角度-距离复合变换法消除边界积分方程近奇异性  

Near-Singularity Cancellation With the Angle-Distance Transformation Method for Boundary Integral Equations

作　　者：周枫林 谢贵重 张见明[1] 李落星[1] ZHOU Fenglin;XIE Guizhong;ZHANG Jianming;LI Luoxing(College of Mechanical and Vehicle Engineering,Hunan University,Changsha 410082,P.R.China;School of Mechanical Engineering,Hunan University of Technology,Zhuzhou,Hunan 412007,P.R.China)

机构地区：[1]湖南大学机械与运载工程学院,长沙410082 [2]湖南工业大学机械工程学院,湖南株洲412007

出　　处：《应用数学和力学》2020年第5期530-540,共11页Applied Mathematics and Mechanics

基　　金：中国博士后科学基金(2016M602403,2019M652753);国家自然科学基金(11602082,11602229)。

摘　　要：针对薄型结构边界单元分析过程中出现的近奇异积分问题,研究了采用一种角度变换和距离变换相结合的方法,节省了计算量,提高了计算精度.研究发现,当积分单元上与配置点距离最近的点落在积分单元的边沿或者顶点附近时,经过基础变换后的积分在两个方向都表现出奇异性,因此,对两个方向同时使用一维非线性变换能够切实消除近奇异性.数值算例验证了复合变换对近奇异积分计算精度的提升效果.To address the near-singularity computation problem involved in the boundary element analysis of thin-walled structures,an angle-distance combined transformation method was developed.With this combined method,the computational accuracy and efficiency can be significantly improved.The near singularity was found not only in the radial direction of the basic transformed space,but also in the circumferential direction.In the case that the nearest point in the integral element to the collocation point is close to the edge of the integral element,the integral kernel exhibits significant near singularity with regard to the circumferential direction.Through angle transformation for circumferential variables and distance transformation for radial variables,the near singularity with regard to both directions can be cancelled.Numerical examples illustrate the efficiency and accuracy of the presented method.

关 键 词：边界元法 薄型结构 近奇异积分 距离变换 角度变换 

分 类 号：O302[理学—力学] O241