Nonlinear Problems of Elasticity

Stuart S. Antman (auth.)9780387941998, 0-387-94199-1, 3-540-94199-1

Within the past few decades, there has been an accelerating development of methods for studying nonlinear equations. Nonlinear analysis offers exciting prospects for certain specific areas of nonlinear problems with continuum mechanics. The objective of this book is to carry out such studies for problems in nonlinear elasticity. This book is directed toward scientists, engineers, and mathematicians who wish to see careful treatments of uncompromised problems. The author’s aim is to retain the orientation toward fascinating problems that characterizes the best engineering texts on structural stability while retaining the precision of modern continuum mechanics and employing powerful methods of nonlinear analysis. The author’s approach is to lay down a general theory for each kind of elastic body, carefully formulate specific problems, introduce the pertinent mathematical methods, and then conduct rigorous analyses of the problems.

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Table of contents :
Front Matter….Pages i-xviii
Background….Pages 1-10
The Equations of Motion for Extensible Strings….Pages 11-48
Elementary Problems for Elastic Strings….Pages 49-84
Planar Equilibrium Problems for Elastic Rods….Pages 85-123
Introduction to Bifurcation Theory and its Applications to Elasticity….Pages 125-172
Global Bifurcation Problems for Strings and Rods….Pages 173-226
Variational Methods….Pages 227-257
The Special Cosserat Theory of Rods….Pages 259-324
Spatial Problems for Cosserat Rods….Pages 325-342
Axisymmetric Equilibria of Cosserat Shells….Pages 343-370
Tensors….Pages 371-383
Three-Dimensional Continuum Mechanics….Pages 385-455
Elasticity….Pages 457-530
General Theories of Rods and Shells….Pages 531-601
Nonlinear Plasticity….Pages 603-628
Dynamical Problems….Pages 629-664
Appendix. Topics in Linear Analysis….Pages 665-673
Appendix. Local Nonlinear Analysis….Pages 675-681
Appendix. Degree Theory….Pages 683-698
Back Matter….Pages 699-752