Boundary Element and Augmented Lagrangian Methods for Contact Problem with Coulomb Friction

Jia Wu,Shougui Zhang

doi:10.1155/2020/7490736

Abstract

In this paper, boundary element and augmented Lagrangian methods for Coulomb friction contact problems are presented. Based on the projection technique, both unilateral contact and Coulomb friction conditions are reformulated as fixed point problems. The original problem is deduced to a variational formulation with boundary integral operators. Then, we propose a new augmented Lagrangian method which can be dealt with the semismooth Newton method. Short theoretical results and the algorithm description are given. Numerical simulations show the performance of the method proposed.

Highlights

In many industrial applications or engineering problems, the contact between a deformable elastic body and a rigid obstacle plays an important role
Erefore, reliable and efficient methods for the numerical simulation of friction contact problems are quite necessary for many areas of solid mechanics
An option is to discrete the problem by the finite element method (FEM) [2,3,4,5] or the boundary element method (BEM) [6,7,8,9,10] and obtain a convex optimization problem in the finite dimensional space

Summary

Introduction

In many industrial applications or engineering problems, the contact between a deformable elastic body and a rigid obstacle plays an important role. Some new methods for the numerical simulation of the friction contact problem have been developed, and we mention the penalty method and Nitsche’s method [19,20,21,22,23,24,25,26,27] Fixed point methods such as projection techniques are widely applied to complementary problems including contact problems in linear elasticity [12,13,14, 22, 25, 26].

Setting of the Problem

Boundary Weak Formulation of the Frictional Contact Problem

Boundary Element and Augmented Lagrangian Methods for the Contact Problem

Numerical Examples

Conclusion