上海交通大学学报

上海交通大学学报 ›› 2004, Vol. 38 ›› Issue (07): 1222-1224,1228.doi: 10.16183/j.cnki.jsjtu.2004.07.044

所属专题： 王建华教授学报发文专辑

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自然单元法原理与三维算法实现

戴斌, 王建华()   

  1. 上海交通大学土木工程系，上海 　200030
  • 收稿日期:2003-04-18 出版日期:2004-07-01 发布日期:2021-04-25
  • 作者简介:戴斌（1978-)，男，安徽蚌埠人，硕士，主要研究方向为自然单元法原理及其实现．|王建华（联系人），男，教授，博士生导师，电话（Tel.): 021-62932915; E-mail: wjh417@sjtu.edu.cn.
  • 基金资助:
    国家自然科学基金资助项目(59879012)

The Natural Element Method and Its Computational Algorithms in Three Dimensions

DAI Bin, WANG Jian-hua()   

  1. Dept. of Civil Eng. , Shanghai Jiaotong Univ. , Shanghai 200030, China
  • Received:2003-04-18 Online:2004-07-01 Published:2021-04-25

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摘要：

自然单元法是一种新兴的无网格数值计算方法，其实质是基于自然相邻插值（C∞）的伽辽金法．文中推导了基于Lasserre凸多面体体积公式的三维自然邻结点坐标及其导数的算法，给出了三维自然单元法算法的流程图．该算法实际上可以用于任意维数的自然单元法计算．对于Lasserre算法带来的多余约束问题，提出了2种可行的解决算法．经验证算例，三维自然单元法的计算结果精度同六面体单元有限元法相当．

关键词: 自然单元法, 自然相邻插值, Delaunay三角化, 伽辽金法

Abstract:

Natural element method (NEM) is a recently developed meshless method and is essentially the Galerkin method based on natural neighbour interpolation. The algorithm for calculating natural neighbour co-ordinates and their derivatives based on Lasserre's algorithm for the volume of a convex polyhedron was derived and the generalized flowchart for NEM in 3D case was presented. The algorithm can be applied to NEM in any dimensions case in fact. Two algorithms to solve the redundant constraint problem lying in Lasserre's algorithm were also presented. The example's numerical results are equal to the results of hexahedral finite element method.

Key words: natural element method (NEM), natural neighbour interpolation, Delaunay triangulation, Galerkin method

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