Analysis of semicoercive contact problems using symmetric BEM and augmented Lagrangians

Abstract

We present a parallel algorithm for identification of the contact interface and evaluation of contact stresses of systems of elastic bodies in contact that may comprise bodies which admit some rigid body motion. The algorithm is based on the discrete reciprocal formulation obtained by the symmetric boundary element method. The solution of the resulting problem is reduced to the solution of a sequence of strictly convex quadratic programming problems with simple bounds by a variant of the augmented Lagrangian method. The algorithm in the inner loop uses projections and adaptive precision control for the solution of auxiliary problems so that it can efficiently identify the contact interface. Both theoretical results and numerical experiments indicate that there are problems which may be solved efficiently by the algorithm presented. Since the coupling procedure is iterative, the algorithm may process most information concerning each body locally so that it is suitable for parallel implementation.