水利水电科技进展2012，Vol.32Issue(2)：37-41,5.DOI:10.3880/j.issn.1006-7647.2012.02.009
自然单元法与有限元法和无单元法的比较
Comparative study on natural element method, finite element method and meshless method
摘要
Abstract
In order to analyze the characteristics of the natural element method (NEM), comparison among NEM and the finite element method (FEM) and the meshless method (MM) is carried out. The basic principles of NEM is introduced in this paper, that is, NEM is based on the Voronoi tessellation of a set of nodes and the Delaunay triangulation of the topological dual of the Voronoi diagram, taking the natural neighbor interpolation as trial function and building the equilibrium equations to solve problems. NEM is considered to be a meshless method, and its shape functions can be constructed simply. By analyzing the basic properties of the three methods, the paper shows that the three methods have the same condition: partition of unity. Similar to FEM, NEM can exactly interpolate piece-wise linear boundary conditions. However, NEM is advantageous over the traditional FEM in solving problems with propagation of crack and large deformation and so on.关键词
自然单元法/有限元法/无单元法/自然邻节点插值/单位分解/形函数Key words
natural element method/finite element method/meshless method/natural neighbor interpolation/partition of unit/shape function分类
数理科学引用本文复制引用
琚宏昌,刘平伟,张胜利..自然单元法与有限元法和无单元法的比较[J].水利水电科技进展,2012,32(2):37-41,5.基金项目
广西教育厅科研项目(200911MS115,201010LX215) （200911MS115,201010LX215）
广西柳州应用技术研究与开发计划(2010020603) （2010020603）
