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Analytical derivation and numerical experiment of degenerate scale by using the degenerate kernel of the bipolar coordinates

机译:利用双极坐标的简并核进行简并尺度的解析推导和数值实验

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摘要

Degenerate scales of an eccentric annulus and an infinite plane with two identical circular holes in the boundary integral equation method (BIEM) are analytically derived and numerically implemented in this paper. To analytically study the degenerate scale of the BIE, the closed-form fundamental solution of the two-dimensional Laplace equation, In r, is expanded by a degenerate (separate) kernel in terms of the bipolar coordinates. It is proved that unit radius of the outer circle dominates the degenerate scale of eccentric annulus. An analytical formula of degenerate scale for the infinite plane with two identical circular boundaries was also derived at the first time. In addition, null fields of the domain and complementary domain for the ordinary and degenerate scales are both shown, respectively. Finally, comparison with available results and the BEM data are well done.
机译:本文对边界积分方程法(BIEM)中偏心环和具有两个相同圆孔的无限平面的简并尺度进行了解析推导,并进行了数值计算。为了分析研究BIE的简并尺度,将二维Laplace方程In r的闭式基本解由简并(独立)核根据双极坐标展开。事实证明,外圆的单位半径主导着偏心环的简并尺度。首次还导出了具有两个相同圆形边界的无限平面的退化尺度的解析公式。此外,分别显示了普通和简并标度的域和互补域的空字段。最后,与可用结果和BEM数据的比较做得很好。

著录项

  • 来源
    《Engineering analysis with boundary elements》 |2017年第12期|70-86|共17页
  • 作者单位

    Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan,Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung, Taiwan;

    Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan;

    Department of Civil Engineering, Tamkang University, New Taipei City, Taiwan;

  • 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

    Degenerate scale; Degenerate kernel; Bipolar coordinates; Eccentric annulus;

    机译:退化规模;退化的内核;双极坐标;偏心环;

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