Journal
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
Volume 48, Issue -, Pages 32-42Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2014.07.004
Keywords
3D BEM; 2D nearly singular integrals; High-order geometry elements; Transformation; Elastostatics
Funding
- State Key Laboratory of Structural Analysis for Industrial Equipment [GZ1017]
- Natural Science Foundation of Shandong Province of China [ZR2010AZ003]
- Slovak Science and Technology Assistance Agency [APVV-0014-10]
- Slovak Grant Agency [VEGA-2/0011/13]
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This paper presents a general methodology for numerical evaluation of the nearly singular 2D integrals over the eight-node second-order quadrilateral geometry elements arising in 3D BEM. An accurate formula of distance between the source and the field point is proposed firstly. And then an extended form of the exponential transformation, which was firstly proposed by present author to regularize nearly singular integrals arising in 2D BEM, is developed to smooth out the rapid variation of the aforementioned formula of distance. Finally, several numerical examples involving boundary layer effect and thin body problems in 3D elastostatics are investigated to verify the proposed scheme, yielding very promising results. Moreover, it should be stressed that the proposed scheme is suitable for any high-order surface elements. (C) 2014 Elsevier Ltd. All rights reserved.
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