| 曲面单元上超奇性与近超奇性边界积分数值计算的几何变换法 |
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| 引用本文： | 马杭.曲面单元上超奇性与近超奇性边界积分数值计算的几何变换法[J].上海大学学报(英文版),2002,6(2):101-110. |
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| 作者姓名： | 马杭 |
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| 作者单位： | DepartmentofMechanics,collegeofSciences,ShanghaiUniversity,Shanghai200436,China |
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| 基金项目： | ProjectsupportedbytheScienceFoundationofShanghaiMunic ipalCommissionofEducation ( 2 0 0 0A13) |
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| 摘 要： | With the aid of the properties of the hypersingular kernels,a geometric conversion approach was presented in this paper.The conversion leads to a general approach for the accurate and reliable numerical evaluation of the hypersingular surface boundary integrals encountered in a variety of applications with boundary element method.Based on the conversion,the hypersingularity in the boundary integrals could be lowered by one order,resulting in the simplification of the computer code.Moreover,an integral transformation was introduced to damp out the nearly singular behavior of the kernels by the distance function defined in the local polar coordinate system for the nearly hypersingular case.The approach is simple to use,which can be inserted readily to computer code,thus getting rid of the dull routine deduction of formulae before the numerical implementatins,as the expressions of these kernels are in general complicated.The numerical examples were gien in three-dimensional elasticity,verifying the effectiveness of the proposed approach,which makes it possible to observe numerically the behavior of the boundary integral values with hypersingular kernels across the boundary.
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| 关 键 词： | 边界积分方程 曲面 奇异性数字计算 几何变换 |
| 收稿时间： | 30 August 2001 |
Geometric conversion approach for the numerical evaluation of hypersingular and nearly hypersingular boundary integrals over curved surface boundary elements |
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| Hang Ma Ph. D..Geometric conversion approach for the numerical evaluation of hypersingular and nearly hypersingular boundary integrals over curved surface boundary elements[J].Journal of Shanghai University(English Edition),2002,6(2):101-110. |
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| Authors: | Hang Ma Ph D |
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| Institution: | Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200436, China |
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| Abstract: | With the aid of the properties of the hypersingular kernels, a geometric conversion approach was presented in this paper. The conversion leads to a general approach for the accurate and reliable numerical evaluation of the hypersingular surface boundary integrals encountered in a variety of applications with boundary element method. Based on the conversion, the hypersingularity in the boundary integrals could be lowered by one order, resulting in the simplification of the computer code. Moreover, an integral transformation was introduced to damp out the nearly singular behavior of the kernels by the distance function defined in the local polar coordinate system for the nearly hypersingular case. The approach is simple to use, which can be inserted readily to computer code, thus getting rid of the dull routine deduction of formulae before the numerical implementations, as the expressions of these kernels are in general complicated. The numerical examples were given in three dimensional elasticity, verifying the effectiveness of the proposed approach, which makes it possible to observe numerically the behavior of the boundary integral values with hypersingular kernels across the boundary. |
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| Keywords: | boundary element method numerical evaluation hypersingular boundary integral nearly hypersingular boundary integral geometric conversion |
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