Duality based solution of contact problem witb Coulomb friction

Abstract

Numerical solution of quasi-variational inequalities that describe the equilibrium of elastic bodies in contact with friction is presented. The problem is first reduced to a sequence of well conditioned problems with given friction that are reformulated by means of duality as quadratic programming problems with box constraints. Then the algorithm for the solution of quadratic programming problems with proportioning and projections is applied to the solution of the resulting contact problem with Coulomb friction. The characteristic feature of this active set-based algorithm is that it accepts approximate solutions of auxiliary problems and that it is able to drop and add many constraints whenever the active set is changed. The results of our numerical experiments indicate that the algorithms presented are efficient. The algorithm may prove to be useful in parallel implementation.