A self-adaptive projection method for contact problems with the BEM

Abstract

• A new and simple computational method is developed for the contact problem. • We use the variational method to analyze the convergence of proposed method. • We give the self-adaptive rule and the boundary element approximation for the method. • The performance of the method is demonstrated by the numerical results. A self-adaptive algorithm, based on the projection and boundary integral methods, is designed and analyzed for frictionless contact problems in linear elasticity. Using the equivalence between the contact problem and a variational formulation with a projection fixed point problem of infinite dimensions, we develop an iterative algorithm that formulates the contact boundary condition into a sequence of Robin boundary conditions. In order to improve the performance of the method, we propose a self-adaptive rule which updates the penalty parameter automatically. As the iteration process is given by the displacement and the stress on the boundary of the domain, the unknowns of the problem are computed explicitly by using the boundary element method. Both theoretical results and numerical experiments show that the method presented is efficient and robust.