An Iterated Sinh-Sigmoidal Combined Transformation Method for Calculating Nearly Singular Integrals of Boundary Elements

LIU Jing; YAO Qishui; YANG Wen; ZHOU Fenglin; YU Jianghong

doi:10.21656/1000-0887.410167

Volume 42 Issue 4

Apr. 2021

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Article Navigation > Applied Mathematics and Mechanics > 2021 > 42(4): 385-393

LIU Jing, YAO Qishui, YANG Wen, ZHOU Fenglin, YU Jianghong. An Iterated Sinh-Sigmoidal Combined Transformation Method for Calculating Nearly Singular Integrals of Boundary Elements[J]. Applied Mathematics and Mechanics, 2021, 42(4): 385-393. doi: 10.21656/1000-0887.410167

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An Iterated Sinh-Sigmoidal Combined Transformation Method for Calculating Nearly Singular Integrals of Boundary Elements

doi: 10.21656/1000-0887.410167

¹School of Mechanical Engineering, Hunan University of Technology,Zhuzhou, Hunan 412007, P.R.China
²School of Rail Transit Rolling Stock, Hunan Railway Professional Technology College, Zhuzhou, Hunan 412001, P.R.China

Funds: The National Natural Science Foundation of China（11602082）

Received Date: 2020-06-10
Rev Recd Date: 2020-07-17
Publish Date: 2021-04-01

Abstract

Abstract

Accurate and effective elimination of the near singularity of integrals is the primary problem in engineering application of 3D BEM. Nearly singular integrals will appear when the distance between source points and the triangle integral element approaches zero indefinitely. The shape of the integral element and the position of the projection points are both important factors influencing the computation accuracy of nearly singular integrals. Most of the existing nonlinear transformation methods only focus on the near singularity of integrals in the radial direction, ignoring the angular direction and the shape of triangular integral elements, so the calculation accuracy is always unsatisfactory and very sensitive to the shape of the integral elements of subtriangles in the case of projection points near the boundary. An improved iterated sinhsigmoidal combined transformation method based on the adaptive partitioning technology and different coordinate transformations was proposed to eliminate the near singularity of integrals in radial and angular directions respectively, which can greatly reduce the calculation scale while ensuring the calculation accuracy. Numerical examples were presented to verify the proposed method.
- nearly singular integral,
- different coordinate transformations,
- adaptive partitioning technology,
- combined transformation method

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References(16)

References

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