Application of boundary element method to solve three-dimensional elastic contact problems without friction

Abstract

A technique, based on the boundary element method, to analyse three-dimensional domains in frictionless contact is presented in this paper. Following an iterative procedure, the size of the contact zone is determined by finding a boundary solution compatible with the contact conditions (no interpenetrations between the domains outside the contact zone and no tractions on the final contact zone). The variables involved in the procedure are the displacements and the stress vectors of the nodes of the boundaries which can change their boundary conditions (nodes of the potential contact zone), the remaining variables being condensed applying a standard substructuring technique. In this way, although fine discretizations are usually required over the contact zone, systems of equations of a reduced order are obtained. Three examples have been selected in order to show the applicability of the proposed method to the three possible contact situations: conforming, advancing or receding contact. The results have been compared with those obtained using the finite element method or with analytical or numerical two-dimensional representations when reasonable, special attention having been given to aspects that cannot be observed in plane models, however.