Application Of Element Free Method For Elastic And Plastic Mechanics

Meshless method is a new numerical analysis method which developed rapidly in recent years. Meshless method is mainly by virtue of node and shape function in local support area to realize the numerical value of calculation in the whole field, which can thoroughly or partly eliminate the mesh influence. Therefore it can avoid remeshing completely, while compared with the finite element method it not only has more flexibility and validity but also can keep the exactness.The point interpolation method was originated by G.R.Liu and Gu(1999)based on Galerkin formulation using polynomial PIM shape functions. Conformability can be ensured by simply using a constrained Galerkian form that formulates conforming PIMs. In PIM, the probem domain is represented by properly scattered points as in any Meshless method. PIM shape functions of delta function property are constructed based only on a group of field nodes arbitrarily distributed. Similar to the EFG method, a background mesh of cells for integration will be used. PIM has been improved over the past few years, especially the techniques for dealing with possible singularity in the moment matrix.This paper is based on the research production of G.R.Liu, and begins with both reasoning mathematics and practical application. Firstly, simply introduces the basic problems of Elasticity and FEM; Secondly, systematically introduces the history of messhless development at home and abroad and the general approximate meshless method, while on base of these theories introduces Meshless method how to deal with the boundary conditions; then, introduces the more sophisticated method: the element free Galerkin method, and theoretically proves the practice of the method; the 4th chapter introduces the point interpolation method, and give some numerical instances; at last, we use meshless method to make some numerical computations and detail analysis of some practical engineering problems, while in order to interpret the feasibility and validity of this method. In order to prove the feasibility of Meshless method in solving the problem of elasticity and plasticity mechanics, this paper compares the numerical solution with the exact solution and the ANSYS solution, from the two perspectives of theory and application we know that the Meshless method is of high practicability and good application prospect in engineering domain.