Nonlinear Problems of Elasticity

Stuart S. Antman (auth.)0387208801, 9780387208800

Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity, general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.

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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