A Numerical Integration For Reproducing Kernel Particle Method

Now,meshfree method is an active topic of the recent research in the areasof computational science and approximation theory.This method used a kind offunctions approximation which are based on a finite number of nodes instead ofboth nodes and meshes as in finite element method.When using it to solve partialdifference equations,meshes can be completely or partly eliminated. Over the pastdecade, meshfree approximation methods have found their way into many differentapplication areas ranging from artifcial intelligence,computer graphics,imageprocessing and optimization to the numerical solution of many kinds of (partial)differential equations.As one of meshfree methods,Reproducing Kernel Particle Method not onlymaintains general characteristics of meshfree method,but also possesses the flexibletime-frequency characteristic,ect. Therefore,RKPM is a novel alternative forlarge deformation analysis,structural dynimics,nonlinear analysis of superplasticrubber,high gradient shear zone analysis,and other nonlinear problems.Thus structuralandhigh RKPM has important theoretical significance and practical value.In this paper,we introduce a Stabilized Conforming nodal integration.thismethod can avoid considerable comlexity to solution proceduce by high order'sGauss quadrature,and it eliminate instability by Direct nodal integration.The numericalresults show that the accuracy and convergent rates in RPKM with Directnodal integration are improved considerably by the Stabilized Conforming nodalintegration method.This paper consists of four chapters. In the second section,we propose thetheoretical basis of meshfree Galerkin method, the familiar numerical integrationmethods and the brief of Voronoi plan. In the third section,we recommend thetheoretical basis of RPKM and stablilized conforming nodal integration. I provethis method meet Stabilized Conforming Nodal Integration conditions(IC), andapply this method to 1D and 2D problems and give flow chart. In the fourthpart,we give the numerical results,analyse SC nodal integration method's the meritand weakness and analyse the choice of expanding gene. In the end of the paper,wedraw a conclusion of this work and make a prospect.