Mathematical Theory of Elastic Equilibrium: Recent Results (Ergebnisse der angewandten Mathematik, 7)

It is not my intention to present a treatise of elasticity in the follow­ ing pages. The size of the volume would not permit it, and, on the other hand, there are already excellent treatises. Instead, my aim is to develop some subjects not considered in the best known treatises of elasticity but nevertheless basic, either from the physical or the analytical point of view, if one is to establish a complete theory of elasticity. The material presented here is taken from original papers, generally very recent, and concerning, often, open questions still being studied by mathematicians. Most of the problems are from the theory of finite deformations [non-linear theory], but a part of this book concerns the theory of small deformations [linear theory], partly for its interest in many practical questions and partly because the analytical study of the theory of finite strain may be based on the infinitesimal one. Front Matter....Pages I-VIII Kinematic Introduction....Pages 1-7 Basic Equations of the Statics of Continuous Media....Pages 8-12 Isotropic bodies — Thermodynamic potential....Pages 12-31 Transformations Depending on a Parameter. Successive Equations of Elasticity....Pages 31-47 Analytical Problems Regarding the Fundamental Equations of Isothermal Static Elasticity....Pages 47-62 Inequalities for the Equilibrium of Slightly Deformable Elastic Bodies....Pages 62-92 Integration of the Fundamental Problem of Static Elasticity....Pages 92-119 Plane Elasticity....Pages 120-131 Hypo-Elasticity....Pages 131-141 Asymmetric Elasticity....Pages 141-160 Back Matter....Pages 161-168