Boundary Element Methods for Contact Problems

Abstract

In the theory of machine-dynamics, one needs for a thorough analysis detailed models of contact problems as well as of the dynamics and, moreover, the coupling relations between them.

For the linear elastic formulation of the dynamic contact problem there occur linear boundary conditions and the Signorini conditions on the boundary which yield corresponding variational inequalities. Since the unknown contact area is situated on the boundary varying there dynamically we use a Boundary Element Method (BEM). Consequently, variational inequalities on the boundary and equivalent formulations on corresponding function spaces are to be established by using the Betti formula in connection with the given boundary data. We use spatial discretization by a boundary element Galerkin method and various time discretizations.

Currently, for the stationary problem, solution methods based on the Yosida approximation of the Signorini problem are analyzed only for simple model problems with the Laplacian. We extend these analyses first to the two-dimensional elasticity problem without friction. Later on this method is to be extended to the time dependent three-dimensional contact problem with friction.

This paper has been supported by the Priority Research Programme of Baden-Württemberg: “Contact Problems in Machine Dynamics”.