Base Force Element Method for Space Truss

Abstract

Base force element method (BFEM) is a new method of finite element method which takes the base forces as fundamental unknown variables. In recent years, base force element method has great development and wide applications. In this chapter, a new 3D model of base force element method (BFEM) on complementary energy principle is presented using the concept of base force which is a new physical quantity to describe the stress state by Gao. First, a three-dimensional model of compliance matrix for space truss is derived through complementary energy principle which is described using base forces by dyadic vectors. Then, the explicit control equations of base force element method on complementary energy principle are derived using Lagrange multiplier method. Thereafter, the forming method of the overall compliance matrix of the BFEM on complimentary energy principle is proposed according to the stress and deformation characteristics of space truss. And the procedure of base force element method for space truss is developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the formulation and the procedure.