Nonlinear Problems of Elasticity

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: ipst.umd.edu/Faculty/antman.htm.

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: ipst.umd.edu/Faculty/antman.htm.

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: ipst.umd.edu/Faculty/antman.htm.

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.