The Application Study Of The Element Free Galerkin Method To Fracture Analysis

As the development of computational science and software technique,the Finite Element Method (FEM) has become much powerful both in the estimation of error and foundation of theory.However,because of the FEM's inherent defect,it can not be used in many fields.For example,the FEM become powerless or can not solve the problems such as tremendous distortion,dynamic crack propagation,geometry aberration by high-speed bump,and so on. Under such a conditions.the element free method become been recognized and gain more and more attention because of its original idea and advanced technology in the numerical calculation.Firstly ,this paper investigate the history and actuality that element free method developed in the world,and analyzes the advantage and disadvantage of the element free method,and then outlines some popular methods in element free method such as the approximation method, discontinuity disposal method and essential boundary conditions disposal method. Stiffness equation of EFGM are derived.General program of the EFGM is programmed by MATLAB software.Through to two example computation solution and the exact solution contrast.The accuracy and a the precision of the procedure are conformed.Aimed at the basis function choice, Shape function, essential boundary conditions and obtain of the domain of influence in the most popular method-element free Galerkin method (EFGM),this paper studys particularly and gives out the basic rules.Secondly, by using the theory of linear elastic fracture mechanics,the J-integral method and the contour integral method,a new type of weight function basing on partially enriched basis function,analysis of displacement and stress field is given for finite plates with single edge crack and single inclined edge crack.Furthermore,the caculation esults of the meshless methord is approached to the calculation result of two analysis software of ANSYS.Based on the stress field of crack tip,stress intensity factor is solved,and simulated crack propagation.The analysis of crack propagation is dramatically simplified.The examples reveal the effectiveness of the present method. Finally,this paper studies particularly the influences of the weight function,the basis functions,the extent of distribution nodes,the discontinuities guidelines,the integral contours,the lamd with diffraction rules and the distrubution of nodes and gives out the basic rules.Meantime,Stress field and displacement feld of concrete wall with holes under complicated stress and Gravity dam are simulated by the program of EFGM to solve fracture mechanics problems and the result is not only satisfactoried but also available for the application in engineering.