Cover image for Nonlinear problems of elasticity
Title:
Nonlinear problems of elasticity
Personal Author:
Series:
Applied mathematical sciences ; v. 107
Edition:
2nd ed.
Publication Information:
New York, NY : Springer, 2005
ISBN:
9780387208800

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30000010138504 QA931 A57 2005 Open Access Book Book
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Summary

Summary

During the nine years since the publication of the ?rst edition of this book, therehasbeensubstantialprogressonthetreatmentofwell-setpr- lemsofnonlinearsolidmechanics. Themainpurposesofthissecondedition are to update the ?rst edition by giving a coherent account of some of the new developments, to correct errors, and to re?ne the exposition. Much of the text has been rewritten, reorganized, and extended. The philosophy underlying my approach is exactly that given in the following (slightly modi?ed) Preface to the First Edition. In particular, I continue to adhere to my policy of eschewing discussions relying on tech- cal aspects of theories of nonlinear partial di?erential equations (although I give extensive references to pertinent work employing such methods). Thus I intend that this edition, like the ?rst, be accessible to a wide circle of readers having the traditional prerequisites given in Sec. 1.2. I welcome corrections and comments, which can be sent to my electronic mail address: ssa@math.umd.edu. In due time, corrections will be placed on my web page: http://www.ipst.umd.edu/Faculty/antman.htm.


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