Research And Application Of Element-Free Galerkin-Finite Element Coupling Method

Element-free Galerkin-finite element coupling (EFG-FE coupling) method is a new engineering numerical method in recent years. EFG-FE coupling method couples Element-free Galerkin method and finite element method by constituting a series of interim elements between domains of element-free method and elements of finite element method, and corresponding approximate function is constructed. EFG-FE coupling method congregates the advantages of Element-free Galerkin method and finite element method. This new method is capable of resolving massive problems, and there has been some decrease in operations, thereby this method improves the operational capability and avoids disadvantage of element-free Galerkin method in imposition of essential boundary conditions.Firstly, this paper briefly introduces the development of EFG-FE coupling method and introduces several main methods of EFG-FE coupling method. Secendly, the differences of EFGM and FEM, such as the meshing, the choice of weighting function, shape function generation and the treatment of boundary conditions are described, moreover gives EFGM and FEM calculation process. EFG-FE coupling method of shape function is mainly studied, and then verifies the feasibility of the method by solving concrete examples. EFG-FE coupling method is applied to temperature field problems, and we derive two-dimensional temperature field in the discrete equations. Through concrete examples show that the method is applicable in the temperature field has a good application prospect. In this paper, we also establish a contact problem solving element-free Galerkin-finite element - linear programming model, and verify the reliability and rationality of the method by solving examples. At last we study the cell based on the generalized definition of element-free Galerkin-finite element coupling method, and expatiate on the process of element stiffness matrix into the overall stiffness matrix, and finally by calculating the results show that the method is feasible and effective.