A two-dimensional base force element method using concave polygonal mesh

Abstract

Using the concept of base forces given by Gao [12] as fundamental variables to describe the stress state of an elastic system, this paper presents an explicit expression of two-dimensional element compliance matrix on the complementary energy principle with concave polygonal meshes. The detailed 2-D formulations of governing equations for the new finite element method—the base force element method (BFEM) are written in terms of the base forces concept using the Lagrange multiplier method. The explicit displacements expression of nodes is given. To verify the model proposed in this paper, a program on the 2-D BFEM using MATLAB language is made and a number of examples on concave polygonal meshes and aberrant meshes are provided to illustrate the BFEM. Good agreement has been obtained comparing numerical results using the proposed BFEM to available theoretical results. The concave polygonal element model can be used efficiently for the elasticity analysis with increasing element aspect ratios and distortion meshes compared with the traditional finite element method (FEM).