MLS Method: Numerical Error and Solution of a Unilateral Contact Problem Using Penalty and Lagrange Multiplier

Abstract

In this paper we propose a meshless approach (MLS) to solve two-dimensional unilateral contact problems. The convergence error of this method is studied, the element free Galerkin method and Galerkin formulation for two dimensional elasticity problems are considered. Then, the penalization method for the imposition of a contact constraint is proposed and the Lagrange multiplier method is used to impose essential boundary conditions. The implementation of the penalty / lagrange multiplier algorithm is described and the efficiency of our algorithm is illustrated by various examples.