Penalty method for three-dimensional elastic contact problems by boundary element method

Abstract

An effective boundary element method (BEM) for three-dimensional elastostatic contact problems is developed by using the penalty method. The contact condition of the slip, stick and releasing states on the contact surface of the two bodies are assembled into a total virtual work functional and a system of integral equations for boundary values is formulated without any increase in the unknown parameters by introducing a penalty coefficient. A BEM based on this formulation is applied to typical three-dimensional contact problems such as the contacts between a cylinder and a block, and between cylinders. The shapes and displacements are also measured by an experiment with silicon rubber. The numerical results agree well with the analytical solutions and the experimental results.