W. T. Koiter's Elastic Stability of Solids and Structures

✍ Scribed by Arnold M. A. van der Heijden

• Publisher: Cambridge University Press
• Year: 2008
• Tongue: English
• Leaves: 240
• Series: Proceedings of the Internation
• Edition: 1
• Category: Library

✦ Synopsis

This book deals with the elastic stability of solids and structures, on which Warner Koiter was the world's leading expert. It begins with fundamental aspects of stability, relating the basic notions of dynamic stability to more traditional quasi-static approaches. The book is concerned not only with buckling, or linear instability, but most importantly with nonlinear post-buckling behavior and imperfection-sensitivity. After laying out the general theory, Koiter applies the theory to a number of applications, with a chapter devoted to each. These include a variety of beam, plate, and shell structural problems and some basic continuum elasticity problems. Koiter's classic results on the nonlinear buckling and imperfection-sensitivity of cylindrical and spherical shells are included. The treatments of both the fundamental aspects and the applications are completely self-contained. This book was recorded as a detailed set of notes by Arnold van der Heijden from W. T. Koiter's last set of lectures on stability theory, at TU Delft.

✦ Table of Contents

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 9
1.1 Discrete systems......Page 11
2.1 Thermodynamic background......Page 17
2.2 Theorems on stability and instability......Page 21
2.3 The stability limit......Page 28
2.4 Equilibrium states for loads in the neighborhood of the buckling load......Page 37
2.5 The influence of imperfections......Page 51
2.6 On the determination of the energy functional for an elastic body......Page 57
3.1 The incompressible bar (the problem of the elastica)......Page 65
3.2 Bar with variable cross section and variable load distribution......Page 69
3.3 The elastically supported beam......Page 71
3.4. Simple two-bar frame......Page 77
3.5 Simple two-bar frame loaded symmetrically......Page 82
3.6 Bending and torsion of thin-walled cross sections under compression......Page 88
3.7 Infinite plate between flat smooth stamps......Page 94
3.8 Helical spring with a small pitch......Page 111
3.9 Torsion of a shaft......Page 120
3.10 Torsion of a shaft with a Cardan (Hooke’s) joint......Page 129
3.11 Lateral buckling of a beam loaded in bending......Page 136
3.12 Buckling of plates loaded in their plane......Page 147
3.13 Post-buckling behavior of plates loaded in their plane......Page 168
3.14 The “von Kàrmán-Föppl Equations”......Page 176
3.15 Buckling and post-buckling behavior of shells using shallow shell theory......Page 179
3.16 Buckling behavior of a spherical shell under uniform external pressure using the general theory of shells......Page 192
3.17 Buckling of circular cylindrical shells......Page 211
3.18 The influence of more-or-less localized short-wave imperfections on the buckling of circular cylindrical shells under axial compression†......Page 231
Selected Publications of W. T. Koiter on Elastic Stability Theory......Page 237
Index......Page 239