無網格法在彈塑性力學中的應用.pdf

1、 Classified Index: O176 U.D.C.: 51 Dissertation for the Master Degree in Science APPLICATION OF ELEMENT FREE METHOD FOR ELASTIC AND PLASTIC MECHANICS Candidate: Supervisor: Academic Degree Applied for:Speciality: Unive

2、rsity: Liu Cong Associate Prof. Xia Maohui Master of Science Computational Mathematics Yanshan University II Abstract Meshless method is a new numerical analysis method which developed rapidly in recent years. Meshless

3、 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

4、 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 （1

5、999）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

6、 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 backgroun

7、d 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 produ

8、ction 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 de

9、velopment 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 metho