A macro element method to improve computational efficiency in large-scaled nonlinear analysis

Compared with dealing with a linear system, solving a nonlinear system equation in numerical simulation requires generally more CPU time since iterative approach is usually used in the latter. To cut down the computing cost, a direct way is to reduce the degree of freedoms (DOF) of the problem under investigation. However, this kind of treatment may result in poorer accuracy. In this manuscript, a macro element method is proposed to improve computational efficiency in large-scaled nonlinear analysis. When this concept is incorporated into finite element analysis (FEA), all the members in the linear zones of a structure can be grouped into just one macro element. By using weak member approach, the stiffness matrix of this macro element can be evaluated through unit force method. Numerical examples prove that the proposed macro element method can increase the computational efficiency significantly without obvious negative influence on accuracy.