Preliminary Study And Application Of The Improved Element-free Galerkin Method

As one of the new numerical analysis methods,the meshless method was developed rapidly in recent years.In this method,mesh is not needed for the interpolation of the solution variables.And the mesh-free characteristic has distinct advantage to deal with high-speed impact,extremely large deformation,fracture and fragmentation problems,etc.Meshless method is promising in application. Of many kinds of meshles smethods,element-freeGalerkin method draw more attentions for itsstability,high accuracy,in sensitivity to distribution of discrete points. In the present dissertation,the method is introduced indetail.This paper presents an improved moving least-squares(IMLS).The IMLS approximation has greater computational efficiency and precision than the existing moving least-squares(MLS) approximation,and does not lead to an ill-conditioned system of equations.By combining the element-free Galerkin(EFG) method and the IMLS approximation ,an improved element-free Galerkin method is derived.Numerical results show the efficiency。One of the major difficulties in the implementation of element-free Galerkin method is the noninterpolatory character of the approximation.As a consequence,the imposition of boundary conditions is quite awkwat。So a coupled improved element-free Galerkin-finite element method is suggested.With the coupled suggested before crack promblem and the crack propagation are calculated.For two-dimensional fracture problems,the enriched basis function is used at the tip of the crack to give an enriched IEFG method.When the enriched IEFG method is used,the singularity of the stresses at the tip of the crack can be shown better than that in the IEFG method.The examples reveal the method has the advantages of excellent convergence rate,high accuracy and efficiency.It is very promising in engineering application.