-14: Temperature probed in the location shown in figure 8-1 Select Response in the Probe window to display a graph showing the temperature at the probed location as a function of time (figure 8-15).
125
Finite Element Analysis with COSMOSWorks
"
topontt
Graph
File Options Help Study r Ploi 33-
.
. ~s
„
ir^rE^^z^Tl
3231 •
B 29-
'
;
;
;
:
:
:
"
"
/
I»: 2?
/
/:
/ /
2680.00
1
,
,
,
168.00
,
i.
,
i
76.00 384.1 Time (sec)
' <1| .
,
i
^__w.
«2.0G
)
J
600.00
' „
Figure 8-15: Temperature as a function of time in the probed location To produce a response graph (here temperature as a function of time), you may probe temperature from any of the 10 performed steps. A quick examination of the graph in figure 8-15 proves that after 600 seconds the model has almost achieved steady state temperature.
126
Engineering Analysis with COSMOSWorks
9: Static analysis of a hanger Topics covered Q Static analysis of assembly •
Global and local Contact/Gaps conditions
Project description In this exercise we will investigate the structural analysis of assemblies, but first we need to review different options available for defining the interactions between assembly components (we have touched on this topic in the previous exercise). Let's look more closely at the pop-up menu that opens when you right-click the Contact/Gaps icon, shown in figure 8-2 and repeated in figure 9-1 for easy reference.
Global conditions Touching Faces;: *£} Bonded Set Global Contact,. Define Contact S e t . ,
0 Mods to node1
Define Contact far Components.,,
Component conditions
Local conditions
Figure 9-1: Pop-up menu associated with the Contact/Gaps icon The pop-up menu, opened by right-clicking the Contact/Gaps icon folder in COSMOSWorks Manager window, distinguishes between global, component, and local Contact/Gaps conditions. The default choice in global conditions, (as well as in component and local conditions) is that touching faces are bonded. The differences between different Contact/Gaps conditions are as follows: u
Global condition - affects all faces in an assembly
•
Component condition - affects one component
•
Local condition - affects only the two specified faces (must belong to different components of an assembly)
127
Finite Element Analysis with COSMOSWorks
A description of the available options in Global, Component and Local Contact/Gap conditions is given in the following tables. GLOBAL Option
Description
Touching Faces: Bonded
Touching areas of different components are bonded. Bonded areas behave as if they were welded. This option is available for structural (static, frequency, and buckling) and thennal studies. If touching faces are left as Bonded and Global conditions are not overridden by Component or Local conditions, then an assembly behaves as a part.
Touching Faces: Free
The meshcr will treat parts as disjointed bodies. This option is available for structural (static, frequency, and buckling) and thermal studies. For static studies, the loads can cause interference between parts. Using this option can save solution time if the applied loads do not cause interference. For thennal studies, there is no heat flow due to conduction through touching faces.
Touching Faces: Node to Node
The mesher will create compatible meshes at areas common to parts. The nodes associated with the two parts on the common areas are coincident but different. The program creates gap elements connecting each two coincident nodes. This option is available for static, nonlinear, and thermal studies. For static studies, a gap element between two nodes prevents part interference but allows the two nodes to move away from each other.
128
Engineering Analysis with COSMOSWorks
COMPONENT Option
Description
Touching Faces: Bonded
The mesher will bond common areas of the selected components at their interface with all other components. This option is available for structural (static, nonlinear, frequency, and buckling) and thermal studies.
Touching Faces: Free
The mesher will treat the selected components as disjointed from the rest of the assembly. This option is available for structural (static, frequency, and buckling) and thermal studies. For static studies, the loads can cause interference between parts. Using this option can save solution time if the applied loads do not cause interference. For thermal studies, the program prevents heat flow due to conduction through common part areas.
Touching Faces: Node to Node
The mesher will create compatible meshes at areas of the selected components that are common to other components. The nodes associated with the two parts on the common areas are coincident but different. The program creates a gap element connecting each two coincident nodes. This option is available for static, nonlinear, and thermal studies. For static studies, a gap element between two nodes prevents part interference but allows the two nodes to move away from each other.
129
Finite Element Analysis with COSMOSWorks
LOCAL Option
Description
Bonded
The mesher will bond common areas of the source and target faces. Bonded areas behave as if they were welded. This option is available for structural (static, frequency, and buckling) and thermal studies.
Free
The mesher will treat the source and target faces as disjointed. This option is available for structural (static, frequency, and buckling) and thermal studies. For static and nonlinear studies, the loads can cause interference between parts. Using this option can save solution time if the applied loads do not cause interference. For thennal studies, the program prevents heat flow due to conduction through common source and target areas.
Node to Node
The mesher will create compatible meshes at areas common to source and target faces. The nodes associated with the two parts on common areas are coincident but different. The program creates a gap element connecting each two coincident nodes. This option is available for static and thermal studies. For static studies, a gap element between two nodes prevents interference but allows the two nodes to move away from each other.
Surface
Surface contact is more general than node-to-node contact. Select source entities (faces, edges, and vertices) from a component and target faces from a different component. The program creates a node-tosurface gap element for each node on the source entities. The surface associated with each gap element is defined by all the target faces. Surface contact is available for static and thermal studies. For static studies, a node-to-surface gap element prevents interference but allows the node to move away from the target faces. For thermal problems, you can specify thermal contact resistance between source and target faces.
Shrink fit
The program creates a shrink fit condition between the source and target faces. The faces may or may not be cylindrical but should be partially or fully interfering.
130
Engineering Analysis with COSMOSWorks
An assembly always needs to be re-meshed after editing any contact option. Global Contact/Gaps conditions can be overridden by Component and/or Local conditions. For example, using Global Contact/Gaps conditions, we can request that all faces be bonded. Next, we can locally override this condition and define local conditions for one (or more) pair(s) as Touching Faces: Node to Node. The hierarchy of Global, Component, and Local Contact/Gaps conditions is shown in figure 9-2.
A LOCAL £ , i /
\
COMPONENT /
\
Figure 9-2: Hierarchy of Contact/Gaps conditions In the hierarchy of Contact/Gap conditions, local conditions override both Component and Global conditions. Component conditions override Global conditions. Local Contact/Gaps conditions can be specified as Bonded, Free, Node to Node, Surface, and Shrink fit. We will now discuss the important distinction between Node to Node and Surface conditions. A Node to Node condition can be specified both globally and locally. It can only be applied to faces that are identical in curvature, even if the faces are not of the same size; the faces just have to share some common area. Node to Node conditions can be specified between two: •
Flat faces
_l
Cylindrical faces of the same radius
•
Spherical faces of the same radius
With these options, the mesh on both faces in the area where they touch each other is created in such a manner that there is node to node correspondence (nodes are coincident) on both touching surfaces; hence the name Node to Node. Surface contact may be specified between two faces of different shapes and can only be specified as a local condition. The faces can but don't have to touch initially but are expected to come in contact once the load has been
131
Finite Element Analysis with COSMOSWorks
applied to model. The mesh on both surfaces is not identical, so there is no node to node correspondence. The difference between Node to Node and Surface conditions is illustrated in figure 9-3.
?.,?•>. •0') m
Type'
T?v
-f i
••-..;. \ Node to Node
|
CM
m
Face < 1 > I ace
Figure 9-3: The contact between a spherical punch and a plate (left) is defined as a Surface contact. I'he contact between a Hat end punch and a plate (right) is defined as a Node to Node contact. Faces in Surface contact condition don 7 have to touch initially. They are just expected to come in contact under the load. Surface contact is more general, but less numerically efficient than the Node to Node contact. Any Node to Node contact could be defined as a Surface condition, but that would unnecessarily complicate the model.
132
Engineering Analysis with COSMOSWorks
Procedure Open the assembly part file HANGER (figure 9-4). Material (AISI 304) has already been assigned to all assembly components and will be automatically transferred to COSMOSWorks.
Fixed support
1,000 N bending load (down)
Figure 9-4: Hanger assembly The hanger assembly consists of three parts (compare with figure 9-6). A 1,000 N load is applied to the split face, and support is applied to the back of vertical flat.
133
Finite Element Analysis with COSMOSWorks
If you do not modify the Contact/Gaps parameters, then by default all touching faces are bonded, and the FEA model will behave as one part. A sample result is shown in figure 9-5.
Figure 9-5: Displacement results for a model with all touching faces bonded Notice that the hanger assembly model is adequate for analysis of displacements. However, due to stress singularities in the sharp re-entrant corners, it is not statable for analysis stresses in those sharp re-entrant corners. Now, we will modify the Contact/Gaps conditions on selected touching faces. We leave the global conditions set to Touching Faces: bonded, but locally we override them by defining a local Contact/Gaps condition. One of the three pairs of touching faces will be defined using local condition Free, meaning that there is no interaction between faces. The faces, shown in figure 9-6, will be able to either come apart or "penetrate" each other with no consequences.
134
Engineering Analysis with COSMOSWorks
Figure 9-6: Touching Faces: Free When faces 1 and 2 are locally defined as Free, there is no interaction between them. Note that exploded view of the hanger makes it possible to define local Contact/Gaps conditions. Every time Contact/Gaps conditions are changed COSMOSWorks prompts you to remesh (figure 9-7).
Figure 9-7: COSMOSWorks prompt when Contact/Gaps conditions change Any change in Contact/Gaps conditions requires remeshing. Remeshing will delete the previous results. If we wish to keep the earlier results, we need to define local Contact/Gaps conditions in a new study. Once local or component Contact/Gaps conditions have been defined, an icon is placed in the Contact/Gaps folder, as shown in figure 9-8.
135
Finite Element Analysis with COSMOSWorks
| Contact/Gaps (-Global: Bonded-) JgL Contact Set- i (-F Figure 9-8: Contact/Gaps
folder
The Contact/Gaps folder holds definitions of local Contact/Gaps
conditions.
The lack of interference between faces in a pair locally defined as Free, is best demonstrated by showing displacement results (figure 9-9).
Figure 9-9: Displacement results in a pair defined as Free The plot on the left shows results for load directed downwards and the plot on the right has the load direction reversed.
Let's now change the local contact conditions between faces shown in figure 9-6 from Free to Node to node. To change the local condition, right-click the Contact Pairl icon in the Contact/Gaps folder (figure 9-8), which opens a pop-up menu. From the popup menu select Edit definition... in order to open the Contact Pair window (figure 9-10).
136
Engineering Analysis with COSMOSWorks
Type;
Mode to Node
Figure 9-10: Contact pair window The Contact set window allows yon to create or edit local Contact/Gaps conditions. In the Contact Set window, change the local condition to Node to Node. Remesh the model when prompted, and run the solution once again. Notice that the solution now requires much more time to run because the contact constraints must be resolved (figure 9-11). Node to Node conditions (as well as Surface conditions), represent nonlinear problems and require an iterative solution.
i.
Nodss' 105^
%SB
Figure 9-11: Iterative solution for the hanger assembly using a Node to Node condition A Node to Node condition requires an iterative solution to solve contact constraints and takes significantly longer to complete than a linear solution. The displacement results, displayed in figure 9-12, show that the two faces defined as Node to Node now slide when a downward load is applied (left) and separate when the load is applied upward (right).
137
Finite Element Analysis with COSMOSWorks
Figure 9-12: Displacement results for two locally defined Node to Node faces The two faces in the pair defined locally as Node to Node slide (left) or separate (right) depending on the load direction.
Closer examination of the displacement results for the sliding faces (figure 913) shows that the sliding faces partially separate. />
Figure 9-13: Partial separation of the sliding faces (figure 9-12, left) Only a portion of face 1 contacts face 2. The mesh in the contact area is too coarse to allow for the analysis of contact stresses. While the mesh is adequate for the analysis of displacements, the mesh is not sufficiently refined for the analysis of the contact stresses that develop between the two sliding faces.
138
Engineering Analysis with COSMOSWorks
10: Analysis of contact stresses between two plates Topics covered u
Assembly analysis with surface contact conditions
a
Contact stress analysis
•
Avoiding rigid body modes
Project description We will perforin one more contact stress analysis. This analysis requires the Surface type of contact conditions. The model (figure 10-1), consists of two identical plates that touch each other on their curved outside surface. The material for both parts is Nylon 6/10 and has already been assigned to the part. Our objective is to find the distribution of von Mises stress and the maximum contact stresses that develop in the model under a 1,000 N of compressive load. Please open assembly file TWO PLATES. l.OOONloadin negative y direction Restraints in x and z directions
Surface contact condition between two cylindrical faces
Rigid support
Figure 10-1: Two plates with their cylindrical surfaces in contact Preparation of the model for analysis requires restraining the loaded part to prevent rigid body motion and, at the same time, make it free to move in the direction of the load. This can be accomplished by restraining the loaded face in both in-plane direction while leaving the normal direction (the direction in which load is applied) unrestrained (figure 10-2).
139
Finite Element Analysis with COSMOS Works
Figure 10-2: Restraint windows Restraints are conveniently applied to the loaded face using SolidWorks Top reference plane as a reference to determine restrained directions.
The restraints shown in figure 10-2 are required to prevent rigid body motion, because the analyzed contact is frictionless.
140
Engineering Analysis with COSMOSWorks
We are now ready to mesh the assembly model. Adequate mesh density in the contact area is of paramount importance in any contact stress analysis. It is the responsibility of the user to make sure that there are enough elements in the contact area to properly model the distribution of contact stresses. In this exercise we adjust global element size as shown in figure 10-3.
Mesh Parameters;
Coarse
•*•
'''
\
J$Ss£
Fine
'
»
Wsm
Figure 10-3: Assembly meshed with global element size 1.5mm
141
'"iH&U^
Finite Element Analysis with COSMOSWorks
A contact stress results plot complete with windows used to define it is shown in figure 10-4.
Mode! n&m? two cylinders Study nsme: surface contact Plot type: Static nodal siiess Ptot2
^ • . J}
lj
Display '>/'•
«,' Options
•*•
tit !™
•
TTfi!
f b 1CP; Contact ptessure P
N/mny : (MPs)
v
;C:
°
;
> Match coforchaH: .
(Mode values
}Ssnqte cob;-
Figure 10-4: Contact stress results for the coarse mesh presented using an exploded view. The maximum contact stress reported is 144 MPa The plot presents Contact pressure defined in Stress Plot window (left). Contact pressure plot uses Vector type of display which can be modified using Vector plot options window (middle).
142
Engineering Analysis with COSMOSWorks
Von Mises stresses are shown in figure 10-5.
Model name: t w o cylinders Stuffy name: surface contact Plot type: Static nodal stress Plot! Deformation scale: 1
von Mises (M'rt»ffi*2 (MPall ^ ^
1.441e+002 216*002
I
. 1 201e+002 1
"t82e+002
.9.6166+001 ?8e+001
I
" .195+001 i.021 e+001 . 4.822e+001
II: IF. :. ::
236+001
25e+001 H . 1.2286+001
:rfy
Figure 10-5: Von Mises stress results presented using exploded view We leave it to the reader to decide if this stress level is acceptable for Nylon 6/10 material which yield stress is 139 MPa. Before concluding this exercise, please further investigate the effects of mesh refinement and type of material (such as steel or aluminum) on contact stress. Note that our mesh is adequate for modeling contact stresses between two Nylon parts because low modulus of elasticity of Nylon makes the contact area quite large. The same mesh it may prove too coarse when analyzing more rigid materials.
143
Engineering Analysis with COSMOSWorks
11: Thermal stress analysis of a bi-metal beam Topics covered •
Thermal stress analysis
•
Use of various techniques in defining restraints
•
Shear stress analysis
Project description The temperature of the bi-metal beam, shown in figure 11-1, increases uniformly from the initial 298K to 600K. We need to find how much the beam will deform.
Procedure Please open the assembly file BIMETAL. Note that the assembly consists of two instances of the same parts. For this reason material can not be assigned to the SolidWorks part. We must assign it in COSMOSWorks to components of Solids folder.
\
\
L
Titanium Ti-10V-2Fe-3Al
\ Aluminum 1060
\
X
\N:
Figure 11-1: Hi-metal beam consisting of bonded titanium and aluminum strips. The bi-metal beam will deform when heated because of the different thermal expansion ratios of titanium and aluminum
145
Finite Element Analysis with COSMOSWorks
To account for thennal effects, we still define the study as Static, but in the Properties of this study, under Flow/Thermal Effects we select the option Include thermal effects (figure 11-2).
|T
£*) input temperature
I!
(,) Tempetaiutes horn therm-sf i^jd^
f;
ft
O Temperature from ftXtSMOSFIoV/otks
ft
SdidWoiks model name
11
Geflfigufatbri nsme
It
Tempetatuie from fee step:
11
:
Reference temperature at seto
tf'mr
:2S8
I i
D Include fluid pressure effectstornCOSMOSFIaW'oik
| ;: I i
Soi;d:-A'osksffindeiname Configuration rtsne
li
:
!
i
Ffow iteration na
i
w
:
; : :::::::-::
OK,
~-~—
i j
Cancel
——
1
fe;;:*;
|
*
Help
1
-
Figure 11-2: Static study window, where we request that thermal effects be included. This window is also used to define the reference temperature at zero strain; here: 298K Before proceeding, let's take this opportunity to review all thermal options available in the study window.
Definition
Thermal Option Input temperature
Use if prescribed temperatures will be defined in the Load/Restraint folder of the study to calculate thermal stresses. This is our case.
Temperature from thermal study
Use if temperature results are available from previously conducted thermal study.
Temperature from COSMOSFloWorks
Use if temperature results are available from previously conducted COSMOSFloWorks study
Now assign the material properties of titanium and aluminum to the assembly components as shown in figure 11-1.
146
Engineering Analysis with COSMOSWorks Restraints in this model will be applied in the least '"invasive'" manner, just enough to prevent rigid body modes while minimizing their interference with thermal expansion. Restraints are explained in figures 1 1-3 and I 1-4.
Figure 1 1-3: Restraint applied to cylindrical face of the hole in aluminum part. Only circumferential translations are restrained. This still leaves one unrestrained rigid bodv motion in v direction. Notice that restrain/ symbol size has been increased using Symbol settings. Model is shown in exploded view.
147
Finite Element Analysis with COSMOSWorks
J £) ;U5« reference georrie.v:
QJ|ll /
Top f*3 Show preyiew
Tr-arisiatforvE
bsfei— ®»
mm J rfirn
-
SymhoS swings
1 m&.
Edit
rota ^
| V
Figure 11-4: Restraint applied to one vertex in direction normal to Top reference plane to remove the rigid body motion in v direction. Notice that restraint symbol size has been increased using Symbol settings. Model is shown in exploded view. To apply temperature load right-click Load/Restraint folder and select Temperature to open Temperature window. From the fly-out menu select both assembly components and enter temperature 600K which means that assembly temperature will be increased by 302K from the initial 298K. Definition of temperature load is explained in figure 11-5. g bimetal \M Annotation; "*0
Design Bind
>~W: Lighting '<$> Front -<$>, lop
I
•'-<$; Right
I
!-* Otigin
^11 jsnoiv ptevs&w T*fiW30ii
Sr ax
Figure 11-5: Temperature 600K is applied to both assembly components which are most conveniently selected from the Solid Works fly-out menu.
148
Engineering Analysis with COSMOSWorks Mesh the model with default element size which creates the total of 4 layers of elements. Displacement results are shown in figure 11-6, von Mises stress results are shown in figure 11-7 URES (mm) ^ ^ 4.4948+000 ,4.121e+000 . 3.7476+000 .3.3748+000 _ 3.000e+000 . 2 8278+000 . 2.2548+000 .1 .SSOe+000 ,1,507e+000 .1,1346+000 .7.6018-001 . 3.887ft-001
H11.3346-002
Figure 11-6: Displacement results for the bi-metal beam Due to the different thermal expansion ratios of titanium and aluminum, thermal strains develop and deform the bimetal beam in a pattern that resembles bending.
149
Finite Element Analysis with COSMOSWorks
von Mises CN.'mm"2 (W'aY 3.0706+002
I
*1Se+002 502
5066+002 . 2.0S2e+002 ... 1,7976+002 +002 . 1.2886+002 . 1.034e+002 _7732e+001 :. J-'U'e+OOl
J ""
2.7028+001
1.5638+000
Figure 11-7: Von Mises stress results for the bi-metal beam Thermal stresses do not follow the stress pattern typical for bending. Aluminum and titanium components are bonded. Therefore, it may be interesting to review shear stresses on the boundary between these two parts. Considering assembly orientation in the global coordinate system, we need to display TZX shear stress (TZX is the stress component selectable in the Stress Plot window). Please refer to figure 11-8 for explanation of normal and shear stress directions (this figure is identical to figure 1-11).
Figure 11-8: Stress cube explaining convention used in defining directions of stress components. The stress cube is aligned with the global coordinate system.
150
Engineering Analysis with COSMOSWorks
Displaying shear stress in X direction on the bonded faces requires stress plot specifying TXZ or TZX.(these two shear stress components are equal due to symmetry of shear stress) as shown in figure 11-9.
i^j-Mj
TauKZ (t#nm A 2 (MPs)) ^9
n
TX2: Shear ifi 2 dc. m^
; Fringe
?••?:]
(*)Mode values Osisri^rt-vaiuss
xt\
Deformed Shape
Property
ff§3l|*
3.7178+001
III
\ .f-}/mm^£tMP3f
.' **":
HI®.. S.OOSe+OOl 8,300e+0Q1
11•i^t
.4.5926+001 »3e+001
^lliih, *•! m
•"mm lis
^%
GfodudetftN*fes$;
. -5.3388+000 -2.242e*001
*m
•*.
.1.1756*001
.-3.9518+001 598*001 308+001 • f t -8.0??e+00!
5
'-— name view orientation I l l -1.0798+002 S * ^ % X A-'-:T-::CO tesulte acres? • : ; b o u r . d 3 r / f q r parts : ;
Figure 11-9: Shear stresses TXZ Note that the stress plot for assembly offers the option of averaging stress residts across boundary of the parts. This is the default, and is not selected here.
The maximum shear stress is located at the free ends of the bimetal beam. This indicates that bonding failure (if any) will start in these locations.
151
Finite Element Analysis with COSMOS Works
NOTES:
152
Engineering Analysis with COSMOSWorks
12: Buckling analysis of an L-beam Topics covered a
Buckling analysis
•
Buckling load safety factor
a
Stress safety factor
Project description An L-shaped perforated beam is compressed with a 40,000 N load, as shown in figure 12-1. The material has already been assigned to the assembly components. Our goal is to calculate the factor of safety related to the yield stress and factor of safety related to buckling.
Procedure Open the assembly file L BEAM. The beam and endplates material is alloy steel with yield strength of 620 MPa.
Figure 13-1: L-beam geometry A perforated angle is compressed by a 40,000 N force uniformly distributed over the endplate.
153
Finite Element Analysis with COSMOSWorks
Before we run a buckling analysis, let's first obtain the results of a static analysis based on the load and restraint shown in figure 12-1. The results of static analysis show the maximum stress below the yield strength 640MPa. Figure 12-2 identifies the location of the highest stress.
Model name: i beam Study name: stress s PM type: Static no*. Deformation scale: 8. von Mis-es (»»n"2 (MPs)) 534
111490
jppy l^v*
/
26 7
ii
223 178
h
•gr
' "^
"*.>
Figure 12-2: Location of the maximum von Mises stress is close to the loaded endplate Plot displays the location of the maximum stress and uses floating format to display numerical values. Both are selected in Chart Options.
154
Engineering Analysis with COSMOSWorks
As is always the case with slender members under compressive load, the factor of safety related to material yield stress may not be sufficient to describe the structure's safety. This is because of a possibility of buckling occurring. We still need to calculate the safety factor for a buckling load and this requires running a buckling analysis. Figure 13-4 shows two studies: the already completed stress analysis (static analysis) and buckling analysis that we are now starting. Please copy loads and restraints from the stress analysis study to buckling analysis study.
figure 12-3: Definition of a buckling study (left) and the Buckling window, where properties are defined for a buckling study. Defining a buckling study requires specifying the number of desired buckling modes. Here we ask for only one buckling mode When defining a buckling study, we need to decide how many buckling modes should be calculated. This is a close analogy to the number of modes in a frequency analysis. In most practical cases, the first buckling mode determines the safety of the analyzed structure. Therefore, we limit this analysis to calculating the first buckling mode. Once the buckling analysis has been completed, COSMOSWorks automatically creates two Results folders: Displacement and Deformation. Even though displacement results are available, they do not provide much useful infomiation. In a buckling analysis, the magnitude of displacement results is meaningless, just like in frequency analysis. The deformation plots are much more informative (figure 12-4) and do not include confusing information on the magnitude of displacement.
155
Finite Element Analysis with COSMOSWorks
Modfrl riatrie: J ttesun
Sftotte S'hspe : 1 Load Fsotot - 0JS7116 Deformation se&e: 33.5o5
Figure 12-4: Deformation plot 77ze deformation plot provides visual information on the shape of the buckled structure. It also lists the buckling factor, here equal to 0.87. This plot shows the buckled shape along with the undeformed model. The buckling load factor, shown in the deformation plot, provides information on how many times the load magnitude would need to be increased in order for buckling to actually take place. In our case, the magnitude of load causing buckling is 0.87*40,000N = 34,800 N. Therefore, buckling will take place because the actual load is 40,000N. The buckling load factor can be also called the buckling load safety factor. Notice that the calculated buckling load safety factor is actually lower than the previously calculated safety factor related to material yield strength. This condition means that the beam will buckle before it develops stresses equal to the yield strength. Our conclusion is that buckling is the deciding mode of failure. Also notice that high stress affects the beam only locally, while buckling is global. It should be pointed out that the calculated value of the buckling load is nonconservative, meaning that it does not account for the always-present imperfections in model geometry, materials, loads, and supports. With this in mind, the real buckling load may be significantly lower than the calculated 34,800N.
156
Engineering Analysis with COSMOSWorks
13: Design optimization of a plate in bending Topics covered L)
Structural optimization analysis
O
Optimization goal
•
Optimization constraints
•
Design variables
Project description A rectangular plate is subjected to a 500 N bending load resisted by built-in support (figure 13-1). We suspect that the plate is over-designed and wish to find out if material can be saved by enlarging the diameter of the hole. Because of certain design considerations, the diameter cannot exceed 40 mm. Also, from previous experience with similar structures, we know that the highest von Mises stress should not exceed 500 MPa anywhere in the plate. Fixed support
s.
/ Bendine load 500 N
Fimirc 13-1: Rectangular plate with a round hole is bent by a 500 N load. The model is shown in its initial configuration, before optimization As with every design optimization problem, this one is defined by the optimization goal, design variables, and constraints. We explain these terms before proceeding.
157
Finite Element Analysis with COSMOSWorks
Term
Definition
Optimization goal
Our objective is to minimize the mass. Other examples of optimization goal are to maximize stiffness, maximize the first natural frequency, etc. The optimization goal is often called the optimization objective or optimization criterion.
Design variable
The entity that we wish to modify is a design variable. In this example, this is the hole diameter. The range for the diameter is from its initial 20mm to a maximum of 40mm. For simplicity, this exercise has only one design variable, but there is no limit on the number of design variables.
Constraints
Limits on the maximum deflection or the minimum natural frequency are examples of constraints. Constraints in optimization exercises are also called limits. In this exercise, the constraint is the maximum von Mises stress, which must not exceed 500 MPa.
Procedure Please open and review part file PLATE IN BENDING. It comes with defined material Alloy steel). Before starting the design optimization exercise that will result in changing the diameter of the hole, it is necessary to determine the stresses in the plate "as is", which requires running a static study. Static study is a prerequisite to the subsequent optimization study. Figure 13-2 shows the model's dimensions before optimization, and figure 13-3 shows the mesh created with the default element size. Notice that the mesh has two layers of second order elements across the member in bending, as is recommended for bending problems. Von Mises stress results are presented in figure 13-4.
158
Engineering Analysis with COSMOSWorks
Figure 13-2: Model dimensions before optimization
Figure 13-3: Mesh of the model before optimization
159
Finite Element Analysis with COSMOSWorks
von Mises [M*nm"2 (MPa)) ^ ^ 2.6930e+002
s'"
2.4691e+002 l i t 2.24516+002 . 2.0212e+002 . 1.7973e+002 . 1.57346+002 1.34946+002 . 1.1255e+002
fir
. 9.01576+001 . 6.7764e+001 53726+001 ?979e+001 I _ j 5.8608e-001
Figure 13-4: Von Mises stresses in the model before optimization Stress results (figure 13-4) show the maximum von Mises stress of 269 MPa at the edge of the hole. This is below the allowable 500MPa, so we can proceed with the optimization exercise by increasing the diameter of the hole. The optimization study is defined as any other study except that mesh type does not need to be defined since the optimization study must use the same type of mesh as the prerequisite static study (figure 13-5).
j optimisation
Optimization
Dstete
Active study rwvie; pie tequisite static
Figure 13-5: Optimization study and static study The optimization study called optimization, is defined after the static study called pre requisite static.
160
Engineering Analysis with COSMOSWorks
When the optimization study is defined, COSMOSWorks automatically creates three folders specific to an optimization study (figure 13-6): _l Objective •
Design Variables
•
Constraints
An optimization study requires that all these folders be defined. Design optimization is an iterative process. The maximum number of design cycles is defined in the Optimization window, which is opened by right-clicking the Optimization study, and from there, you can select the number of iterative cycles (figure 13-7).
i plate in bending -€•!» Parameters + ct* pre requisite static (~Def aulfc-) 5 f » optimization (-Default-) ;•—iff Objective f H Design Variables f3j Constraints .. .Report Fiuure 13-6: Design optimization study contains three automatically created folders: Objective. Design Variables, and Constraints.
161
Finite Element Analysis with COSMOS Works
Figure 13-7: Optimization window The maximum allowed number of design cycles in an optimization study is 20 by default. The optimization goal is defined in the Objective window. To open this window, right-click the Objective folder (figure 13-6). For this exercise, we accept the default optimization goal, which is to minimize the mass.
162
Engineering Analysis with COSMOSWorks
Mir./Max ; Responsei i;: B e c o m e
Available M>
! Volume I Ffequency ! Suckling
tnyefgene-e fcolessnc-e: I 1 Help
Figure 13-8: Optimization goal defined in the Objective window, as to minimize mass To define the design variable, first select the dimension, which will be modified by this design variable. You can display the dimensions by selecting Show Feature Dimensions in Annotations folder in the SolidWorks Manager. To define the design variable, right-click the Design Variable folder to open the Design Variable window, shown in figure 13-9. The allowed variation of the hole diameter is from 20 mm to 40 mm. Note that it may not be possible to reach the diameter of 40 mm if, during the process of increasing the diameter, the maximum stress exceeds 500 MPa.
163
Finite Element Analysis with COSMOSWorks
Design Variable
;
Units
initial Value : I o w a Bo... ; Upper E tt.dd.
• Mams:
iight@SkeJdi3#p!ate in bending,Part
• initial value:. 1
Update
Lower bound;
:20
\
1
X I
Cancel
*J|
He
•yy:yy^^yyyy^^^yyy-yy,y;y-^^-yyy!y,^^^yyyyyyyy;y^^-yyyy^
: Upper bound MO Convergence tolerance:: 1 OK
J of Range
Cancel
Help
Figure 13-9: Design Variable window The allowed range of the hole diameter is specified as from 20 mm (value before optimization) to 40 mm, which is the maximum allowed hole diameter. Finally, to define the constraints, right-click the Constraints folder to open the Constraint window, shown in figure 13-10.
Stud, i Study name
i Type
Component
iTVZ: Shear st?ess|Y-2 plane j | PI; Normal stiessj 1 si principal} j P2: Normal stress! 2nd principal) IP3; Norrrsai r-itessi 3idpfincipaH Help
Units.
N.'rwo 3n
: Lower bound:
16
i Upper bound:
|500
! Tolerance:
11
OK
[
M NAwh'*2(MP*) |
N/mm'~2|MPaJ
I XofBa-nge
Cancel
j
:
He
Figure 13-10: Constraint window The maximum allowed stress is defined as von Mises stress equal to 500 MPa. .
164
Engineering Analysis with COSMOSWorks Notice that loads, supports, and materials are not defined anywhere in the optimization study. The necessary information is transferred from the prerequisite static study defined in the Constraint window (figure 13-10). Having defined the optimization goal, design variable(s), and constraint(s), we are ready to run the optimization study. When the solution is complete, COSMOSWorks creates several result folders, which are shown in figure 1311. ^|p plate in bending ;--JH Parameters + d|f pre requisite static (-Default-) - f 9 optimization (-Default-) i"-fff Objective ;•- l f(| Design Variables ! U Constraints j y Report - | b : Design Cycle Result ^ j | Initial Design | f | Final Design ~ j b j Design History Graph
iWotl - j y Design Local Trend Graph
1111**1
Figure 13-11: COSMOSWorks results folders in Optimization study. The following folders are automatically created once design optimization completes: •
Design Cycle Result
•
Design History Graph
•
Design Local Trend Graph
To view the optimized model, double-click the Final Design icon in the Design Cycle Result folder. To view the original model for comparison, double-click the Initial Design icon in the Design Cycle Result folder (figure 13-11).
165
Finite Element Analysis with COSMOSWorks
Figure 13-12: Model after optimization In the optimized model, the diameter of the hole is 36.39 mm. If desired, we can display the model configuration in any step of the iterative design optimization process. To open the Design Cycle Result window rightclick the Design Cycle Result folder and select the desired iteration number (figure 13-13).
Figure 13-13: Design Cycle Result window To examine displacements or stresses in the optimized model, we need to review the plots in the prerequisite static study, the results of which have been updated to account for the new model geometry.
166
9
Engineering Analysis with COSMOSWorks Mode! name: piste in bending Study name: pre requisite static Plot type: Static riodai stress Plot! Deltsrmation scale 4.24821
,-A^ von ttfces (N/miri'<2 ( * a j ) ^ ^ S.003e<-002 » 5boe+002 .4 1698*002 . 3,7S2e+O02 .3.3368+002 2.319e*0Q2 !:;.#:. 25Q2e*002 . 2,085e+002 ie+002 i S " . 1,2S2e*002 8.3S2e+O0i ^.4.1846*001 U t
8528-001
—•Yield strength: 6.204e+002
Figure 13-14: Von Mises stresses in the optimized model Note that the maximum stress is 500.3 MPa. This value is within the requested 1% accuracy of stress constraint. The history of the optimization process can be reviewed by examining plots in the Design History Graph folder and in the Design Local Trend Graph folder. An example is shown in figure 13-15.
'• Convsrgencs Pk« of Design Vsriabfef 40 3020 ;
10+ 0 1
4
fi
Figure 13-15: Graph showing changes in the design variable during the iterative optimization process.
167
Engineering Analysis with COSMOSWorks
14: Static analysis of a bracket using p-elements Topics covered •
p-elements
Q p-Adaptive solution method •
Comparison between h-elements and p-elements
Project description A hollow cantilever bracket, shown in figure 14-1, is supported along the backside. A bending load of 10,000 N is uniformly distributed on the cylindrical face. We need to find the location and the magnitude of the maximum von Mises stress. Please open part file BRACKF.T. The part material is AIS1 304. Fixed support
v
Bending load 10.000 N
Figure 14-1: Hollow cantilever bracket under a bending load Due to the symmetry of the bracket geometry, loads, and supports, we could simplify the geometry further by cutting it in half, but decide against it because the work involved would not save time overall. Another reason for not simplifying the geometry is that you are encouraged to use the same geometry later to perform a frequency analysis which requires the full model geometry.
169
Engineering Analysis with COSMOSWorks
14: Static analysis of a bracket using p-elements Topics covered
Project
•
p-elements
•
p-Adaptive solution method
•
Comparison between h-elements and p-elements
description A hollow cantilever bracket, shown in figure 14-1, is supported along the backside. A bending load of 10,000 N is uniformly distributed on the cylindrical face. We need to find the location and the magnitude of the maximum von Mises stress. Please open part file BRACKET. The part material is A1S1 304.
!
Bending load 10,000 N
Figure 14-1: Hollow cantilever bracket under a bending load Due to the symmetry of the bracket geometry, loads, and supports, we could simplify the geometry further by cutting it in half, but decide against it because the work involved would not save time overall. Another reason for not simplifying the geometry is that you are encouraged to use the same geometry later to perform a frequency analysis which requires the full model geometry.
169
Finite Element Analysis with COSMOSWorks
The presented problem is a straightforward structural analysis and hardly seems to deserve a place towards the end of this book. However, we will use this problem to introduce a whole new concept in FEA; we will solve this problem using a different type of finite elements, called p-elements. Before we begin, we need to explain what p-elements are. If you recall, in chapter 1, we said that COSMOSWorks can use either first order element also called draft quality or second order element called high quality. We also said that first order elements should be avoided. Furthermore, recall that first order elements model a linear (or first order) displacement and constant stress distribution, while second order elements model a parabolic (second order) displacement and linear stress distribution. We now have to amend the above statements. Besides first and second order elements, COSMOSWorks can work with elements up to the 5th order. You can access these higher order elements, (called p-elements) if Use p-Adaptive for solution is selected in the Study window under the Adaptive tab (figure 14-2). This option is available only for static analysis using solid elements.
170
Engineering Analysis with COSMOSWorks
E J Use p-Adsplsve iot solution p-Adaptive options
Stop when; Total SliwEnetgy
1
%oitets
Update eferoents with relative $ii$m Energy error of \2
Zormoie
Starting p-order
-
Maximum potdet
5
; "*
Maxima no d loop:: 4
: ~
v
charge is
Z
Camel
Figure 14-2: Adaptive tab in the Static window The selection "Use p-Adaptive for solution " made in Adaptive tab in the Static window, activates the use ofp-Adaptive solution method. For the pAdaptive solution we use the settings as shown in this illustration. Referring to figure 14-2, the Starting p-order is set to 2, which means that all elements are first defined as second order elements. Risking some oversimplification we may say that the p-Adaptive solution runs in iterations, called loops, and with each new loop the order of elements is upgraded. The highest order available is the 5 n order. The highest order to be used is defined by Maximum p-order. The Maximum no. of loops is set to 4. Looping continues until the change in Total Strain Energy between the two consecutive iterations is less than 1%, as specified in the p-Adaptive options area. If this requirement is not satisfied, then looping will stop when the elements reach the 5" order; this will be 4th loop. Please investigate other available options in p-Adaptive options fields shown in figure 14-2. Elements used in p-Adaptive solutions do not have a fixed order, and can be upgraded "on the fly", that is, automatically during the iterative solution process without our intervention. These types of elements with upgradeable order are called p-elements. The p-Adaptive solution process is analogous to the iterative process of mesh refinement, which also continues until the change in the selected result is no longer significant. Let's pause for a moment and explain some terminology:
171
Finite Element Analysis with COSMOS Works Please refer to figure 2-14 which explains that h denotes the characteristic element size. This size is manipulated during the mesh refinement process. While the mesh is refined, the characteristic element size, h, becomes smaller. Therefore the mesh refinement process that we conducted in chapters 2 and 3 is called the h-convergence process, and the elements used in this process are called h-elements. Note that h-elements retain their order. Once created, they cannot be upgraded to a higher order. The iterative process that we are discussing now does not involve mesh refinement. While the mesh remains unchanged, the element order changes from the 2nd all the way to 5tn or less if the convergence criterion (here the change in Total Strain Energy) is satisfied sooner. The element order is defined by the order of polynomial functions that describe the displacement field in the element. Because the polynomial order experiences changes, the process is called p-convergence process, and the upgradeable elements used in this process are called p-elements. Adaptive means that not necessarily all p-elements need to be upgraded during the solution process. Indeed, as you can see in figure 14-2, in the pAdaptive options area, the field in Update elements with relative Strain Energy error of % or more is set to 2, meaning that only those elements not satisfying the above criterion will be upgraded (please investigate other criteria). We say, therefore, that element upgrading is "Adaptive", or driven by the results of consecutive iterations.
Procedure First solve the model using second order solid tetrahedral h-elcments. Use the default element size, but to better capture stresses, apply Mesh Control to both fillets (figure 14-3) while deselecting Automatic transition in the Options window under the Mesh tab. Automatic transition and Mesh Control are seldom combined in one mesh. The h-element mesh is shown in figure 14-4 and the von Miscs stress results in fleure 14-5.
172
Engineering Analysis with COSMOSWorks
ij
) Selected Entitles
Mesh Parameters;
f l ill 1111111:11 Coarse
'
Fine mm
lis
0,38668985
mm
O Show preview Control Parameters
iReset to default steel f~|Ruri analysis after —meshirig
Low
:
^
High
Options.,, «
3,3668935
|(rnm
v
% t.S
Figure 14-3: Mesh window (left) and Mesh Control window (right) used to create an h-element mesh The Mesh window (left) displays the Mesh Parameters. The Mesh Control window (right) displays the mesh controls, applied to both fillets.
173
Finite Element Analysis with COSMOSWorks
Figure 15-4: h-element mesh of second order solid elements
,.- : -
van Mises (NtamA2 (MPa)) 7.971 e+001 ™ _ 7,30?e+001
197.96+001 ;.315e+0D1 .8518+001 :.98?e+001
|P»;";';""T
llllpL.]
: .3228+001
308*001
—•YieW strength: 2,08fc+0D2
Figure 14-5: Von Mises stress results obtained using h-elements The maximum stress is 79.71 MPa. Now, create a new study identical the one we just finished, except that in the study window under the Adaptive tab, select Use p-Adaptive for solution. Please use all defaults for p-adaptive study definition as shown infigure14-2. Restraints and Loads can be copied from the previous study. Before meshing we make one observation. Considering that p-adaptive solution will be used, we can manage with a very coarse mesh. Please specify global element size 20mm, do not use Automatic Transition or Mesh Control. Mesh intended for analysis with p elements is shown in figure 14-6.
174
Engineering Analysis with COSMOSWorks
wS
/ ^ ""•-H"
<
v-
vi^
Figure 14-6: Mesh for use with p-Adaptive solution The mesh shown in figure 14-6 would not be acceptable for use with helements. There would not be enough elements to capture the complex stress field along the fillets. However, if we use higher order elements, which is equivalent to refinement of an h-element mesh, even this coarse mesh will deliver accurate results. Indeed, having solved the study with p-elements, we produce the stress plot shown in figure 14-7.
175
Finite Element Analysis with COSMOSWorks
von Mises (N/mm*2 (MPs))
mi
8.1358+901 ,4576+001 . 6.7806+001 .8.1028+001 . S .4246+001 . 4,7476+001
m
. 4 OS36+001 ;.3S2e*0Q1 .2.7146+001 >
•
li;.
. 2.03Se+001 1,3S9e*001 .813e*000
111,3.8916-002 Yield strength: 2.068e+002
Figure 14-7: Von Mises stress results obtained using p-elements The maximum stress is 81.35 MPa, very close to the 79.71 MPa obtained previously when using h-elements. Once the p-Adaptive solution is ready, we can display the stress result, as shown in figure 14-7. We can also access the history of the iterative solution. To do this, right-click the study folder to open a pop-up window (figure 14-8, left) where you can select Convergence Graph.... The Convergence Graph window opens, from where you can specify what information to display on the graph (figure 14-8, right).
176
Engineering Analysis with COSMOSWorks
Run
•
Run Design Scenar o £>:Dort.. Convergence Grap^.,.
•
•
.
,
:
.
< • • •
,
I
Dptkm
I
L J ^ Change t^ rjfobaj ciiteibn
1
f~l Toiaf sUa;n eteiqy
1
D Degiae; of fisedran (OOFi [ 3 Maximum iesjian* displacement
1
i^j Maximum von Mises stress
L™2L~J I
^vcoilpiow 55,TE-:r.:c-s
Cancel
JI
H»J>
i
Figure 14-8: Pop-up window used to define the Convergence Graph window To display the Convergence Graph window, right-click the p elements study icon, which opens a pop-up window (left). In the pop-up menu, select Convergence Graph.... The Convergence Graph window (right) appears, where you can select options for the convergence graph. We are interested in the accuracy of the maximum von Mises stress. Therefore, select the Maximum von Mises stress to be graphed throughout all performed iterations (figure 14-9).
177
Finite Element Analysis with COSMOSWorks
80000000+ _. 78000000
:-
:
:
-J/-"**-'
:
;
i
. ; > >r;
;
:
| 78000000 »g >
y
;
"
y
•
] -;y-
74000000
\
:
\
\
]
;
«<*• •{•*< • •-> - - •;
72000000 — • • > ^ > - - ; y
:
•
'
,
'
,
'
• •':
••••-! •
'
,
'
.
.
70000000*—-*——* ' •'•'• ' -••'' " ••' • — ~ < 1.00 1.40 1.80 2.20 2.60 3.00
Figure 14-9: Graph showing maximum von Mises stress calculated in each loop of a v-Adaptive solution process This graph also shows that four iterations were required to converge within 1% of Total Strain Energy as specified in figure 14-2. The shape of the curve (convex) indicates that convergence is taking place. Note that while the convergence process was controlled by Total Strain Energy, the graph in figure 14-9 shows the convergence of the maximum von Mises stress. Which solution method is better: the "regular" method using h-elements or the p-Adaptive solution method presented in this chapter? Experience indicates that second order h-elements offer the best combination of accuracy and computational simplicity. For this reason, the automesher in is tuned to meet the requirements of an h-element mesh. The p-Adaptive solution method is much more computationally demanding and significantly more timeconsuming. Therefore, the p-Adaptive solution method is reserved for special cases where, the solution accuracy must be known explicitly. The p-Adaptive solution is also a great learning tool, leading to better understanding of element order, the convergence process, and discretization error. For this reason, readers are encouraged to repeat some of previous exercises using p-Adaptive solution method.
178
Engineering Analysis with COSMOSWorks
15: Design sensitivity analysis Topics covered •
Design sensitivity analysis using Design Scenario
Project description A beam is loaded with 1,000N uniformly distributed load (500N to each split face) and supported by two pins placed in lugs which are initially spaced out at 200mm (figure 15-1) We wish to investigate the beam deflection at locations 1 and 2 (figure 15-1) while the distance between the lugs changes from 60mm to 340mm (figure 15-2). Please open part file BEAM WITH LUGS. The model has material 1060 Alloy already assigned. The pins themselves are not modeled; instead the pin support is modeled by restraints applied to cylindrical faces of both lugs as shown in figure 15-3.
500N 500N
1 Hinge support " "" -^..._ / Hinge support ——^ --4
Figure 15-1; Beam with lugs in the initial configuration The numbered vertexes on the beam are where we need to determine deflection, white the position of the lugs is changed, as shown in figure 15-2.
179
Finite Element Analysis with COSMOSWorks
Er—•>
7"~-~~...
crt>'
V'j
\0 1
Figure 15-2: Model shown in the two extreme configurations The distance between two lugs is controlled by the dimension in Sketch2 in the SolidWorks model.
Type i On cylindrical face »';;••:•••;-•—•
-:—•:/
\ " ~ g
! t
liSl'i
Q Show preview Iran sistions jrnm
<* i V :::•
:i
\
§1
i mm
&..
Ill
! mm | ~<,,~~,~~.~~~™™-^
Figure 15-3: The presence of pins, which provide hinge support for the lugs, is modeled by using the On cylindrical face restraint type. Onlv circumferential translations are allowed on cylindrical faces of both lugs.
180
Engineering Analysis with COSMOSWorks
Procedure If we proceeded by changing the distance from 60 mm to 340 mm in 40-mm intervals, this would require running 8 analyses and a rather tedious compiling of all results. COSMOSWorks offers an easier way to accomplish our objective by implementing Design Scenario. Using Design Scenario, the distance defining the position of the hole is defined as a Parameter, and is automatically changed in desired intervals. This allows for an easy analysis of all configurations in one automated step. The results of the design scenario can then be plotted using COSMOSWorks tools. A Design Scenario is often called a sensitivity study as it investigates the sensitivity of the selected system responses (here beam deflections) to changes in certain parameters defining the model (here the distance between two lugs). Define loads and restraints as always.
> >
«% plate with lugs i * | Parameters - C^5 log distance (~f>efauit~) S %Sofcfc •••••?% plate two lugs (-[SW]1060 Alloy-) S - 4 J toad/Restraint ^
Restraint-1
J L Force-1 ! f p Design Scenario [....«% Mesh j y Report + jbj Stress * Ebj Displacement * &i Strain + fiji Deformation * &j Design Check * Ey Design Scenario Results
Figure 15-4: Parameters and Design Scenario folders Parameters and Design Scenario folders are created automatically but are used only when a Design Scenario is run. Notice that the Parameters folder is created before any study is defined. Right-click the Parameters folder and select Edit/Define... to open the Parameters window (figure 15-5 top). In the Parameters window, select Add, which opens the Add Parameters window (figure 15-5, bottom). In the Filter option, select Model dimensions. We want to select the dimension that will be undergoing changes. Doing this requires that the model dimensions are visible. The easiest way to display the dimensions is to right-click the Annotations folder in the SolidWorks Manager window. This opens the associated pop-up menu from which we select Show Feature Dimensions. With dimensions showing we can select the desired dimension.
181
Finite Element Analysis with COSMOSWorks
Naifie TypB lugs_cL. length/Di.
Ursft mm
; User defined va... "200""
: Cutrenf. value ; Express.., : Comment! 200 " D5@Ste.„
Name:
Comment (optional): Fite; Type: User defined value:
Model dimension: Cancel
Help
Figure 15-5: Parameters window (top) and Edit Parameter window (bottom) In this exercise, lug_distance is the parameter defining the distance between two lugs Having defined the parameter, we can now define the Design Scenario. Right-click the Design Scenario folder to open a pop-up menu and select Edit/define. Since we wish to change the distance between the lugs from 60 mm to 340 mm in 40-mm intervals, the number of scenarios is 8. Because more than one parameter can be defined in the Define Scenarios tab. the parameter must be checked as active (figure 15-6).
182
Engineering Analysis with COSMOSWorks
eftm Scenarios s Rest* Locations \ M i n e design scenario •to. of scenarios: j g
:i:i^:
Parameters i Unit* Eliugs_
i User Defined 200
Se'l
S?j
60
100
11
I
•Run o p t i o n s — " © All scenarios © One scenario 03 Stop and prompt with error messages when a scenario fails.
Figure 15-6: Define Scenarios tab in the Design Scenario window. Each one of 8 scenarios is distinguished by the particular value of the distance between the lugs characterized by parameter lugjdistance. The name and lug distance, which appears at the top of this window, is the study name. To complete the definition of the Design Scenario, we need to inform COSMOSWorks what needs to be reported in these 8 steps. Select the Result Locations tab in the Design Scenario window (figure 15-6) to access the screen shown in figure 15-7.
183
Finite Element Analysis with COSMOSWorks
Define Scenarios
Result Locations
Define resit!; locatem Choose, up to 25 vertices for response graph. Selected tecafertR
lilllillllSllll
)elete all locations and clear summary
OK
Cancel
j
Help
Figure 15-7: Result Locations tab in the Design Scenario window. As the parameter is modified by the Design Scenario, results for selected locations are recorded. The location must be a vertex. If desired, defined locations can be renamed by right-clicking the item and selecting Rename from the associated pop-up menu. Here Vertex and Vertex <2> correspond to pints 1 and 2 in figure 15-1. Since only vertexes are allowed as locations in the design scenario definition, it is now clear why split lines were added to the examined model geometry. To run the design scenario, right-click the study folder, open the associated pop-up menu and select Run Design Scenario. Meshing is not required prior to executing the Design Scenario. Once the run completes, COSMOSWorks creates a Design Scenario Results folder, in addition to the other result folders. Notice that results stored in all the other result folders pertain to the geometry from the last step performed in the Design Scenario. The graphs summarizing the results of all configurations analyzed in Design Scenario are defined by right-clicking the Design Scenario Results folder. This opens the associated pop-up menu, from which select Define Graph. Figure 15-8 presents the Graph window and the corresponding graph showing displacements in locations 1 and 2. Figure 15-9 shows the Graph window and the corresponding graph with maximum global displacement.
184
Engineering Analysis with COSMOSWorks
Frie
Oatms
rtcb
S i u d y n a m e : luq d i s t a n c e
hVe.
: Single ResyHor Muibie Uc
M
100
HO
!80
220
Vertex l >
260
J00
;40
Vertex 2 >
•(.•mm. 033671
Figure 15-8: Graph definition window and corresponding graph showing displacement in the locations 1 and 2 shown in figure 15-1.
I I
i
>
ti
>
( !
<
<,,>
:
i
3tap!'f.":'::Sfi3pf»T
£ 0.8
^vafebte location^'
Gtaph L o c a t e :
1
0.8 •
I :
; Vertex-; 2 >
1 „:; 60
108
140
ISP
220
260
300
3*
Figure 15-9: Graph definition window and corresponding graph showing global maximum displacement in the model. Note that the minimum displacement occurs for lug distance close to 220mm. The parameter increment would have to be further refined to determine this minimum value more precisely. You are encouraged to investigate the other options in the 2D Chart Control Properties window. The options offer ample opportunities to manipulate graph display (figure 15-10).
185
Finite Element Analysis with COSMOSWorks
'-:X
Ill Legend
ChartArea
ConUol
Ayes
PloWrea ChsrtGroups
>>\<$S •-" ChartStvtes
AlarmZones Tiles
Genera! | Border ] Interior J About J
D Instated 0
OK
l*DoutoteBttffered
Cancel
Help
Figure 15-10: 2D Chart Control Properties window The graph options allow customized graph display. You may wish to use the same model to run Design Scenario in frequency analysis to find the distance between lugs that maximizes the first natural frequency.
186
Engineering Analysis with COSMOSWorks
16: Drop test of a coffee mug Topics covered
Project
•
Drop test analysis
a
Stress wave propagation
a
Direct time integration solution
description A porcelain mug is dropped from the height of 200mm and lands flat on a horizontal, flat rigid floor (figure 16-1). We will simulate the impact using COSMOSWorks Drop Test analysis.
'"•••m
Figure 16-1: Mutx landing square on a rigid floor
Procedure Please open the part file called MUG. It has ceramic porcelain material properties already assigned. Examine the SolidWorks model and notice the split lines added to mug geometry and move into COSMOSWorks. Create study Drop 200 ms specifying Drop Test as analysis type and Solid mesh as mesh type (only solid mesh is available in Drop Test analysis). COSMOSWorks creates two folders in Drop Test study: Setup and Results Option (figure 16-2), which are used to define the analvsis.
187
Finite Element Analysis with COSMOSWorks
: | K Parameters i '^ drop 200 ms (-Crefautt-) - ^Solids ^ coffee mug (-[SW]Ceramie Porcelain-) h | j Setup U-^ 1 Result Options Figure 16-2: .Sefap and Result Options folders in Drop Test study.
Right-click Setup folder and select Define/Edit to open Drop Test Setup window shown in figure 16-3.
Spsci © P r o p height 0 Velocity at impact HeioN;
*
O From cen&oid -•• ••;'.'' (*? From fewest point
tt -00
S; ;
Gravity _
Target Orierttatiofs ^ 1 Normal togr-svity O P * * I to Ref, Plans
Figure 16-3: Drop Test Setup window
Select Drop height and From the lowest point and enter 200mm as the drop height. From the fly-out SolidWorks menu (not shown in figure 16-3), select Top Plane to define the line of action of the gravitational acceleration. Adjust the direction as shown in figure 16-3. Enter the magnitude of gravitational acceleration as 9.81m/s2. Finally, select Normal to gravity as Target Orientation. After completing the exercise, please experiment with different Target Orientation using Parallel to Ref. Plane option in Drop Test Setup window.
188
Engineering Analysis with COSMOSWorks Having defined all required entries in Drop Test Setup window, we now define the results options. Right-click Result Options folder and select Define/Edit to open Result Options window (figure 16-4).
'•*»*>?
~'Hik**r
';'~**^
Sdufcion time after impact ¥) \ 200
•*
| mictosec
Save Results
Figure 16-4: Result Options window A section view is usedfor a more convenient display of vertices locations. Vertices are defined by split lines. To monitor what happens to the mug during the first 200 microseconds after first impact, enter 200 as Solution time after impact. This overwrites the default solution time based on the time that it takes for the elastic wave to travel through the model. Because the impact time is very short, it is measured in microseconds. The maximum deformation or stress may occur during the first impact or later when the model is rebounding. Sufficiently long solution time needs to be specified to analyze multiple rebounds. While there is no limit on Solution time after impact, a longer solution time requires a longer time to run the analysis. If a solution is going to take more than 60 minutes a message shown in figure 16-5 is displayed.
189
Finite Element Analysis with COSMOSWorks
ilSIIIlEi ^ W f l ^ f l ^ l l l l Estimated executiort time 03: 13:15 Woufcf you ike to change the solution time and rerun the analysis?
Yes
J
Figure 16-5: Long analysis time must be acknowledged before proceeding with Drop Test study solution.
In Save Results area of Result Options window, accept the default 0 (microseconds) meaning that results will be saved immediately after the first impact. Also, accept the default 25 for the No. of plots. The solution time is divided into twenty five intervals and full results (available as plots) are saved only for those intervals. In the vertices field of Result Options window, select the two vertices shown in figure 16-4. Results for these two vertices will be available in time history plots. Note that full results are saved for 25 plots spaced out evenly over a 200 microseconds time period. Results pertaining to time points "in-between" plots are saved only for selected points (here two vertices). In the last entry in the Results Options window we define how many of these partial results are saved. This is done in No. of graph steps per plot field. If we accept the default 20 results then the total number of data points for each graph (displacement, stress etc.) is equal to the number of plots times the number of graph steps per plot. Note that the number of graph steps per plot is not equal to the number of actual time steps. Time steps are selected internally by the solver and may vary as required for the stability of the numerical solution. Accepting the default 20 as the No. of graph steps per plot completes Results Options window definition. The Drop Test study is ready to run. Upon completion of solution, COSMOSWorks creates the following result folders: Stress, Displacement, Strain, Deformation and Response. Right-click the Response folder and select Edit Definition to open the Time History Graph window (figure 16-6).
190
Engineering Analysis with COSMOSWorks
Response i Predefined locations
X axis: Time (microsec) Y- Axis i (*) Stress
1
O Displacement
I
lk
Pi: 1st principal stres v | j
U
N/mmA2 (MPa)
Figure 16-6: lime History Graph window Select Vertex I and Vertex 2 in Predefined Locations, then select 1st principal stress in MPa to be plotted. This creates plots of the first principal stress in these two locations as a function of time (figure 16-7).
191
Finite Element Analysis with COSMOS Works
j
-5OOOQO0O1
-:
.'
;
:
40.31
80.23
120.15
160.0?
:._ 139.39
233.31
Time (ffiictosec;
Figure 16-7: Time History Graph window showing von Mises stress as function of time. Also shown are 2D Chart Control Properties. The Time History Graph has been modified using selections under ChartStyle/LineStyle (line color and thickness) and ChartStyle/SymholStyle (removal of symbols). Please explore other possibilities available in this window.
Based on the review of Time History Graph we find that the highest von Mises stress occur at time of 44 microseconds (move cursor over the plot to find this time value). Please create a von Mises stress plot approximately corresponding to this time point. Right-click the Stress folder to open the Stress Plot window. In the Stress Plot window select the time step that is closest to 44 microseconds (this is step 6). Stress results are shown in figure 16-8.
192
Engineering Analysis with COSMOSWorks
..*.'
Ms?
Mode! name: mug Stgtfy name: diop 200 ms Rot type: Piotl Plot step: S tiras: 4? .9908 Microseconds Detormstion scale: 238,38© .*~SSP*K3^^*-^ ""
%
\PU 1st principal stres .vj\ f*i rf»i : < f > d j
'
^
P1 (NjhimA2 (tvlpa)) 1 .?i::e+002 1.541e+002 1.3?1 e+002
;>#••;
J .2008+002 1,0298+002 8,5378+001 O'Hfe^snt values
6.8808*001 5J73e+fl01
f%
47.9908fflffcosee
El
DePwnied Shape .
3.4S7S+001 1 ,?60e+001 S .3226-001
„*
(*>AutoroaUc;
-1.6548*001
fin •
-3,3808*001
O Defined;
:fe[s?;4?ii
Figure 16-8: Maximum principle stress results for time step 6 corresponding to 48 microseconds. Maximum principle stress is used because is better characterizes brittle ceramic porcelain material .
Will the mug Break? Drop Test analysis does not directly provide pass/fail results. It is best used to compare the severity of impact for different drop scenarios. For example, comparing the ultimate strength of ceramic porcelain (172MPa) with the maximum principal stress stresses with (171MPa) indicates that damage to the mug case is very likely especially that mug will never land perfectly flat on the floor. To see the mug bouncing off the floor and stress wave propagating in the model, please animate stress plot. Also, repeat the study using a longer solution time. If a long enough solution time is used for the analysis you will see the mug bouncing off the floor and hitting it in different locations. The Drop Test is an analysis intended to model the dynamic impact force of a very short durations; this is where damage is most likely to occur. Drop Test analysis takes into consideration inertial effects but no damping. Drop Test analysis uses a numerically intensive but stable direct time integration method.
193
Engineering Analysis with COSMOSWorks
17: Miscellaneous topics Topics covered a • a • • • a • • a a • a
Selecting the automesher Solvers and solvers options Displaying mesh in result plots Automatic reports E drawings Non uniform loads Bearing load Frequency analysis with pre-stress Large deformation analysis Shrink fit analysis Rigid connector Pin connector Bolt connector
The analysis capabilities of COSMOSWorks go far beyond those we have discussed so far. Readers are now sufficiently familiarized with this software to explore options and topics we have not covered. To aid this effort, in this chapter we provide a variety of topics that have not yet been addressed in previous exercises along with a sample of less frequently used, but useful and interesting modeling techniques and types of analyses. Selecting the automesher You can select the Standard or Alternate automesher in the Preferences window under the Mesh tab (figure 2-15). The Standard automesher is the preferred choice. It uses the Voronoi-Delaunay meshing technique and is faster than the alternate automesher. The Alternate automesher uses the Advancing Front meshing technique and should be used only when the Standard automesher fails, even when you try various element sizes. The Alternate mesher ignores mesh control and automatic transition settings.
195
Finite Element Analysis with COSMOS Works
Mesh quality The ideal shape of a tetrahedral element is a regular tetrahedron. The aspect ratio of a regular tetrahedron is assumed as 1. Analogously, an equilateral triangle is the ideal shape for a shell element. The further the shape departs from its ideal shape, the higher the aspect ratio becomes (figure 17-1). Too high of an aspect ratio causes element degeneration and negatively affects the quality of the results provided by this element.
Figure 17-1: Tetrahedral element shapes A tetrahedral element in the ideal shape (top) has as aspect ration of 1. "Spiky" and "flat" elements shown in this illustration (bottom) have excessively high aspect ratios. The aspect ratio of a perfect tetrahedral element is used as the basis for calculating the aspect ratios of other elements. While the automesher tries to create elements with aspect ratios close to 1, the nature of geometry makes it sometimes impossible to avoid high aspect ratios (figure 17-2).
196
Engineering Analysis with COSMOSWorks
Figure 17-2: Mesh of an elliptical fillet Meshing an elliptical fillet creates highly distorted elements near the tangent edges. A failure diagnostic can be used to spot problem areas if meshing fails. To run a failure diagnostic, right-click the Mesh icon, which opens the associated pop-up window, and select Failure Diagnostic .... It is important to note that meshing difficult geometries may sometimes result in degenerated elements without any warning. If mesh degeneration is only local, then we can simply not look at results (especially the stress results) produced by those degenerated elements. If degeneration affects large portions of the mesh, then even global results cannot be trusted. Solvers and solvers options In finite element analysis, a problem is represented by a set of algebraic equations that must be solved simultaneously. There are two classes of solution methods: direct and iterative. Direct methods solve the equations using exact numerical techniques, while iterative methods solve the equations using approximate techniques. With the iterative method, a solution is assumed with each iteration and the associated errors are evaluated. The iterations continue until the errors become acceptable. Three solvers in combination with three solver options are available in COSMOSWorks (figure 17-3), but not all solvers are available for all types of
197
Finite Element Analysis with COSMOSWorks analyses and not all options are active with each solver. The fastest solver for most types of analyses is FFEPlus.
I
OK
M
Cancel
Help
Figure 1 7-3: Solver and Solver options available in COSMOSWorks.
198
Engineering Analysis with COSMOSWorks
COSMOSWorks offers the following choices: •
Direct Sparse solver
•
FFE (iterative)
•
FFEPlus (iterative)
In general, all solvers give comparable results if the required options are supported. While all solvers are efficient for small problems (25,000 DOFs or less), there can be big differences in performance (speed and memory usage) in solving larger problems. I f a solver requires more memory than available on the computer, then the solver uses disk space to store and retrieve temporary data. When this situation occurs, you get a message saying that the solution is going out of core and the solution progress slows down. If the amount of data to be written to the disk is very large, the solution progress can be very slow. The following factors help you choose the proper solver: Size of the problem. In general, FFEPlus is faster in solving problems with degrees of freedom over 100,000. It becomes more efficient as the problem gets larger. Computer resources. The direct sparse solver in particular becomes faster with more memory available on your computer. Analysis options. For example, the in-plane effect, soft spring, and inertial relief options are not available if you choose the FFE solver. Klement type. For example, contact problems and thick shell formulation are not supported by the FFE solver. In such cases, the program switches automatically to FFEPlus or the Direct Sparse solver. Material properties. When the moduli of elasticity of the materials used in a model are very different (like Steel and Nylon), then iterative solvers are less accurate than direct methods. The direct solver is recommended in such cases.
199
Finite Element Analysis with COSMOSWorks
Three solver options are available:
Option Use in plane effect
Purpose In a static analysis, use this option to account for changes in structural stiffness due to the effect of stress stiffening (when stresses are predominantly tensile) or stress softening (when stresses are predominantly compressive). In a frequency analysis, use this option to run a pre-stress frequency analysis
Use soft springs to stabilize the model
Use this option primarily to locate problems with restraints that result in rigid body motion. If the solver runs without this option selected and reports that the model is insufficiently constrained (an error message appears), the problem can be re-run with this option selected (checked). Insufficient restraints can then be detected by animating the displacement results. An alternative to using this option is to run a frequency analysis, identify the modes with zero frequency (these correspond to rigid body modes), and animate them to determine in which direction the model is insufficiently constrained.
Inertial relief
Use this option if a model is loaded with a balanced load, but no restraints. Because of numerical inaccuracies, the balanced load will report a non-zero resultant. This option can then be used to restore model equilibrium.
Several options are available in an assembly analysis when solving contact problems, i.e., when Contact/Gaps conditions are defined as Node to Node, Surface, or Shrink Fit. Those options are defined in the study properties, as shown in figure 17-3.
200
Engineering Analysis with COSMOSWorks
The three options are described as follows:
Option
Purpose
Include friction
If selected (checked), friction between contacted surfaces is considered.
Ignore clearance for surface contact
Use this option to ignore the initial clearance that may exist between surfaces in contact. The contacting surfaces start interacting immediately without first canceling out the gap.
Large displacement contact
Use this option if contacting surfaces need significant displacement before contact is made. "Significant" means that linear or angular displacements are significant in comparison with the size of the contacting surfaces. When in doubt, use this option, but note that it is quite computationally intensive.
Displaying mesh in result plots The default brightness of Ambient light, defined in SolidWorks Manager in the Lighting folder, is usually too dark to display mesh, especially a highdensity mesh. A readable display of mesh (figure 17-4) requires increasing the brightness of Ambient light.
I'igure 1 7-4: Mesh display in default Ambient light (left) and adjusted Ambient light (right) A finite element mesh is displayed with ambient light brightness suitable for a CAD model (left), and with the brightness adjusted for the displaying mesh (right).
201
Finite Element Analysis with COSMOSWorks
Automatic reports COSMOSWorks provides automated report creation. After a solution completes, right-click the Report folder (figure 17-5) and open the Report window (figure 17-6).
•% bracket xll Parameters S C^ h elements (-Default-) B ^ J i Solids ^hollow bracket (-[SWjAISI 304-) - | J Load/Restraint g4- Restraint-1 J:. Force-1 |§§ Design Scenario it ^jpMesh '+: i|hj Report + ifej Stress -t jj|jj Displacement ft §B s t r d i n ft St) Deformation ft [&) Design Check t JS|* P elements (-Default-)
Figure 1 7-5: Report folder A Report folder may contain several reports. A report can be created only after analysis has been completed.
202
Engineering Analysis with COSMOSWorks
'3i?5i«g8 for
^Cover Page v> Introduction iil/jDesofiption V.FteintormaiJCrt ^Materials y l o a d'ty.Restraint information hglStudy Property y Stress Results jylSttain Results jVjDispiaeeroent Results • Deformation Results ViOesign Check Results Design Scenario Results ^Conclusion ^Appends
; Report trie name
Cover Page Logo File:
C:\logos\DG logo.pg
|
Brows*
|
Title:
SUess an-ai^sis of bracked
\
Author.
PaufM Kusowski
\
Company:
Design Generator Inc.
^
Date:
MstchlO 2005
bracke!-h elements-1.htm
M Show report on OK
O Automatically update all plots in JPEG files
OK
Cancel
I
Q Print version
LiifiL*.
Figure 17-6: Report window Right-click the Report folder to open this window and specify desired report components. The report contains all plots from the result folders that were selected (checked) in the Report window (figure 17-6) along with information on mesh, loads, restraints, etc. E drawings Each results plot can be saved in various graphic formats, as well as in SolidWorks eDrawing format. The eDrawing fonnat offers a very convenient way of communicating results of an analysis to users who do not have COSMOSWorks. Non-uniform loads Although all the examples to this point have used uniformly distributed force or pressure, loads with non-uniform distribution can be easily defined. We will illustrate this with an example of hydrostatic pressure acting on the walls of a 1.95-m deep tank, presented in the SolidWorks part file called NON UNIFORM LOAD. Note that the model uses meters for the unit of length. The pressure magnitude expressed in [N/m2] follows the equation p = 10,000A:, with x being the distance from the top of tank (where the coordinate system csl is located).
Engineering Analysis with COSMOSWorks
The pressure definition requires selecting the coordinate system and the face where pressure is to be applied. The formula governing pressure distribution can then be entered in, as shown in figure 17-8.
Pressure Type ,«-.s Normal to selected fsce
KJ
I) Use reference
c (5J Show previe Pressure Vaiue
UliV 1
i
hi/m
[vj Nonuniform Distribute) * • i '
H csl
Reference coordinate system
Equation coefficients
1
+
I 1000 lm
100,000 Pa
Figure 17-7: A water tank loaded with hydrostatic pressure requires linearly distributed pressure This illustration uses a section view. Note that the vector lengths correspond to pressure magnitudes that vary with x coordinates ofcsl coordinate system.
204
Engineering Analysis with COSMOSWorks
Bearing load A bearing load can be used to approximate contact pressure applied to a cylindrical face without modeling a contact problem. As seen in figure 17-8, the size of contact must be assumed (guessed) as indicated by the split face. This definition requires a coordinate system on which the z-axis is aligned with the axis of the cylindrical face. See the part file BEARING LOAD for details.
Figure 1 7-8: 10.000 N resultant force applied as bearing load to a split face The pressure distribution follows the sine function.
205
Finite Element Analysis with COSMOSWorks
Frequency analysis with pre-stress A frequency analysis of rotating machinery most often must account for stress stiffening. Stress stiffenmg is the increase in structural stiffness due to tensile loads. We will illustrate this concept with the example of a helicopter blade. Please refer to part file ROTOR which comes with assigned material properties and two defined COSMOSWorks studies: no preload and preload. In order to account for pre-load in a frequency analysis, the option Use in plane effect has been selected in the Frequency window ofpreload study (figure 17-9).
^™
; Options Fisma*
1i
;j£j Number of ffeque
\i:
IHette
<£*DHecf:2p3fse j
gjUseinpbnssfcst Q u a e soil spmg to iabifes fwtieS ...;.;;.
OH : OWPte
l_£E„ 11
>-..*
|
Hsip
|;:
Figure 17-9: Frequency window in no preload study (left) and preload study (right) When the" Use in-plane effects " option is selected, Direct sparse is the only solver supporting this option.
206
Engineering Analysis with COSMOSWorks
Centrifugal load has been defined as shown in figure 17-10. An axis or a cylindrical face is required as a reference to define centrifugal load. Please review the restraint, which is the same in both studies.
W J
Mt J
a
Selected Reference;
. @ Show preview CerArffugal force;
|
rP„,
i
I
fk 0
fpm rpm'"-2
Symbol setting
j h
111 1
Edit c o b - , .
tfl i
Figure 17-10: Centrifugal load window with centrifugal force defined. Centrifugal force is applied to the model, simulating rotation about the axis of the cylindrical face. Notice that units are in RPM and that angular acceleration can also be defined if desired.
207
Finite Element Analysis with COSMOSWorks Solve both studies and compare frequency results (figure 17-11) of without and with pre-stress effect.
8tud>> name: no preload • Mode No. : Frequenoi.'|Ra
2 3 4 5
Ffequencji{Hertz|
Periodf Seconds
1.5391
0.64974
9.6745 3.6755 47.45 47.544
1.5331
0.64372
1.5333
0.64365
7.5489
0.13247
Help
Close
|
i
3.S742
Siuctji name: p-feioad Modefte. :: FrecwenciifRad'sdcV
Fnsquency(Hert.a)
PeiiodfSeconds;
23.457
3.7317
0.26737
23.458
3.7313
0.26736
23.459
3.7322
0.26794
52.121
8.2919
0.1206
52.215
8.3083
0.12038
Save
Help
Figure 17-11: List Modes windows in study without preload (top) and with preload (bottom) Note that modes number 1, 2 and 3 refer to the same physical mode but due to discretization error, the solver assigns slightly different frequencies to each blade. The same applies to modes number 4, 5, 6 and higher. As shown in figure 17-11, the presence of preload very significantly increases the frequency of vibration. In the first mode the frequency increases by 240% and in the second mode by 10%.
208
Engineering Analysis with COSMOSWorks The opposite effect would be observed if, hypothetically, the rotor blades were subjected to compressive load. For more practice, try conducting a frequency analysis of a beam under a compressive load. The higher the compressive load, the lower will be the first natural frequency. The magnitude of the compressive load that causes the first natural frequency to drop to 0 (zero) is the buckling load. This is where frequency and buckling analyses meet! Large deformation analysis If two surfaces, defined in contact pair, experience large displacement before contacting each other, then the Large displacement option must be selected in the properties window of the Static study (17-12).
igrote clearance So! surface contact
Large Jispiecemen'
> Direct spas*
r] Use inplane effect
FFE
Q Use soft spring to standee model
FFFPtus
[^] Use inertia! relief
j
OK
j :
Cancel
i
[
Help
Figure 17-12: Large displacement option checked in Static analysis window.
We need to explain when the displacement should be classified as "large". While there is no set rule, visible relative rotations or translations may have to be considered as large. To illustrate non-linear contact, we examine the analysis of the assembly of CLIP (figure 17-13). Notice that even though the clip is just one part, we had to split it into two parts and make an assembly because the contacting faces must belong to different parts. Global Contact/Gaps conditions are left at the default setting: Touching faces: Bonded. Local Contact/gaps conditions between two surfaces likely to come in contact are defined as: Surface.
209
Finite Element Analysis with COSMOSWorks
Load 100N
Only this small face is assumed to" be able to come in contact with the corresponding small face on the other arm of the clip Figure 17-13: The Clip is modeled as an assembly because contacting faces must belong to different parts Split lines in the SolidWorks model define small faces in contact. The smaller size of the contacting faces speeds up the solution time. Please review the CLIP assembly for details of loads and restraints definition. Note two studies: one with the Large deformation option selected and the other without, and then compare the displacement results obtained from these two studies (figures 17-14).
mm.
Figure 17-4: Correct displacement results produced with the Large displacement option selected (left) and incorrect displacement results produced without Large displacement option (right)
Note that the element size is much too large in the contact area to produce meaningful contact stress results (figure 17-15).
210
Engineering Analysis with COSMOSWorks
Figure 17-15: Large element size in the contact area prevents meaningful analysis of contact stresses Shrink fit analysis Shrink fit is another type of Contact/Gaps condition that complements Bonded, Free, Node to Node, and Surface conditions. We use it to analyze stresses developed as a result of an interference (press fit) between two assembly components. Please open the SolidWorks model SHRINK FIT. The definition of the shrink fit condition is shown in figure 17-16. Please review this model for definitions of restraints, supports and contact conditions. Note that the contact condition does not include friction, therefore the inside cylindrical face of the pressed in component has been restrained in circumferential and axial directions to prevent rigid body motions.
, 4%
•%f\ tfJS :i
Figure 17-16: Cylindrical face<2> has larger diameter than cylindrical face <1>. Solving the model with Shrink Fit contact condition eliminates this interference. Exploded view must be used to select the interfering faces.
211
Finite Element Analysis with COSMOSWorks
A sample result of analysis with Shrink Fit condition is shown in figure 1717. CP (NAnm*2 (MPs)) ^ ^ 1.8138+002 :
662e+002
W-"--.
!.511e+002 . 1.3606+002
rx
•
. 1,20Se+002 J0S8e+Q02 ,9.0856+001 5546+001 .6,0446+001 001 3.0228+001
1
!.S11e+001
0.0006+000
Figure 17-17: Contact pressure caused bv the shrink fit Note very high contact stress magnitude indicates that plastic will lake place in the presence of this press fit.
212
deformation
Engineering Analysis with COSMOSWorks
Connectors Connectors are modeling tools used in defining connections between assembly components. COSMOSWorks offers four types of connectors: Rigid, Spring, Pin, Elastic Support and Bolt. Their use is briefly explained in the following table:
TYPE OF CONNECTOR
FUNCTION
Rigid
Defines a rigid link between the selected faces. Faces connected by a rigid link do not translate or rotate in relation to each other
Spring
Connects a face of a component to a face of another component by defining total stiffness or stiffness per area. Both normal and shear stiffness can be specified. The two faces must be planar and parallel to each other. The springs are introduced in the common area of the projection of one of the faces onto the other. You can specify a compressive or tensile preload for the spring connector.
Pin
A pin connects cylindrical faces of two components. Two options are available: No Translation. Specifies a pin that prevents relative axial translation between the two cylindrical faces. No Rotation. Specifies a pin that prevents relative rotation between the two cylindrical faces. Axial and/or rotational pin stiffness can be defined.
Elastic support
Defines an elastic foundation between the selected faces of a part or assembly and the ground. The faces do not have to be planar. A total or a distributed spring stiffness may be defined in a normal and tangential direction to the affected face. Elastic support is used to simulate elastic foundations and shock absorbers. Elastic support is the only type of connector that can be defined both for part and assembly
213
Finite Element Analysis with COSMOSWorks
FUNCTION
TYPF. OF CONNECTOR Bolt
Defines a bolt connector between two components. The bolt connector accounts for bolt pre-load and contact between the two components connected by bolt. Configurations with and without a nut are available
Connector definition is called by right-clicking the Load/Restraints folder and selecting Connectors (figure 17-18). Hide All Show All Restraints,,. Pressure,.. Force,,, Gravity,,. Centrifugal,,, Remote Load... Bearing Load,,, Connectors,,. Temperature,., Options,..
Fiuure 17-18: Connectors arc called from the same pop up menu as restraints and loads.
214
Engineering Analysis with COSMOSWorks
We will review the use of Rigid and Pin connectors using a model in the assembly file CRANE. This model comes with one already defined Rigid connector and three Pin connectors. The Rigid connector is shown in figure 17-19.
Figure 17-19: Rigid connector rigidly connects two faces. Rigid connector definition does not distinguish between source and target face.
215
Finite Element Analysis with COSMOSWorks
One of the Pin connectors is shown in figure 17-20.
y \ gj Type
^
#* pi:';
%
ipillilliilllil source
•
Si-
' ' - * fjt-<3>
i
target Mwjy^j Connection Type
Iillir
_ W\«RW
<**
13 No fransia&n
it!!
Q N O rotation
1 SI
Elastic Pin
III Pll g»» iBaiyti iiiiii m
,
v
.*.
^J ;£
;
»/m
^ i 0
i . M-m/fad
Figure 17-20 The Pin connector connects the middle face on one component to two faces of the other component Pin connector requires that theface(s) on one component are specified as a source and faces on the other component are specified as a target. Hence, there are two selection fields in Pin connector definition window. Section view is used for clarity. Note that torsional stiffness of Pin connector shown in figure 17-20 is specified as 0 (this is default value). This means that Pin connectors allow for rotation between the two components. All degrees of freedom on the selected faces are coupled (must be the same) except for circumferential translations which are disjoined.
216
Engineering Analysis with COSMOSWorks
To review the Bolt connector, open the assembly file FLANGE, which comes with six bolt connectors already defined. Please right-click one of Bolt Connector icons and select Edit Definition to open Connectors windows (figure 17-21). x::.i,„
Material O Custom
¥**j
M, ,1 S .1
@ Hilary
is ffu25G
* '"'"
between these two faces
Figure 17-21 One of six bolt connectors in the FLANGE assembly model. This illustration has been modified in a graphic program to show all entries in Connectors windows. Normally this would require scrolling. Definition of Bolt Connector offers several options. In this example we model the bolt with a nut. Bolt is made out of AISI 1045 material, has no tight fit, a bolt diameter is 10mm. Bolt is preloaded with an axial force 30,000N. All entries are shown in figure 17-21.
217
Finite Element Analysis with CQSMOSWorks
NOTES:
218
Engineering Analysis with COSMOSWorks
18: Implementation of FEA into the design process Topics covered •
FEA driven design process
•
FEA project management
•
FEA project checkpoints
•
FEA report
We have already stated that FEA should be implemented early in the design process and be executed concurrently with design activities in order to help make more efficient design decisions. This concurrent CAD-FEA process is illustrated in figure 18-1. Notice that design begins in CAD geometry and FEA begins in FEA-specific geometry. Every time FEA is used, the interface line is crossed twice: the first time when modifying CAD geometry to make it suitable for analysis with FEA, and the second time when implementing results. This significant interfacing effort can be avoided if the new design is started and iterated in FEA-specific geometry. Only after performing a sufficient number of iterations do we switch to CAD geometry by adding all manufacturing specific features. This way, the interfacing effort is reduced to just one switch from FEA to CAD geometry as illustrated in figure 18-1.
219
Finite Element Analysis with COSMOSWorks
=ULLY FEATURED CAD GEOMETRY CAD DESIGN
•0-
!
FEA GEOMETRY
FULLY FEATURED CAD GEOMETRY
SIMPLIFIED FEA GEOMETRY FEA
__
n
Jl
FEA
* 3§^
FEA
CAD DESIGN
Jt CAD DESIGN
J2^ T
I
FEA
r
„„.«-
_,.,„,
FEA
CAD DESIGN
Figure 18-1: Concurrent CAD-FEA product development processes deft) and FEA driven product development process (right) CAD-FEA design process is developed in CAD-specific geometry while FEA analysis is conducted in FEA-specific geometry. Interfacing between the two geometries requires substantial effort and is prone to error. CAD-FEA interfacing efforts can be significantly reduced if the differences between CAD geometry and FEA geometry are recognized and the design process starts with FEA-specific geometry.
Let's discuss the steps in an FEA project from a managerial point of view. The steps in an FEA project that require the involvement of management are marked with an asterisk (*).
Do I really need FEA? * This is the most fundamental question to address before any analysis starts. FEA is expensive to conduct and consumes significant company resources to produce results. Therefore, each application should be well justified. Providing answers to the following questions may help to decide if FEA is worthwhile: •
Can I use previous test results or previous FEA results?
•
Is this a standard design, in which case so no analysis is necessary?
•
Are loads, supports, and material properties known well enough to make FEA worthwhile?
•
Would a simplified analytical model do?
220
Engineering Analysis with COSMOSWorks •
Does my customer demand FEA?
•
Do I have enough time to implement the results of the FEA?
Should the analysis be done in house or should it be contracted out? * Conducting analysis in-house versus using an outside consultant has advantages and disadvantages. Consultants usually produce results faster while analysis performed in house is conducive to establishing company expertise leading to long-term savings. The following list of questions may help in answering this question: •
How fast do I need to produce results?
•
Do I have enough time and resources in-house to do complete a FEA before design decisions must be made?
•
Is in-house expertise available?
•
Do I have software that my customer wants me to use?
Establish the scope of the analysis* Having decided on the need to conduct FEA, we need to decide what type of analysis is required. The following is a list of questions that may help in defining the scope of analysis. Is this project: •
A standard analysis of a new product from an established product line?
•
The last check of a production-ready new design before final testing?
Q A quick check of design in-progress to assist the designer? •
An aid to an R&D project (particular detail of a design, gauge, fixture etc.)?
•
A conceptual analysis to support a design at an early stage of development (e.g., R&D project)?
•
A simplified analysis (e.g., only a part of the structure) to help making a design decision?
221
Finite Element Analysis with COSMOSWorks
Other questions to consider are: •
Is it possible to perform a comparative analysis?
•
What is the estimated number of model iterations, load cases, etc.
•
How should I analyze results? (applicable evaluation criteria, safety factors)
•
How will I know whether the results can be trusted?
Establish a cost-effective modeling approach and define the mathematical model accordingly Having established the scope of analysis, the FEA model must now be prepared. The best model is of course the simplest one that provides the required results with acceptable accuracy. Therefore, the modeling approach should minimize project cost and duration, but should account for the essential characteristics of the analyzed object. We need to decide on acceptable simplifications and idealizations to geometry. This decision may involve simplification of CAD geometry by defeaturing, or idealization by using shell representations. The goal is to produce a meshable geometry properly representing the analyzed problem.
Create a Finite Element model and solve it The Finite Element model is created by discretization, or meshing, of a mathematical model. Although meshing implies that only geometry is discretized, discretization also affects loads and supports. Meshing and solving are both a largely automated step, but it still require input, which depending on the software used, may include: •
Element type(s) to be used
Q Default element size and size tolerance a
Definition of mesh controls
•
Automesher type to be used
•
Solver type to be used
Review results FEA results must be critically reviewed prior to using them for making design decisions. This critical review includes: a
Verification of assumptions and assessment of results (an iterative step that may require several analysis loops to debug the model and to establish confidence in the results)
•
Study of the overall mode of deformations and animation of deflection to verify if the supports have been defined properly
•
Check for Rigid Body Motions
222
Engineering Analysis with COSMOSWorks •
Check for overall stress levels (order of magnitude) using analytical methods in order to verify applied loads
•
Check for reaction forces and compare them with free body diagrams
•
Review of discretization errors
•
Analysis of stress concentrations and the ability of the mesh to model them properly
a
Review of results in difficult-to-model locations, such as thin walls, high stress gradients, etc.
•
Investigation of the impact of element distortions on the data of interest
Analyze results* The exact execution of this step depends, of course, on the objective of the analysis. •
Present deformation results
•
Present modal frequencies and associated modes of vibration (if applicable)
•
Present stress results and corresponding factors of safety
•
Consider modifications to the analyzed structure to eliminate excessive stresses and to improve material utilization and manufacturability
•
Discuss results, and repeat iterations until an acceptable solution is found
Produce report* •
Produce report summarizing the activities performed, including assumptions and conclusions
•
Append the completed report with a backup of relevant electronic data
FEA project management requires the involvement of the manager during project execution. The correctness of FEA results cannot be established by only reviewing the analysis of the results. A list of progress checkpoints may help a manager stay in the loop and improve communication with the person performing the analysis. Several checkpoints are suggested in figure 18-2.
223
Engineering Analysis with COSMOSWorks a
Check for overall stress levels (order of magnitude) using analytical methods in order to verify applied loads
•
Check for reaction forces and compare them with free body diagrams
•
Review of discretization errors
•
Analysis of stress concentrations and the ability of the mesh to model them properly
•
Review of results in difficult-to-model locations, such as thin walls, high stress gradients, etc.
•
Investigation of the impact of element distortions on the data of interest
Analyze results* The exact execution of this step depends, of course, on the objective of the analysis. •
Present deformation results
•
Present modal frequencies and associated modes of vibration (if applicable)
•
Present stress results and corresponding factors of safety
•
Consider modifications to the analyzed structure to eliminate excessive stresses and to improve material utilization and manufacturability
•
Discuss results, and repeat iterations until an acceptable solution is found
Produce report* •
Produce report summarizing the activities performed, including assumptions and conclusions
a
Append the completed report with a backup of relevant electronic data
FEA project management requires the involvement of the manager during project execution. The correctness of FEA results cannot be established by only reviewing the analysis of the results. A list of progress checkpoints may help a manager stay in the loop and improve communication with the person performing the analysis. Several checkpoints are suggested in figure 18-2.
223
Finite Element Analysis with COSMOSWorks
DO YOU REALLY NEED FEA?
O.K.
MODELING APPROACH
O.K.?
GEOMETRY, LOADS, RESTRAINTS
O.K.?
O.K.?
RESULTS
Figure 18-2: Checkpoints in an FEA project Using the proposed checkpoints, the project is allowed to proceed only after the manager/supervisor has approved each step. Even though each FEA project is unique, the structure of an FEA report follows similar patterns. Here are the major sections of a typical FEA report and their contents.
224
Engineering Analysis with COSMOSWorks
Section
Content
Executive Summary
Objective of the project, part number, project number, essential assumptions, results and conclusions, software used (including software release), information on where project backup is stored, etc.
Introduction
Description of the problem: Why did the project require FEA? What kind of FEA? (static, contact stress, vibration analysis, etc.) What were the data of interest?
Geometry;
Description and justification of any defeaturing and/or idealization of geometry
Material Loads Restraints
Justification of the modeling approach (e.g. solids, shells) Description of material properties Description of loads and supports, including load diagrams Discussion of any simplifications and assumptions, etc.
Mesh
Description of the type of elements, global element size, any mesh control applied, number of elements, number of DOF, type of automesher used Justification of why this particular mesh is adequate to model the data of interest
Analysis of results
Presentation of displacement and stress results, including plots and animations Justification of the type of stress used to present results (e.g., max. principal, von Mises). Discussion of errors in the results Discussion of the applicability of the safety factors in use
225
Finite Element Analysis with COSMOSWorks
Conclusions
Recommendations regarding structural integrity, necessary modifications, further studies needed Recommendations for testing procedure (e.g., strain-gauge test, fatigue life test) Recommendations on future similar designs
Project documentation
Full documentation of design, design drawings, FEA model explanations, and computer back-ups Note that building in-house expertise requires very good documentation of the project besides the project report itself. Significant time should be allowed to prepare project documentation.
Follow-up
After completion of tests, report on test with test results appended Presentation of correlation between analysis results and test results Presentation of corrective action taken in case correlation is unsatisfactory (may involve revised model and/or tests)
226
Engineering Analysis with COSMOSWorks
19: Glossary The following glossary provides definitions of terms used in this book. Term
Definition
Adiabatic
An adiabatic wall is where there is no heat going in or out; it is perfectly isolated. An adiabatic wall is one with no convection or radiation conditions defined.
Boundary Element Method
An alternative to the TEA method of solving field problems, where only the boundary of the solution domain needs to be discretized. Very efficient for analyzing compact 3D shapes, but difficult to use on more "spread out" shapes.
CAD
Computer Aided Design
Clean-up
Removing and/or repairing geometric features that would prevent the mesher from creating the mesh or would result in an incorrect mesh.
Constraints
Used in an optimization study, these are measures (e.g., stresses or displacements) that cannot be exceeded during the process of optimization. A typical constraint would be the maximum allowed stress magnitude.
Convergence criterion
Convergence criterion is a condition that must be satisfied in order for the convergence process to stop. In COSMOSWorks this applies to studies where the p-Adaptive solution has been selected. Technically, any calculated result can be used as a convergence criterion. The following convergence criteria can be used in COSMOSWorks: Total Strain Energy, RMS Resultant Displacement, and RMS von Mises stress.
227
Finite Element Analysis with COSMOSWorks
Term
Definition
Convergence process
This is a process of systematic changes in the mesh in order to see how the data of interest change with the choice of the mesh and (hopefully) prove that the data of interest are not significantly dependent on the choice of discretization. A convergence process can be preformed as h-convergence or p-convergence. An h-convergence process is done by refining the mesh, i.e., by reducing the element size in the mesh and comparing the results before and after mesh refinement. Reduction of element size can be done globally, by refining mesh everywhere in the model, or locally, by using mesh controls to refine the mesh locally. An h-convergence analysis takes its name from the element characteristic, dimension h, which changes from one iteration to the next. An h-convergence analysis is performed by the user who runs the solution, refines the mesh, compares results, etc. A p-convergence analysis, performed in programs supporting p-elements, does not affect element size, which stays the same throughout the entire convergence analysis process. Instead, element order is upgraded from one solution pass to the next. A p-convergence analysis is done automatically in an iterative solution until the user-specified convergence criterion is satisfied. A p-convergence analysis is done automatically. Sometimes, the desired accuracy cannot be achieved even with the highest available pelement order. In this case, the user has to refine the p-element mesh manually in a fashion similar to traditional h-convergence, and then re-run the iterative p-convergence solution. This is called a p-h convergence analysis.
Defeaturing
Defeaturing is the process of removing (or suppressing) geometric features in CAD geometry in order to simplify the finite element mesh or make meshing possible.
Design scenario
In COSMOSWorks, this is an automated analysis of sensitivity of selected results to changes of selected parameters defining the model.
228
Engineering Analysis with COSMOSWorks
Term
Definition
Design variable
Used in an optimization study, this is a parameter (e.g. dimension) that we wish to change within a defined range in order to achieve the specified optimization goal.
Discretization
This defines the process of splitting up a continuous mathematical model into discrete "pieces" called elements. A visible effect of discretization is the finite element mesh. However, loads and restraints are also discretized.
Discretization error
This type of error affects FEA results because FEA works on an assembly of discrete elements (mesh) rather than on a continuous structure. The finer the finite element mesh, the lower the discretization error, but the solution takes more time.
Element stress
This refers to stresses at nodes of a given element that are averaged amongst themselves (but not with stresses reported by other elements) and one value is assigned to the entire element. Element stresses produce a discontinuous stress distribution in the model.
Element value
See Element stress.
Finite Difference Method
This is an alternative to the FEA method of solving a field problem, where the solution domain is discretized into a grid. The Finite Difference Method is generally less efficient for solving structural and thermal problems, but is often used in fluid dynamics problems.
Finite Element
Finite elements are the building blocks of a mesh, defined by position of their nodes and by functions approximating distribution of sought after quantities, such as displacements or temperatures.
Finite Volumes Method
This is an alternative to the FEA method of solving field problem, similar to the Finite Difference Method.
Frequency analysis
Also called modal analysis, a frequency analysis calculates the natural frequencies of a structure as the associated modes (shapes) of vibration. Modal analysis does not calculate displacements or stresses.
229
Finite Element Analysis with COSMOSWorks
Term
Definition
Gaussian points
These points are locations in the element where stresses are first calculated. Later, these stress results can be extrapolated to nodes.
h-element
An h-element is a fine element for which the order does not change during solution. Convergence analysis of the model using faelements is done by refining the mesh and comparing results (like deflection, stress, etc.) before and after refinement. The name, Itelement, comes from the element characteristic dimension h, which is reduced in consecutive mesh refinements.
Idealization
This refers to making simplified assumptions in the process of creating a mathematical model of an analyzed structure. Idealization may involve geometry, material properties, loads and restraints.
Idealization error
This type of error results from the fact that analysis is conducted on an idealized model and not on a real-life object. Geometry, material properties, loads, and restraints all are idealized in models submitted to FEA.
Linear material
This is a type of material where stress is a linear function of strain.
Mesh diagnostic
This is a feature of COSMOSWorks that determines which geometric entities prevented meshing when meshing fails.
Meshing
This refers to the process of discretizing the model geometry. As a result of meshing, the originally continuous geometry is represented by an assembly of finite elements.
Modal analysis
See Frequency analysis.
Modeling error
See Idealization error.
Nodal stresses
These stresses are calculated at nodes by averaging stresses at a node as reported by all elements sharing that node. Nodal stresses are "smoothed out" and, by virtue of averaging produce continuous stress distributions in the model.
230
Engineering Analysis with COSMOSWorks
Node value
See Nodal stresses.
Numerical error
The accumulated rounding off of numbers causes this type of error by the numerical solver in the solution process. The value of numerical errors is usually very low.
Optimization goal
Also called an optimization objective or an optimization criterion, the optimization goal is the objective of an optimization analysis. For example in an optimization study, you could choose to minimize mass or maximize frequency.
p-element
P-elements are elements that do not have predefined order. Solution of a p-element model requires several iterations while element order is upgraded until the difference in user-specified measures (e.g., total strain energy, RMS stress) becomes less than the requested accuracy. The name p-element, comes from the p-order of polynomial functions (e.g., defining the displacement field in an element) which are gradually upgraded during the iterative solution.
p-Adaptive solution
This refers to an option available for static analysis with solid elements only. If the p-Adaptive solution is selected (in the properties window of a static study), COSMOSWorks uses p-elements for an iterative solution. A padaptive solution provides results with narrowly specified accuracy, but is time-consuming and therefore impractical for large models.
Pre-load
Pre-load is a load that modifies the stiffness of a structure. Pre-load may be important in a static or frequency analysis if it significantly changes structure stiffness.
231
Finite Element Analysis with COSMOSWorks
Principal stress
Principal stress is the stress component that acts on the size of an imaginary stress cube in the absence of shear stresses. General 3D state of stress can be presented either by six stress components (normal stresses and shear stresses) expressed in an arbitrary coordinate system or by three principal stresses and three angles defining the cube orientation in relation to that coordinate system.
Rigid body mode
This refers to a mode of vibration with zero frequency found in structures that are not fully restrained or not restrained at all. A structure with no supports has six rigid body modes.
or Rigid body motion
Rigid body mode is the ability to move without elastic deformation. In the case of a fully supported structure, the only way it can move under load is to deform its shape. If a structure is not fully supported, it can move as a rigid body without any deformation. RMS stress
Root Mean Square stress. This name comes from the fact that it is the square root of the mean of the squares from stress values in the model. RMS stress may be used as a convergence criterion if the p-adaptive solution method is used.
Sensitivity study
See Design scenario.
Shell element
Shell elements are intended for meshing surfaces. The shell element that is used in COSMOSWorks is a triangular shell element. Triangular shell elements have three comer nodes. If this is a second order triangular element, it also has mid-side nodes, making the total number of nodes equal to six. Each node of a shell element has 6 degrees of freedom. Quadrilateral shell elements are not available in COSMOSWorks.
232
Engineering Analysis with COSMOSWorks
Small Deformations assumption
Analysis based on small deformations assumes that deformations caused by loads are small enough to not significantly change structure stiffness. Analysis based on this assumption of small deformations is also called linear geometry analysis or small displacement analysis. However, the magnitude of displacements itself is not the deciding factor in determining whether or not those deformations are indeed small or not. What matters, is whether or not those deformations significantly change the stiffness of the analyzed structure.
SRAC
© 2003 Structural Research & Analysis Corp., SRAC are the creators of the family of COSMOS products. Phone: 800-469-7287; +1-310-207-2800 Email: [email protected]
Steady state thermal analysis
Steady state thermal analysis assumes that heat flow has stabilized and no longer changes with time.
Structural stiffness
Structural stiffness is a function of shape, material properties, and restraints. Stiffness characterizes structural response to an applied load.
Symmetry boundary conditions
These refer to displacement conditions defined on a flat model boundary allowing only for inplane displacement and restricting any out-ofplane displacement components. Symmetry boundary conditions are very useful for reducing model size if model geometry, load, and supports are all symmetric. The model can then be cut in half and symmetry boundary conditions are applied to simulate the "missing half.
Tetrahedral solid element
This is a type of element used for meshing volumes of 3D models. A tetrahedral element has four triangular faces and four corner nodes. If used as a second order element (high quality in COSMOSWorks terminology) it also has midside nodes, making then the total number of nodes equal to 10. Each node of a tetrahedral element has 3 degrees of freedom.
Thermal analysis
Thermal analysis finds temperature distribution and heat flow in a structure.
233
Finite Element Analysis with COSMOSWorks
Transient thermal analysis
Transient thermal analysis is an option in a thermal analysis. It calculates temperature distribution and heat flow changes over time as a result of time dependent thermal loads and thermal boundary conditions.
Tensile strength
This refers to the maximum stretching that can be allowed in a model before plastic deformation takes place.
Ultimate strength
This refers to the maximum stress that may occur in a structure. If the ultimate strength is exceeded, failure will take place (the part will break). Ultimate strength is usually much higher than tensile strength.
Von Mises stress
This is a stress measure that takes into consideration all six stress-components of a 3D state of stress. Von Mises stress, also called Huber stress, is a very convenient and popular way of presenting FEA results because it is a scalar, non-negative value and because the magnitude of von Mises stress can be used to determine safety factors for materials exhibiting elasto-plastic properties, such as steel.
Yield strength
See Tensile strength.
234
Engineering Analysis with COSMOSWorks
20: Resources Available to FEA User Many sources of FEA expertise are available to users. Sources include, but are not limited to: •
Engineering textbooks
•
Software manuals
•
Engineering j ournal s
•
Professional development courses
•
FEA users' groups and e-mail exploders
•
Government organizations
Readers of this book may wish to review the book "Finite Element Analysis for Design Engineers" which expands on topics we discussed in "Finite Element analysis with COSMOSWorks" book. "Finite Element Analysis for Design Engineers" is available through the Society of Automotive Engineers ("www.sae.org)
Figure 20-1 "Finite Element Analysis for Design Engineers" book
235
fl^D^DETDfiMa
B89090290842A
Finite Element Analysis with COSMOS Works
Engineering literature offers a large selection of FEA-related books, a few of which are listed here. •
Adams V., Askenazi A. "Building Better Products with Finite Element Analysis", Onword Press, 1998.
•
Macneal R. "Finite Elements: Their Design and Performance", Marcel Dekker, Inc., 1994.
•
Spyrakos C. "Finite Element Modeling in Engineering Practice", West Virginia University Printing Services, 1994.
•
Szabo B., Babuska I. "Finite Element Analysis", John Wiley & Sons, Inc., 1991.
c
Zienkiewicz O., Taylor R. "The Finite Element Method", McGrawHill Book Company, 1989.
Several professional organizations like the Society of Automotive Engineers (SAE) and the American Society of Mechanical Engineers (ASME) offer professional development courses in the field of the Finite Element Analysis. More information on FEA related courses offered by the SAE can be found on www.sae.org With so many applications for FEA, various levels of importance of analysis, and various FEA software, attempts have been made to standardize FEA practices and create a governing body overlooking FEA standards and practices. One of leading organizations in this field is the National Agency for Finite Element Methods and Standards, better know by its acronym NAFEMS. It was founded in the United Kingdom in 1983 with a specific objective "To promote the safe and reliable use of finite element and related technology". NAFEMS has published many FEA handbooks like: •
A Finite Element Primer
•
A Finite Element Dynamics Primer
•
Guidelines to Finite Element Practice
•
Background to Benchmarks
The full list of these excellent publications can be found on www .nafems.org
236
Engineering Analysis with COSMOSWorks Professional Finite Element Analysis with COSMOSWorks 2005
Paul M. Kurowski Ph.D., PEng.
-2^
PS
SolidWorks PUBLICATIONS
Design Generator, Inc.
Schroff Development Corporation www.schroff.com www.schroff-europe.com
Engineering Analysis with COSMOSWorks P
BTDWIDSMS
Finite Element Analysis with COSM b89090290842a
SDC PUBLICATIONS
CAD, CAM, FEA and Engineering Graph ics Books SDC publishes books for these software packages: CAD 3D Studio VIZ Autodesk VIZ Architectural Desktop AutoCAD AutoCAD LT
Inventor Land Desktop Mechanical Desktop Autodesk Revit
CAM CNC Workshop GibbsCAM Mastercam Pro/MANUFACTURING
CATIA l-DEAS IronCAD Microstation SilverScreen Solid Edge
Pro/ENGINEER Pro/INTRALINK Pro/SHEETMETAL SolidWorks thinkdesign
FEA ALGOR ANSYS l-DEAS Pro/MECHANICA
All books from SDC Publications are available through our online bookstore. Free Shipping • No Sales Tax
www.schroff.com
ISBN: 1-58503-249-2
PUBLICATIONS
Schroff Development Corporation www.schroff.com www.schroff-europe.com
