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＜電子ブック＞
Nonlinear Problems of Elasticity / by Stuart Antman
(Applied Mathematical Sciences. ISSN:2196968X ; 107)

版	1st ed. 1995.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1995
本文言語	英語
大きさ	XVIII, 752 p. 36 illus : online resource
著者標目	*Antman, Stuart author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Mathematical physics LCSH:Computational intelligence FREE:Analysis FREE:Theoretical, Mathematical and Computational Physics FREE:Computational Intelligence
一般注記	I. Background -- II. The Equations of Motion for Extensible Strings -- III. Elementary Problems for Elastic Strings -- IV. Planar Equilibrium Problems for Elastic Rods -- V. Introduction to Bifurcation Theory and its Applications to Elasticity -- VI. Global Bifurcation Problems for Strings and Rods -- VII. Variational Methods -- VIII. The Special Cosserat Theory of Rods -- IX. Spatial Problems for Cosserat Rods -- X. Axisymmetric Equilibria of Cosserat Shells -- XI. Tensors -- XII. Three-Dimensional Continuum Mechanics -- XIII. Elasticity -- XIV. General Theories of Rods and Shells -- XV. Nonlinear Plasticity -- XVI. Dynamical Problems -- XVII. Appendix. Topics in Linear Analysis -- XVIII. Appendix. Local Nonlinear Analysis -- XIX. Appendix. Degree Theory -- References 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 HTTP:URL=https://doi.org/10.1007/978-1-4757-4147-6

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