摘要
边界元法中高阶单元上的几乎奇异积分一直难以计算。针对正交各向异性位势问题,提出一个半解析算法准确计算了其高阶单元上的几乎奇异积分。首先将正交各向异性材料中源点到单元的距离函数在局部坐标系下渐近展开,采用级数展开式构造出与奇异积分核函数具有相同奇异性的可积近似核函数;然后利用扣除法的思想,原奇异积分核减去近似积分核后再加回,几乎奇异积分便转换为规则部分和奇异部分之和,规则积分采用Gauss数值积分计算,奇异积分由文中推导出解析公式计算。通过两个正交各向异性的热传导算例表明,本文建立的高阶单元半解析算法能准确高效地计算近边界内点位势和位势梯度。
In boundary element analysis(BEA),the evaluations of the nearly singular integrals on the higher order elements have been difficult.In this paper,a semi-analytic algorithm is proposed to calculate the nearly singular integrals in the BEA of two dimensional(2 D)orthotropic anisotropic potential problems.Firstly,the distance function on the higher order element for the orthotropic anisotropic material is expanded into its Taylor’s series in terms of the local coordinate on the element.The Taylor series expansions are introduced to construct the approximate kernel functions of the nearly singular integrals,which have the same singularity as the integral kernels on the higher order elements.Then substracting the approximate kernel functions from and adding them back to the original kernels.As a result,the original singular integrals are divided into the sum of both regular part and singular part by the subtraction method.The regular integrals can be calculated by conventional Gauss numerical quadrature.The singular integrals are calculated by the analytic integral formulations derived in the present paper.Finally,two examples are given to demonstrate the accuracy and effectiveness of the present semi-analytic algorithm to evaluate the potential and flux of interior point near the boundary for 2 D orthotropic anisotropic potential problems.
作者
胡斌
牛忠荣
胡宗军
丁信哲
孙学根
Hu Bin;Niu Zhongrong;Hu Zongjun;Ding Xinzhe;Sun Xuegen(School of Civil Engineering,Hefei University of Technology,230009,Hefei,China)
出处
《应用力学学报》
CAS
CSCD
北大核心
2019年第5期1042-1048,1256,共8页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(11272111
11772114)
