Implementation of sinh method in integration space for boundary integrals with near singularity in potential problems

Abstract

As a widely used numerical method, boundary element method (BEM) is efficient for computer aided engineering (CAE). However, boundary integrals with near singularity need to be calculated accurately and efficiently to implement BEM for CAE analysis on thin bodies successfully. In this paper, the distance in the denominator of the fundamental solution is first designed as an equivalent form using approximate expansion and the original sinh method can be revised into a new form considering the minimum distance and the approximate expansion. Second, the acquisition of the projection point by Newton-Raphson method is introduced. We acquire the nearest point between the source point and element edge by solving a cubic equation if the location of the projection point is outside the element, where boundary integrals with near singularity appear. Finally, the subtriangles of the local coordinate space are mapped into the integration space and the sinh method is applied in the integration space. The revised sinh method can be directly performed in the integration element. A verification test of our method is proposed. Results demonstrate that our method is effective for regularizing the boundary integrals with near singularity.

Keywords

computer aided engineering (CAE) / boundary element method (BEM) / near singularity / sinh method / coordinate transformation / integration space

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11472102 and 51476149), the Research Found for the Doctoral Program of Zhengzhou University of Light Industry, Educational Commission of Henan Province (Grant Nos. 15A460002 and 15A460037), and Xi’an Jiaotong University State Key Laboratory for Manufacturing Systems Engineering (Grant No. sklms2015012).

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2016 Higher Education Press and Springer-Verlag Berlin Heidelberg