关于平面区域的三角形剖分

TRIANGULAR PARTITION OF PLANE DOMAIN

本文讨论了与有限元素法代数计算和几何计算有关的、用电子计算机快速地把平面区域剖分为三角形元素的问题.本文从两个方面改进了Zienkiewicz和林泰道提出并发展的块组合法.第一,把广义四边形块拓广为各边皆允许为折线的“四边块” 或“三边块”;第二,改变了处理三角形元素从疏到密过渡时采用的“虚点” 配置方式.由于作了这样的改进,使得“块”的剖分可以比较任意,因此,减少了预剖分的块数和输入的数据;同时使最后得到的三角形元素网格剖分疏密过渡自然,从而既减少了工作量又提高了剖分的质量.

This paper deals with the problem of partitioning the plane domain into triangular elements by computer, which is related to the algebraic operation and geometric calculation of the finite element method.The "Pieces Assembling Method" developed by Zienkiewicz[1] and Hayasi[2] has been improved in two aspects: 1 . Extended the generalized quadrilateral pieces to broken-line-side quadrilateral or trilateral pieces; 2. Altered the manner of the location of "imaginary points" being adopted in the arrangement of the triangular elements from sparsity to density.The improvements made it possible to carry out the partition with freedom and thus reduced the piece number of the pre-partition and the amount of the input data. As a result, the shape and size of the final elements are rather resonable and equitable; the amouut of work needed is less than usual and the quality of the partition is evidently improved.