BEM and Tangent Operator Technique Applied to Analysis of Contact Problems

Abstract

The boundary element method (BEM) is a robust and accurate numerical technique to deal contact problems, because the contact among solids occurs along its boundaries. In this regard, this work presents a nonlinear BEM formulation applied to contact problems simulation. The formulation is based on the use of singular or hyper-singular integral equations of BEM, for multi-region contact, and the dual version of BEM to simulate the contact between crack surfaces. The mechanical nonlinear behaviour introduced by the contact is represented by the Coulomb’s friction law. The nonlinear formulation uses the tangent operator technique, in which one uses the derivate set of algebraic equations to construct the corrections field for the nonlinear process. This implicit formulation has shown accurate as the classical approach. However it is faster, in terms of computational time consuming, than the classical nonlinear approach. Examples of simple and multi-region contact problems are presented in order to illustrate the applicability of the proposed nonlinear numerical scheme.