Grid - Finite Element Coupling Method The Application Of Fracture Mechanics

Element-free Galerkin Method (EFGM) is a effective method for solving partial differential equations with the help of shape functions coming from moving least squares approximation. It is well-suited to problems involving large deformation and crack propagation etc on which Finite Element Method (FEM) can not be used easily. But EFGM is computationally expensive and it is hard to impose the essential boundary condition. Coupling the EFGM and FEM can fetch up the defect of EFGM and improve the efficiency highly.At first, EFGM and kinds of methods used to couple EFGM and FEM are studied. In this part, the basis of EFGM, for example , weight function and parameters involving the precision of the method are studied. A coefficient used to control the relative weight and compact domain is proposed. Numerical examples show methods with the controlling coefficient can compute displacement field accurately and effectively. Then, Study on the EFGM-FEM Coupling Method Based on the weak forms of control equations is carried out. The mathematical and physical meanings of the coupled part are discussed. Then, a new method named EFGM-FEM Direct Coupling Method which is based on the concept of generalized element is brought forward. This method does not need construct a complicated transition shape function or involve additional computational cost like methods coupling EFGM and FEM with lagrange multiplier. Numerical studies show that the coupling method can get the displacement field correctly and efficiently which proved it is a potential method. At last, the EFGM-FEM Direct Coupling Method is used on the stress intensity factor analysis of classic structure and the computed results are compared with theory values which proved the direct coupling method is correct and effective.The C++ language is used to make up the mainly computing part while APDL language is used in the preprocessing part and Matlab is in the postprocessing part. The connecting between these three parts is carried out too. All of these programming works establish a base of a generalized soft.