The application of 2D base force element method (BFEM) to geometrically non-linear analysis

Based on the concept of the base forces by Gao, a new finite element method – the base force element method (BFEM) on complementary energy principle for two-dimensional geometrically non-linear problems is presented. A 4-mid-node plane element model of the BFEM for geometrically non-linear problem is derived by assuming that the stress is uniformly distributed on each sides of a plane element. The explicit formulations of the control equations for the BFEM are derived using the modified complementary energy principle. The BFEM is naturally universal for small displacement and large displacement problems. A number of example problems are solved using the BFEM and the results are compared with corresponding analytical solutions and those obtained from the standard displacement finite element method. A good agreement of the results, and better performance of the BFEM, compared to the displacement model, in the large displacement and large rotation calculations, is observed.

► Two-dimensional model of base force element method (BFEM). ► 2D BFEM with complementary energy principle. ► 2D BFEM for geometrically non-linear problems. ► Good performance of BFEM compared with the traditional FEM for large displacement problems. ► Good convergence characteristics of BFEM under large load step for large rotation problems.