A GENERAL BENCHMARK TEST FOR NUMERICAL METHODS FOR GEOMETRICAL NON-LINEAR DYNAMIC PROBLEMS

A general benchmark test for accuracy analysis of numerical methods for solid mechanics is proposed. Based on assuming mapping from the initial configuration to the current configuration, the exact displacements、velocities、accelerations、strains and stresses can be obtained by given body forces satisfying the governing equations. Furthermore, these exact solutions are used as the basis of benchmark tests for various numerical methods such as finite element methods, finite difference methods and meshless methods. The standard patch test is a special case of the present benchmark test in which the displacement fields were assumed as linear fields. The present method is applicable to 2D and 3D problems、 implicit and explicit schemes, small and large deformation, elastic and hyper-elastic materials. Several examples are given to show the accuracy of Element-Free Garlerkin Method (EFGM) in the analysis of dynamic large deformation problems for elastic and hyper-elastic materials.