弹塑性边界元中强奇异积分的一种新的计算方法

A New Method to Calculate Strongly Integrals for Elastoplastic BEM

采用边界元法分析弹塑性问题时,需要解决塑性域剖分单元上的强奇异积分汁算问题。本文以二维问题为例,建议一种任意等参体单元上强奇异积分的新的计算方法。其主要原理是引入一种恒等分解,使含强奇异部分的积分与坐标变换无关。利用基本解性质,该积分的奇异性可以消除并可降阶,本文的方法是半解析的,计算精度高。方法的基本思想普遍适用于任意二维和三维等参体单元。

When applying BEM to elastoplastic problems,the strongly singular integrals over volume cells have to be estimated.This paper Presents a new method for calculating the integrals.In this method,an identical equation is introduced.The part including strongly singular integrals is made to be independent of coordinate transformation.This part of integral can be semi-analytically estimated.The method Proposed is accurate,and can be applied to 2-D and 3-D isoparameter volume cells.