Nonlinear Problems of Elasticity

Hardcover | September 14, 2005

byStuart Antman

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Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.

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From the Publisher

Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent ch...

From the Jacket

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 ...

Format:HardcoverDimensions:856 pages, 9.25 × 6.1 × 0 inPublished:September 14, 2005Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387208801

ISBN - 13:9780387208800

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Table of Contents

Preface* Chapter 1. Background* Chapter 2. The Equations of Motion for Extensible Strings* Chapter 3. Elementary Problems for Elastic Strings* Chapter 4. Planar Steady-State Problems for Elastic Rods* Chapter 5. Introduction to Bifurcation Theory and it's Applications to Elasticity* Chapter 6. Global Bifurcation Problems for Strings and Rods* Chapter 7. Variational Methods* Chapter 8. Theory of  Rods Deforming in Space* Chapter 9. Spatial Problems for Rods* Chapter 10. Axisymmetric Equilibria of Shells* Chapter 11. Tensors* Chapter 12. 3-Dimensional Continuum* Chapter 13. 3-Dimensional Theory of Nonlinear Elasticity* Chapter 14. Problems in Nonlinear Elasticity* Chapter 15. Large-Strain Plasticity* Chapter 16. General Theories of Rods* Chapter 17. General Theories of Shells* Chapter 18. Dynamical Problems* Chapter 19. Appendix: Topics in Linear Analysis* Chapter 20. Appendix: Local Nonlinear Analysis* Chapter 21. Appendix: Degree Theory and it's Applications* References* Index

Editorial Reviews

From the reviews of the second edition:"This second edition accounts for the developments since the first edition was published, and differs from the first edition in many points. The book has been reorganized and several parts have been added. . The already impressive body of references has been further expanded. The reviewer highly recommends this book both to graduate students and to scholars interested in the theory of elasticity." (Massimo Lanza de Cristoforis, Mathematical Reviews, Issue 2006 e)"The second extended edition of the reviewed monograph gives a fundamental presentation of problems of nonlinear elasticity. Every chapter is equipped by instructive exercises, unsolved problems and exhaustive historical comments. The book could be very useful to applied mathematicians and engineers using in their works the elasticity theory and . to specialists dealing with applications of differential equations and bifurcation theory." (Boris V. Loginov, Zentralblatt MATH, Vol. 1098 (24), 2006)"Antman's impressive work is . a comprehensive treatise on nonlinear elasticity and a quintessential example of applied nonlinear analysis. . The text has been revised and updated, Several new sections have been added . This book is a 'must' for researchers and graduate students interested in nonlinear continuum mechanics and applied analysis. The work is scholarly and well written. . 'This book is directed toward scientists, engineers, and mathematicians who wish to see careful treatments of uncompromised problems.'" (Timothy J. Healey, SIAM Review, Vol. 49 (2), 2007)