The idea for this book was developed in the seminar on problems of con tinuum mechanics, which has been active for more than twelve years at the Faculty of Mathematics and Physics, Charles University, Prague. This seminar has been pursuing recent directions in the development of mathe matical applications in physics; especially in continuum mechanics, and in technology. It has regularly been attended by upper division and graduate students, faculty, and scientists and researchers from various institutions from Prague and elsewhere. These seminar participants decided to publish in a self-contained monograph the results of their individual and collective efforts in developing applications for the theory of variational inequalities, which is currently a rapidly growing branch of modern analysis. The theory of variational inequalities is a relatively young mathematical discipline. Apparently, one of the main bases for its development was the paper by G. Fichera (1964) on the solution of the Signorini problem in the theory of elasticity. Later, J. L. Lions and G. Stampacchia (1967) laid the foundations of the theory itself. Time-dependent inequalities have primarily been treated in works of J. L. Lions and H. Bnlzis. The diverse applications of the variational in equalities theory are the topics of the well-known monograph by G. Du vaut and J. L. Lions, Les iniquations en micanique et en physique (1972).

Klappentext
This book deals with approximation and numerical realization of variational inequalities of elliptic type, having applications in mechanics of solids. Emphasis is devoted to the study of contact problems of elastic bodies and problems of plasticity. The main feature of the book is that problems are treated in all their complexity - from the analysis of the continuous models, existence and uniqueness results, to finite element models and the study of their mutual relation, error estimates, convergence results. Special attention is given to contact problems with friction, where some new results are presented, concerning Coulomb`s model of friction. TOC:Contents: Unilateral Problems for Scalar Functions: Unilateral Boundary Value Problems for Second Order Equations. Problems with Inner Obstacles for Second-Order Operators.- One-Sided Contact of Elastic Bodies: Formulations of Contact Problems. Existence and Uniqueness of Solution. Solution of Primal Problems by the Finite Element Method. Dual Variational Formulation of the Problem with Bounded Zone of Contact. Contact Problems with Friction.- Problems of the Theory of Plasticity: Prandtl-Reuss Model of Plastic Flow. Plastic Flow with Isotropic or Kinematic Hardening.- References.- Index.

Inhalt
Contents: Unilateral Problems for Scalar Functions: Unilateral Boundary Value Problems for Second Order Equations. Problems with Inner Obstacles for Second-Order Operators.- One-Sided Contact of Elastic Bodies: Formulations of Contact Problems. Existence and Uniqueness of Solution. Solution of Primal Problems by the Finite Element Method. Dual Variational Formulation of the Problem with Bounded Zone of Contact. Contact Problems with Friction.- Problems of the Theory of Plasticity: Prandtl-Reuss Model of Plastic Flow. Plastic Flow with Isotropic or Kinematic Hardening.- References.- Index.