Error estimates for a contact problem with the Tresca friction or the simplified Coulomb friction in elastic materials by the element-free Galerkin method

Abstract

• The penalty method is adopted to deal with the clamped boundary conditions. • The duality algorithm is presented for a contact problem with the Tresca friction. • Error estimates depend on the nodal spacing, the penalty factor and the largest degree of basis functions. This article discusses the error estimates for a contact problem with the Tresca friction or the simplified Coulomb friction in elastic materials by the element-free Galerkin method. The penalty method is adopted to deal with the clamped boundary conditions. The error estimates show that the convergence rate depends on the nodal spacing, the penalty factor and the largest degree of basis functions in the moving least-squares approximation. Numerical examples validate our theoretical results.