角度-距离复合变换法消除边界积分方程近奇异性

周枫林; 谢贵重; 张见明; 李落星

doi:10.21656/1000-0887.400229

角度-距离复合变换法消除边界积分方程近奇异性

doi: 10.21656/1000-0887.400229

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

基金项目: 中国博士后科学基金（2016M602403;2019M652753）;国家自然科学基金（11602082;11602229）

详细信息

作者简介:
周枫林(1986—)，男，副教授，博士（E-mail: zhoufl@hnu.edu.cn）;谢贵重（1983—），男，讲师，博士（通讯作者. E-mail: xieguizhong@126.com).

中图分类号: O302|O241
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- 被引次数: 0
出版历程
- 收稿日期: 2019-07-27
- 修回日期: 2019-09-03
- 刊出日期: 2020-05-01

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

¹College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, P.R.China;²School of Mechanical Engineering, Hunan University of Technology, Zhuzhou, Hunan 412007, P.R.China

Funds: China Postdoctoral Science Foundation（2016M602403;2019M652753）;The National Natural Science Foundation of China（11602082;11602229）

摘要

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.
- 边界元法 /
- 薄型结构 /
- 近奇异积分 /
- 距离变换 /
- 角度变换
Abstract: 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.
- boundary element method /
- thinwalled structure /
- nearly singular integral /
- distance transformation /
- angle transformation

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参考文献(26)

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角度-距离复合变换法消除边界积分方程近奇异性

doi: 10.21656/1000-0887.400229

作者简介:
周枫林(1986—)，男，副教授，博士（E-mail: zhoufl@hnu.edu.cn）;谢贵重（1983—），男，讲师，博士（通讯作者. E-mail: xieguizhong@126.com).

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

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留言板

角度-距离复合变换法消除边界积分方程近奇异性

doi: 10.21656/1000-0887.400229

作者简介: 周枫林(1986—)，男，副教授，博士（E-mail: zhoufl@hnu.edu.cn）;谢贵重（1983—），男，讲师，博士（通讯作者. E-mail: xieguizhong@126.com).

计量

出版历程

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

计量

出版历程

目录

作者简介:
周枫林(1986—)，男，副教授，博士（E-mail: zhoufl@hnu.edu.cn）;谢贵重（1983—），男，讲师，博士（通讯作者. E-mail: xieguizhong@126.com).