Analysis Of Calculation Accuracy Of Element-Free Galerkin Method And The Treatment Of Essential Boundary Conditions

Element-free Galerkin Method (EFGM) firstly introduced by Belytschko, Northwestern University's Professor, in 1994. It is partly eliminate the grid, just need the information of node within the displacement. It is fit to deal with the crack propagation, large deformation, material disguised and other problems that not easy to deal with by the finite element method, shows a series of outstanding advantages. In recent years, as the improvement of the method, it has become a very hot research topic in the field of computational mechanics.But the element-free Galerkin method is still in the development of the research phase, there are still some problems to be solved, for example, the accuracy is low, the essential boundary conditions to deal with difficult and limited range of applications. Paper is the discussion of these issues, through research and analysis such problems, and then gives some suggestions and methods for improvement.Firstly, Paper describes the development of the production about the Element-Free Galerkin Method, then gives the definition and construction principles of the basic elements of the method, and derives the calculation of the Element-free Galerkin method.Secondly, the Element-free Galerkin method constructed the shape functions by moving least squares method (MLSM), so the essential boundary conditions are not met usually. Basis on the traditional method, the paper introduces the transformation and coupling methods, and numerical examples show the method feasibility.Then, in view of the accuracy has been the Element-free Galerkin method one of the topics, the paper research the various elements those could affect the accuracy of Element-free Galerkin method calculation by numerical examples, through compare and analyze the calculation results, give some advices and recommendations to improve the element-free Galerkin method accuracy, and prove these programs effectiveness.Finally, In order to expand the element-free Galerkin method scope of application, try to put it practice into the mechanical field, electromagnetic field and temperature field and so on.