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# Calculation of Nearly Singular Boundary Element Integrals in Thin Structures Using an Improved Exponential Transformation

Guizhong Xie1, Jianming Zhang1,2, Cheng Huang1, Chenjun Lu1, Guangyao Li1

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China.
Corresponding author. Tel:+86-731-88823061; Fax:+86-731-88823051; Email: zhangjm@hnu.edu.cn

Computer Modeling in Engineering & Sciences 2013, 94(2), 139-157. https://doi.org/10.3970/cmes.2013.094.139

## Abstract

In this work, an improved exponential transformation is presented for nearly singular boundary element integrals in problems of thin structures. Accurate evaluation of nearly singular integrals is an important issue in the implementation of boundary element method (BEM) for thin structures. In this paper, the exponential transformation, which was firstly developed to evaluate nearly singular integrals arising in 2D BEM, is extended into 3D BEM to deal with nearly singular integrals. Firstly, a novel (α,β) coordinate system is introduced. Then, the conventional distance function is modified into a new form in (α,β) coordinate system. Based on the refined distance function, finally, an improved exponential transformation is employed in the new coordinate system. Furthermore, to perform integrations on irregular elements, an adaptive integration scheme considering both the shape of element and the projection point associated with the improved transformation is proposed. Numerical examples are presented to verify the proposed method. Results demonstrate the accuracy and efficiency of our method. Moreover, the accuracy of our method is less sensitive to the position of the projection point than that of the traditional methods.

## Keywords

APA Style
Xie, G., Zhang, J., Huang, C., Lu, C., Li, G. (2013). Calculation of nearly singular boundary element integrals in thin structures using an improved exponential transformation. Computer Modeling in Engineering & Sciences, 94(2), 139-157. https://doi.org/10.3970/cmes.2013.094.139
Vancouver Style
Xie G, Zhang J, Huang C, Lu C, Li G. Calculation of nearly singular boundary element integrals in thin structures using an improved exponential transformation. Comput Model Eng Sci. 2013;94(2):139-157 https://doi.org/10.3970/cmes.2013.094.139
IEEE Style
G. Xie, J. Zhang, C. Huang, C. Lu, and G. Li "Calculation of Nearly Singular Boundary Element Integrals in Thin Structures Using an Improved Exponential Transformation," Comput. Model. Eng. Sci., vol. 94, no. 2, pp. 139-157. 2013. https://doi.org/10.3970/cmes.2013.094.139

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