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Computation of nearly singular integrals in 3D BEM

机译：3D BEM中几乎奇异积分的计算

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摘要

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.
机译：本文提出了一种通用方法，用于对3D BEM中出现的八节点二阶四边形几何元素上几乎奇异的2D积分进行数值评估。首先提出了源与场点之间距离的精确公式。然后，作者提出了一种扩展形式的指数变换，以平滑二维BEM中出现的奇异积分，以消除上述距离公式的快速变化。最后，研究了一些涉及边界层效应和3D弹性静力学中的薄体问题的数值示例，以验证所提出的方案，产生了非常有希望的结果。此外，应该强调的是，提出的方案适用于任何高阶表面元素。

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  • 来源
    《Engineering analysis with boundary elements》 |2014年第11期|32-42|共11页
  • 作者

    Yaoming Zhang; Xiaochao Li; Vladimir Sladek; Jan Sladek; Xiaowei Gao;

  • 作者单位

    Institute of Applied Mathematics, Shandong University of Technology, Zibo 255049, PR China,State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, PR China;

    Institute of Applied Mathematics, Shandong University of Technology, Zibo 255049, PR China;

    Slovak Academy of Sciences, Institute of Construction and Architecture, 84503 Bratislava, Slovakia;

    Slovak Academy of Sciences, Institute of Construction and Architecture, 84503 Bratislava, Slovakia;

    State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, PR China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    3D BEM; 2D nearly singular integrals; High-order geometry elements; Transformation; Elastostatics;

    机译：3D BEM;2D近似奇异积分;高阶几何元素;转型;静电抑制剂;

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