Contact Analysis Within the Bi-Potential Framework Using Cell-Based Smoothed Finite Element Method

Abstract

This paper presents a cell-based smoothed finite element method (CS-FEM) for solving two-dimensional contact problems with the bi-potential formulation. The contact force and the relative displacements on the contact surface are coupled with each other. The Uzawa algorithm, which is a local iterative technique, is used to solve the contact force. The classic Coulomb friction rule and a unilateral contact relationship are considered. There is no need to select any user-defined parameter in the whole process. Three contact states are investigated accurately, which can be stated as sticking, separating and sliding, respectively. The CS-FEM is performed with six different kinds of smoothing domains which are constructed by dividing the background element into different regions. Only boundary integrations instead of domain integral are required in the calculation, and no coordinate mapping is needed. Three numerical examples are presented to verify the effectiveness of the method. The effect of the friction coefficient for the contact is also investigated. All the obtained numerical solutions agree well with the reference values. The results produced by the CS-FEM are more accurate than those of the traditional FEM. Moreover, the CS-FEM can provide both an upper bound and a lower bound of the strain energy solutions while using different smoothing domains.