固体力学问题数值解的一种验证方法

给出了固体力学几何非线性动态问题数值解的一种精度验证方法。通过假定初始构形和现时构形之间的映射关系,利用固体力学的控制方程即可求得产生这种构形的体积力,则假定构形和所得到的体积力就构成了问题的解析解。在这些解析解的基础上,提出了一种检验数值方法精度的标准试验,可用于二维和三维问题、隐式算法和显式算法、小变形和大变形分析、弹性材料和超弹性材料。在线性位移场的情况下本文方法是和传统的分片检验(patchtest)一致的。文中给出了无网格迦辽金法(EFGM)精度检验的几个算例。

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.