A cell-based smoothed finite element method for multi-body contact analysis within the bi-potential formulation

Abstract

This paper presents a cell-based smoothed finite element method (CS-FEM) for solving contact problems within the bi-potential formulation. The frictional contact and large deformation are modeled based on the CS-FEM. This method performs based on the generalized smoothed Galerkin weak-form which requires only value of shape functions. Because no isoparametric mapping is needed, the CS-FEM has an advantage when dealing with problems with large deformation which may cause mesh distortion. The contact forces and the relative velocity establish an implicit relationship within the bi-potential formulation in which no user-defined parameter is introduced. Numerical examples show the contact between elastic and hyperelastic bodies calculated by CS-FEM models with different smoothing domains. Compared with FEM, the CS-FEM produces robust and more accurate solutions.