边界单元法的改进及其在求解三维问题中的应用

来源期刊：中南大学学报(自然科学版)1986年第2期

论文作者：曹平

文章页码：31 - 36

关键词：虚边界单元法； 点载荷法

Key words：fictitious boundary element method； fictitious point force method.

摘    要：本文提出虚边界单元法和点载荷法,有效地提高了边界上和边界附近域解的精度,并将这两种方法推广到求解三维问题,使问题的求解得到了简化。

Abstract: This paper makes some improvement on the Boundary element method (BEM). First of all, the paper puts forward the conception of fictitious boundary element and fictitious boundary element method (FBEM). The numerical values calculated by FBEM on the boundary and by the boundary are much more exact than that calculated by BEM. On the basis of FBEM, another method can be gained when the fictitious stress in FBEM is replaced by fictitious concentrated force. This method is called fictitious point force method (FPFM). The physical meanings of BEM are extended by the FBEM and FPFM. On the basis of solving plane problems sueessfully with FBEM and FPFM, the article recommends the fictitious boundary element method and fictitious point force method to solve three dimensions problem in solid mechanics. The efficiency of these methods mentioned in this article has been examined by some examples.