Fundamentals of Structural Stability

Fundamentals of Structural Stability 2006 Elsevier Inc. Author(s): George J. Simitses, Professor Emeritus, and Dewey H. Hodges, Professor ISBN: 978-0-7506-7875-9 Table of Contents Preface, Pages xi-xii 1 - Introduction and fundamentals, Pages 3-18 2 - Mechanical stability models, Pages 19-46 3 - Elastic buckling of columns, Pages 47-101 4 - Buckling of frames, Pages 103-144 5 - The energy criterion and energy-based methods, Pages 145-171 6 - Columns on elastic foundations, Pages 173-183 7 - Buckling of rings and arches, Pages 185-234 8 - Buckling of shafts, Pages 235-249 9 - Lateral-torsional buckling of deep beams, Pages 251-277 10 - Instabilities associated with rotating beams, Pages 279-295 11 - Nonconservative systems, Pages 297-328 12 - Dynamic stability, Pages 329-363 Appendix Work- and Energy Related principles and theorems, Pages 367-381 Author index, Pages 383-385 Subject index, Pages 387-389

389

S U B J E C T INDEX

Leipholz problem 309-312 follower force 297-302, 309, 310, 314, 315, 325-327 tangential torque 244, 245, 311,326 Nonlinear elastic 279-289 P

Postbuckling considerations: Koiter's theory 168-169 Principle of: minimum potential energy 374 stationary value of the total potential 373 virtual displacements 369 virtual work 369

energy 9, 145, 146 static (bifurcation, equilibrium) 8 Trefftz 146 models: one-degree-of-freedom 19-27 snapthrough 31-34 two-degree-of-freedom 27-31 with imperfections 34-38 limit point 126, 127, 134, 136-140, 201, 215, 220, 221,283, 330, 335, 336, 338, 339, 346, 350 Stability analysis: bifurcation approach 8 dynamic approach 8 energy approach 9 Strain energy 367

R

Rayleigh quotient 149, 230, 233, 275, 276, 293-295 Rayleigh-Ritz method: for stable equilibrium problems 248, 376 for unstable equilibrium problems 156-161 Rayleigh-Timoshenko method 151-155 Ritz method 156, 157, 163, 176, 183, 295, 304, 307, 310, 311,357 Rotating beams 64, 279-295

T Tilting of forces 62 Timoshenko beam (see Beams, Timoshenko) Timoshenko's method 147 Timoshenko quotient 149 Trefftz criterion: columns by the 161-163 low arches by the 215-221 for stability 147

S

U Unit-displacement theorem 375

Shafts 235-249 Southwell Plot 62 Special functions: Dirac 8-function 48, 52 doublet function 48, 49, 52 Macauley's bracket 48 unit step function 48 Stability: concept of 6 criterion for: dynamic (kinetic) 8, 298, 299

V Virtual displacements: definition 369 principle of 369-373 Virtual work: principle of 369-373 W

Work principles and theorems 367-378