Element-Free Galerkin Method Under Some Boundary Conditions And Its Improvement

Element-free Galerkin Method (EFGM) is a new numerical method in recent years. It is a method which is more often used in all meshless methods. The shape function is constructed by Moving Least Squares Method in EFGM, and 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 simplifies data processing and improves computing speed without grid. And it can solve the problems that can not solve by finite element method.First of all, we elaborate the emergence and development of EFGM in this paper, and research the basic theory of EFGM. We mainly introduce the program design for EFGM and investigate factors which have influence on computing accuracy. We obtain some useful results then.Secondly, since MLS approximation doesn't possess the interpolation character as the field function of finite element and boundary element, we modify the shape function of MLS in this paper, and further bring the constrained displacement boundary conditions into EFGM. Numerical example shows that the method is feasible and efficient.Next, we bring constrained condition into Galerkin weak form by applying the Lagrange multiplier method, and apply it to solving typical planet mechanics problem of EFGM. Problems such as the cantilever beam subjected to even force are analyzed. Then programs are given to each corresponding example. The computation results indicate that EFGM has high precision.Finally, based on finite covering and unit partition, we propose an integral of unit partition and apply it to EFGM, which ameliorate the traditional EFGM. The improved EFG method doesn't need mesh in the progress of node approximation and numerical integral, which can reduce integral error and improve accuracy of the method, because we take space distributing of nodes in sub-domains into consideration.