三维弹性边界元分析中面力不连续和1/r积分奇异性问题的处理

本文将文2]中的方法推广应用于解决三维弹性面积分中1/r的奇异性问题,从数值计算角度,较详细地讨论了消除1/r奇异性的原理。为了取得较高的数值精度及较少的运算时间,本文对高斯点数目的选择原则也作了分析与讨论,提出了一个实用的经验公式。针对三维弹性问题中常见的边界面力不连续问题,提出了一种简单的处理方法,即直接从边界离散化后的边界元方程出发,按力不连续点所处的积分单元分别进行处理。两个典型算例的数值试验结果表明,文中所用的方法是行之有效的。

The Treatment of Discontinuous Tractions and Integrals with 1/r Singularities in 3-D Elastic Boundary Element Method

In this paper, the approach in Ref. 2] is extented and used to solve the integrals with 1/r singularities in elastic problems,and the principle of eliminating 1/r singularities is discussed in detail from the numerical calculations. The selections of the numbers on Gauss s integral points are analyzed and discussed as well. Then a practical and experimental formula is given so that a higher numerical precision can be obtained in less calculating time. For common discontinuous tractions in 3-D elastic problems, a simple approach is proposed in this paper. Integral elements where the points of discotinuous traction are located are separately treated and calculated by applying the discretion of boundary integral equation. The results of numerical experiments on two typical examples show that the approach in this paper is satisfactory.