三维弹塑性有限变形问题边界元法中奇异积分的直接分析去奇解法

ANALYTICAL REMOVAL OF SINGULARITIES AND DIRECT EVALUATION OF SINGULAR INTEGRALS IN3-D ELASTOPLASTIC FINITE DEFORMATION ANALYSIS BY BEM

作为本文作者研究工作的继续,本文提出了处理三维弹塑性有限变形问题边界元法中二次元区域弱奇及Cauchy 主值奇异积分的二次极坐标变换—分析去奇法.该方法先通过适当的二次极坐标变换降低奇异积分的奇异性,然后利用Causs 散度定理去除Cauchy主值积分的奇异性.通过三维弹塑性及三维有限变形问题数值算例说明该方法具有良好的精度及数值稳定性,并且实施较方便.本文方法可直接推广应用于二阶以上高阶元离散模型奇异积分处理.

As the further development of the author's research work,in this paper a method of so-calledquadratic polar co-ordinate transformation and analytical removal of singularity is proposed to evaluatethe strongly singular integrals in the sense of Cauchy principal values and the weekly singular integralsover quadratic internal cells of 3-D clastoplastic finite deformation analysis by BEM.First,a suitablequadratic polar co-ordinate transformation technique is applied to reduce the order of singularity of thesingular integrals.Then,a form of Gauss' theorem is introduced to remvoe the singularity in the Cauchyprincipal value integrals analytically.Numerical examples of 3-D clastoplastic problem and 3-D finitedeformation problem are given to demonstrate that the method possesses good accuracy and numericalstability,and is convenient to perform.the method in this paper can be appplied extensively to cvauatingthe singular integrals over cubic and higher order elements.