基于四边形面积坐标的自然单元法  

Natural Element Method Based on Quadrilateral Area Coordinate Theory

作　　者：覃立宁[1] 

机构地区：[1]广西电力工业勘察设计研究院,广西南宁530023

出　　处：《红水河》2010年第3期149-152,共4页Hongshui River

摘　　要：自然单元法是一种基于自然邻接点插值求解偏微分方程的无网格数值方法。它使用Voronoi图或Delau-nay三角形作为背景积分网格。面积坐标是一种自然坐标,具有任意不变性,在求解离散点集刚度矩阵时可直接得到积分显式而不需依赖于数值积分。基于四边形面积坐标的自然单元法使用平均值定理将求解域内平均应变值由散度定理转化为区域周界上的环路显示积分,改进传统的积分格式。算例表明,这一积分方案能进一步精简计算量,提高计算效率,是一种自适应的数值计算方法。The Natural Element Method is a meshless method based on the evaluation of PDE by the Natural Neighbor Interpolation.It uses the Voronoi chart or Delaunay triangle as the background integration mesh.As a natural coordinate,it is arbitrary and invariant,which can solve explicit integration formula without numerical integration during the procedure of resolving stiffness matrix of scatter data points.Natural element method based on quadrilateral area coordinate uses mean value theorem to translate the average strain value in evaluation domain into perimeter integration in domain circumferences through divergence theorem.It improves the traditional integration format.Numerical examples indicate that this integration can further streamline the calculation of the program and make computation efficient.It is an adaptive numerical method.

关 键 词：面积坐标 平均值定理 边界积分方程 自然单元法 Laplace插值 

分 类 号：TV314[水利工程—水工结构工程]