Research On Calculation Accuracy Of Element-Free Galerkin Method

Element-free Galerkin Method (EFGM) is a new numerical method in recent years. It is a more often used method in all meshless methods. In this paper, shape function is constructed by Moving Least Squares Method. Control equations are produced from the weak form of variational equation. Lagrange multipliers are used to satisfy displacement boundary conditions, and make out numerical solutions. This method simplified data processing and improved computing speed without grid. And it can solve the problems that can not solve by finite element method.This paper includes five chapters. Chapter 1 briefly introduces the development of EFGM and introduces several meshless methods.In chapeter 2, we introduce EFGM, and study shape function, weight function and influence domain.Control equations are produced from the weak form of variational equation.and then we discuss several methods of dealing with displacement boundary conditions, moreover give EFGM calculation process.In Chapter 3, we disscuss the factors of impacting the computation accuracy and obtain some useful conclusions.In Chapter 4, EFGM is applied to elastic problems, and we analyze problems such as the bar subjected to linear loading, the cantilever beam subjected to even force and the easy support beam subjected to even force. Then programmings are given according to each example. The computation results indicate EFGM has high precision.In Chapter 5, EFGM is applied to electromagnetic problems. In the process of solving, the mixed transformation method is used to deal with displacement boundary conditions. Examples are presented and the results show that EFGM is not only easy to implement but also with high precision and good stability.