Application of Base Force Element Method in Engineering

Abstract

A new finite element method—the base force element method (BFEM) has been developed in recent years for the analysis of solid mechanics problems. In this chapter, the 4-mid-node plane model of base force element method (BFEM) on complementary energy principle in Chap. 4 is used to analyze the rock mechanics problems. First, the chapter studies the problem of applying gravity load of rock mass on a 4-mid-node element according to the principle of virtual work. Second, the problem of exerting different material properties in the calculation of BFEM was studied. Then, the method to simulate the crack propagation using the BFEM on complementary energy principle is proposed. And the calculation method of safety factor for rock mass stability was presented for the BFEM on complementary energy principle. Finally, some typical numerical example is used to verify the validity and reliability of the above studies. The performance of the BFEM on complementary energy principle and the large-scale computing problems of the BFEM are tested. The numerical researches show that the results of the BFEM are consistent with the results of the conventional quadrilateral isoparametric element (Q4 model) and quadrilateral reduced integration element (Q4R model). The new nonlinear model of base force element method on complementary energy principle can be applied to rock mechanics and engineering.