Geometrically Nonlinear BFEM for Plane Truss

Abstract

In order to study the performance of base force element method (BFEM), a new 2-node degenerated plane element model based on the BFEM of complementary energy principle is presented for geometrically nonlinear problem, respectively, in this chapter. The plane truss element model can easily be obtained by degenerating from a 4-mid-node plane element of the BFEM based on complementary energy principle for geometrically nonlinear problem. The compliance matrix of the rod element model is the same as the compliance matrix of the 4-mid-node plane element of the BFEM. According to the characteristics of analysis for truss structure, the nodal equilibrium conditions, and the displacement coordination conditions of each rod at the nodes have been considered when the compliance matrix of the structure is integrated. In order to verify the feasibility of the degenerated plane element model, several truss problems are analyzed and their solutions are compared to the analytical solutions and the numerical results, which are calculated with the traditional displacement FEM. It is found that the model has shown high precision and good performance.