Stress analysis of three-dimensional contact problems using the boundary element method

This paper presents a technique based on the boundary element method [1] to analyse three-dimensional contact problems. The formulation is implemented for the frictionless and infinite friction conditions. Following a review of the basic nature of contact problems, the analytical basis of the direct formulation of the boundary element method is described. The numerical implementation employs linear triangular elements for the representation of the boundary and variables of the bodies in contact. Opposite nodal points in similar element pairs are defined on the two surfaces in the area which are expected to come into contact under the increasing load. The use of appropriate contact conditions enables the integral equations for the two bodies to be coupled together. Following an iteration procedure, the size of the contact zone is determined by finding a boundary solution compatible with the contact conditions. Different examples have been analysed in order to verify the applicability of the proposed method to various contact situations. The results have been compared with those obtained using the finite element method in conjunction with the ABAQUS [2] and IDEAS [3] packages which are shown to be in good agreement. © 1998 Elsevier Science Ltd. All rights reserved.