E-Book Overview
The essential aim of the present book is to consider a wide set of problems arising in the mathematical modelling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities, and the transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.
Important new results concern contact problems with friction. The Coulomb friction law and some others are considered, in which relative sliding velocities appear. The corresponding quasi-variational inequality is constructed, as well as the appropriate iterative method for its solution. Outlines of the variational approach to non-stationary and dissipative systems and to the construction of the governing equations are also given.
Examples of analytical and numerical solutions are presented. Numerical solutions were obtained with the finite element and boundary element methods, including new 3D problems solutions.
E-Book Content
VARIATIONAL AND QUASI-VARIATIONAL INEQUALITIES IN MECHANICS
SOLID MECHANICS AND ITS APPLICATIONS Volume 147 Series Editor:
G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada N2L 3GI
Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics.