Title: Solution of variational inequalities in mechanics /
Authors: Hlaváček, Ivan, 1933-
Publisher: Springer Verlag,
Year: 1988
Subjects: Continuum mechanics.; Variational inequalities (Mathematics); Physics.
Abstract: 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.
Contents: 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.