Antman Stuart S. Nonlinear Problems of Elasticity

1-st Edition. — USA, New York: Springer - Verlag, 1995. — 786 p. — ISBN: 0-387-94199-1. — (Series: Applied mathematical sciences ; v. 107) Includes bibliographical references and index. (OCR - есть.).
1. Elasticity.
2. Nonlinear theories.
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con concepts of strain, both extensional and flexural, of contact force with its components of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations.) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel seldom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason.) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter.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.