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 second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is directed toward the scientist, engineer, and mathematician who wish to see careful treatments of precisely formulated problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.

Includes supplementary material: sn.pub/extras

Klappentext

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. 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.

Reviews of the first edition:

``A scholarly work, it is uncompromising in its approach to model formulation, while achieving striking generality in the analysis of particular problems. It will undoubtedly become a standard research reference in elasticity but will be appreciated also by teachers of both solid mechanics and applied analysis for its clear derivation of equations and wealth of examples.'' --- J. M. Ball, (Bulletin of the American Mathematical Society), 1996.

``It is destined to become a standard reference in the field which belongs on the bookshelf of anyone working on the application of mathematics to continuum mechanics. For graduate students, it provides a fascinating introduction to an active field of mathematical research.'' --- M. Renardy, (SIAM Review), 1995.

``The monograph is a masterpiece for writing a modern theoretical treatise on a field of natural sciences. It is highly recommended to all scientists, engineers and mathematicians interested in a careful treatment of uncompromised nonlinear problems of elasticity, and it is a `must' for applied mathematicians working on such problems.'' --- L. v Wolfersdorf, (Zeitschrift fur Angewandte Mathematik und Mechanik), 1995.

Inhalt
Background.- The Equations of Motion for Extensible Strings.- Elementary Problems for Elastic Strings.- Planar Steady-State Problems for Elastic Rods.- to Bifurcation Theory and its 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 Mechanics.- 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.