Nonlinear Problems of Elasticity [electronic resource] / by Stuart S. Antman.
By: Antman, Stuart S [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextSeries: Applied Mathematical Sciences: 107Publisher: New York, NY : Springer New York, 2005Edition: Second Edition.Description: XVIII, 838 p. 110 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387276496.Subject(s): Global analysis (Mathematics)  Engineering  Analysis  Theoretical, Mathematical and Computational Physics  Computational IntelligenceAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

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ISI Library, Kolkata

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Background  The Equations of Motion for Extensible Strings  Elementary Problems for Elastic Strings  Planar SteadyState 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  3Dimensional Continuum Mechanics  3Dimensional Theory of Nonlinear Elasticity  Problems in Nonlinear Elasticity  LargeStrain Plasticity  General Theories of Rods  General Theories of Shells  Dynamical Problems  Appendix. Topics in Linear Analysis  Appendix. Local Nonlinear Analysis  Appendix. Degree Theory.
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 selfcontained 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, threedimensional continuum mechanics, threedimensional elasticity, largestrain 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.
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