Nonlinear Problems of Elasticity

by Stuart Antman

Overview

During the nine years since the publication of the first edition of this book, therehasbeensubstantialprogressonthetreatmentofwell-setpr- lemsofnonlinearsolidmechanics. Themainpurposesofthissecondedition are to update the first edition by giving a coherent account of some of the new developments, to correct errors, and to refine 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 modified) 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 differential equations (although I give extensive references to pertinent work employing such methods). Thus I intend that this edition, like the first, 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: [e-mail]. In due time, corrections will be placed on my web page: http://www.ipst.umd.edu/Faculty/antman.htm.

Product Details

ISBN-13:	9780387208800
Publisher:	Springer New York
Publication date:	09/14/2005
Series:	Applied Mathematical Sciences , #107
Edition description:	2nd ed. 2005
Pages:	838
Product dimensions:	6.10(w) x 9.25(h) x 0.07(d)

Table of Contents

Background.- The Equations of Motion for Extensible Strings.- Elementary Problems for Elastic Strings.- Planar Steady-State 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.- 3-Dimensional Continuum Mechanics.- 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.

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)

From the Publisher