Base force element method (BFEM) on potential energy principle for elasticity problems

Abstract

Using the concept of base forces, the problem of the explicit tensor expression of the element stiffness matrix for a new finite element method (FEM)—the base force element method (BFEM) was studied. The mathematic model of the BFEM on potential energy principle was established by using an explicit expression. A code for the BFEM was developed using MATLAB computer language. The approach was used to solve several problems of elasticity theory, and various shape elements were compared and analyzed. The numerical results are consistent with those of the theoretical solutions, and the applicability of this approach is verified.