基于坐标变换精确计算近奇异积分的双向sinh变换法  

A coordinate transformation based double sinh transformations for evaluation of nearly singular integrals

作　　者：谢贵重 董云桥 钟玉东 周枫林 XIE Gui-zhong;DONG Yun-qiao;ZHONG Yu-dong;ZHOU Feng-lin(College of Mechanical and Vehicle Engineering,Hunan University,Changsha 410082,China;Henan Key Laboratory of Mechanical Equipment Intelligent Manufacturing,Mechanical and Electrical Engineering Institute,Zhengzhou University of Light Industry,Zhengzhou 450002,China;School of Mechanical Engineering,University of South China,Hengyang 421001,China)

机构地区：[1]湖南大学机械与运载工程学院,长沙410082 [2]郑州轻工业大学机电工程学院河南省机械装备智能制造重点实验室,郑州450002 [3]南华大学机械工程学院,衡阳421001

出　　处：《计算力学学报》2021年第2期188-192,共5页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11602229,11902141);中国博士后基金(2019M652753)资助项目.

摘　　要：提出一种与坐标变换相结合的双向sinh变换方法用于精确计算近奇异积分。首先利用坐标变换法对近奇异积分进行双向分离,再针对分离出的两个方向的积分形式,根据复变函数极点理论,构造双向sinh变换。与传统结合环向变换和极坐标变换的单向sinh变换以及迭代sinh变换方法相比,双向sinh变换法的计算精度更高,并且最近点的位置对近奇异积分计算精度的影响明显变小。This paper presents a new method which combines the coordinate transformation and double sinh transformations for nearly singular integrals.Firstly,the coordinate transformation is employed to separate the near singularities in the two directions.From the forms of the nearly singular integrals in the two directions,based on the complex poles theory,dual sinh transformations are constructed.Compared with the original sinh transformation in polar transformation in combination with the circumference transformation,dual sinh transformation in combination with the coordinate transformation,proposed in our paper can achieve a much more accurate result;moreover,the computational accuracy is less sensitive to position of the nearest singular point in the elements.

关 键 词：边界元法 边界积分方程 近奇异积分 sinh变换 坐标变换 

分 类 号：O343.1[理学—固体力学]