Two-dimensional model of base force element method (BFEM) on complementary energy principle for geometrically nonlinear problems

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 nonlinear problems is presented using arbitrary meshes. An arbitrary convex polygonal element model of the BFEM for geometrically nonlinear problem is derived by assuming that the stress is uniformly distributed on each edges 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. A good agreement of the results using the arbitrary convex polygonal element model of BFEM in the large displacement and large rotation calculations, are observed.