Antman Stuart S. Nonlinear Problems of Elasticity

2nd edition. — Springer, 2005. — 838 p. — (Applied Mathematical Sciences 107).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 the role of nonlinear material response. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed.Preface. - Background. - The Equations of Motion for Extensible Strings. - Elementary Problems for Elastic Strings. - Planar Steady-State Problems for Elastic Rods. - Introduction to Bifurcation Theory and it's Applications to Elasticity. - Global Bifurcation Problems for Strings and Rods. - Variational Methods. - Theory of Rods Deforming in Space. - Spatial Problems for Rods. - Axisymmetric Equilibria of Shells. - Tensors. - 3-Dimensional Continuum. - 3-Dimensional Theory of Nonlinear Elasticity. - Problems in Nonlinear Elasticity. - Large-Strain Plasticity. - General Theories of Rods. - General Theories of Shells. - Dynamical Problems. - Appendix: Topics in Linear Analysis. - Appendix: Local Nonlinear Analysis. - Appendix: Degree Theory and it's Applications. - References. - Index.