Geometrical Structure Analysis Based On The Radial Point Interpolation Galerkin Meshfree Method

Recently, so called meshfree methods or meshless methods which are relatively new numerical implementation have been studied and developed quickly,and have been paid much attention in international computational field. The approximation function of meshfree method is built on a series of nodes,undependent on mesh like traditional finite element method,so overcome this drawback of the latter method. Thus it has some advantage to solve nonlinear mechanical problems because of effectively abstaining from complex meshing and disadvantageous influence of elements distorting. Up till now,there are more than ten types of meshfree mehods and among them,the Radial Point Interpolation Method is one of the methods which are extensive studied and used. Its shape function has the Kronecker delta property, so it could impose the essential boundaries easily as the FEM.This paper introduces the research history and current state of mesh free methods. It describes the principle of Radial Basis Function Point Interpolation Method and derivational process of controlling equation, especially considering meshless method based on the geometrical nonlinear cases. Meshfree method program based on RPIM, background integration and penalty function is made by Matlab, and a simple algorithm which can produce irregular nodes is proposed. Parameters such as the radial basic function, Polynomial order, radius of influential domain, irregular nodes, node density and penalty coefficient are studied systematically to observe the accuracy and stability. Several examples considered both linearity and geometrical nonlinearity are calculated and analysised, and are compared the result with the theoretical solutions and the FEM solutions to illustrate the correctness and efficiency of the program which shows the reliability of the theory in the present paper.In the end, form finding of manbrane structure based on RPIM meshfree method is discussed, relevant formulation is described and form finding program is made to show the feasibility and rationality of the meshfree method on membrane.