Geometrical nonlinear problems of truss beam by base force element method

The base force element method (BFEM), formulated according the principle of complementary energy, is a new finite element method (FEM) that deals with nonlinear problems. Using the BFEM, the linear elastic model and large elastic deformation model of the plane truss element are derived, and the large elastic deformation model is expanded into a three-dimensional setting in this study. The rotating part of the element should be considered when deriving the large elastic deformation model. Accordingly, it is necessary to determine whether base force can be used as a fundamental unknown variable. Nonlinear numerical calculation is performed in combination with large elastic deformations of the truss beam and frame. The calculated results conform with the theoretical results of a solid beam with equivalent deflection. In this study, the U.L and T.L formats are used to solve the governing equations iteratively. The calculated results in the T.L format are compared with those of the T2D2 and LINK1 elements in the finite element software. Only a single loading of the T.L format is necessary, rendering it a simple and convenient approach that can improve calculation efficiency. Moreover, the arc-length method is first applied to the BFEM to solve the snap-through problem.

Automated summary

The base force element method (BFEM) is a new finite element method that deals with nonlinear problems based on the principle of complementary energy. This method is used to derive linear elastic and large elastic deformation models of plane truss elements, and expand them into a three-dimensional setting. Results show that using the U.L and T.L formats in BFEM can improve calculation efficiency when compared with traditional finite element software elements.