正交各向异性平面问题边界元——边境元素法研究

STUDY ON BOUNDARY FINITE ELEMENT METHOD IN PLANE ORTHOTROPIC ELASTICITY

摘要: 在文献¹中,本文作者研究了正交各向异性平面问题边界元素法的有关基本理论和计算公式,在上述工作的基础上,本文进一步研究各向异性平面问题边界邻域的应力分析。当采用边界元素法分析应力时,由于边界积分的奇异性,边界邻域应力的计算结果往往存在一定误差。为解决此问题,本文提出一个基于修正余能原理的所谓边境元素,包括四节点边境元素、八节点边境元素和三节点边境元素等。在边界元素法求解的基础上,进一步利用本文所述边境元素法,得到了非常满意的计算结果。

Abstract: When the boundary clement method (BEM) is used to calculate the stresses in the neighborhood of the boundary、there are always some errors.The reason is that the boundary integrals in BEM contain singular factors.To solve this problem, a so-called boundary finite element (BFE) based on the complementary energy theorem is praposed,including four nodes BFE and eight nodes BFE, It is found that based on the solutions of BEM and using BFEM presented in this paper accurate results are obtained.