Nonlinear Problems of Elasticity

Stuart S. Antman (auth.)0387208801, 9780387208800, 9780387276496

This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity, directed toward the scientist, engineer, and mathematician who wish to see careful treatments of precisely formulated problems. Special emphasis is placed on role of nonlinear material response. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus of variations to problems for these bodies. The book continues with chapters on tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.

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