Smoothing Element Free Galerkin Method And Its Application To 2D Elasticity Problems

The Finite Element Method(FEM)is one of the most important methods in the field of engineering numerical analysis.As an efficient numerical method,it has been widely used in engineering engineering such as mechanical engineering,civil engineering and navigation.On the basis of finite element method,this paper propose and study Cell-based Smooth Finite Element Method(CS-FEM)based on quadrilateral mesh grid and Smoothing Element-free Galerkin Method(SEFGM)based on triangle background mesh.The Cell-based Smoothing Finite Element Method,a combination of strain smoothing technique and traditional finite element method.In this paper,we use Hu-Washizu three-field variational principle to derive the weak form of CS-FEM,and study the related properties of this method.Finally,Smoothing Element-free Galerkin Method based on the idea of Smoothing Finite Element Method(SFEM)is added to the mesh of triangle background.The background mesh is once again separated into a smoothed element,and constucting poecewise constant function is used the gradient smoothing technology.It is necessary to linearly interpolate along the smoothing element,and the shape function is not needed to be derived in the construction of the strain field,which greatly reduces the construction workload of the stiffness matrix.In this paper,constructing shape function is applied the Moving Least Squares(MLS)approximation function,And the system equation is deduced by Galerkin method.Based on the background mesh,the T2L method is used to select the effective support point.The essential boundary processing method is similar to the traditional finite element method.In order to verify its stability and accuracy,cantilever and the infinite plate with holes are selected.The results show that the accuracy and convergence rate of the SEFGM method are better than those of the CS-FEM.