直接施加本质边界条件的FE／EFG耦合算法及其数值实现

摘要

A finite element and meshfree Galerkin （FE/EFG） coupled algorithm based on transformation matrices is presented. By means of two transformation matrices, the FE sub-domain and EFG sub-domain can be coupled effectively and the essential boundary condition can be imposed directly on the EFG subdomain boundary. Two transformations are needed to deal with the nodes on the essential boundary and in the influence domain of the nodes on the interface between the two sub-domains. Furthermore,a partitioned-matrix method is proposed to calculate the transferred stiffness matrix which is stored in one-dimension variable bandwidth. The system equation is solved by the LU decomposition method. The cornputer program of the FE/EFG coupling method for three dimensional problems is developed. The efficiency of the algorithm presented in this papre is demonstrated by two numerical examples,a plate with a hole and a plate with a centre-crack under uniform tension.%提出一种可以直接施加本质边界条件的有限元与无网格Galerkin（FE／EFG）耦合算法。将问题域分成FE和EFG两种类型的子域，采用转换矩阵耦舍两子域的交界面；通过另一转换矩阵将无网格区域本质边界上的名义位移转换成真实位移，从而可在其上直接施加本质边界条件；采用二次转换实现两种转换矩阵之间的协调。提出全域统一采用单元思想和分块矩阵法计算刚度矩阵，提高了程序的通用性和刚度矩阵的计算速度。编制了相应计算程序，通过数值算例验证了方法和数值实施过程的正确性和有效性。