Meshless Method For 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. Secondly, aimed at the basis function choice, weight function and its parameter choice 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. Nevertheless, a new method, which is named instant method to solve the radius of influence domain, is offered to conquer the limitation of existing method. Lastly, stiffness equation of EFGM and its integral format in essential boundary and force boundary are derived. General program of the EFGM is programmed by C language.A new method named element free-direct displacement method (EFDDM) is proposed to calculate the stress intensity factors (SIFs) of crack tips. The EFDDM refer to the direct displacement method which is used to calculate the SIFs in the FEM, and take the enriched basis to exactly compute displacement fields around crack tips. Numerical examples show that this method can calculate the SIFs conveniently, effectively and exactly. So the EFDDM provide a powerful approach for the fracture characteristic analysis of structures.