Evaluation of singular integrals for anisotropic elastic boundary element analysis

Chyanbin Hwu, Han Bin Ko, Ting Hsiang Lo, Chia Wen Hsu

研究成果: Article

摘要

To improve the numerical evaluation of weakly singular integrals appearing in the boundary element method, a logarithmic Gaussian quadrature formula is usually suggested in the literature. In this formula the singular function is expressed in terms of the distance between source point and field point, which is a real variable. When an anisotropic elastic solid is considered, most of the existing fundamental solutions are written in terms of complex variables. When the problems with holes, cracks, inclusions, or interfaces are considered, to suit for the shape of the boundaries usually a mapping function is introduced and then the solutions are expressed in terms of mapped complex variables. To deal with the trouble induced by the complex variables, in this study through proper change of variables we develop a simple way to improve the evaluation of weakly singular integrals, especially for the problems of anisotropic elastic solids containing holes, cracks, inclusions, or interfaces. By simple matrix expansion, the proposed method is extended to the problems with piezoelectric or magneto-electro-elastic solids. By using the dual reciprocity method, the proposed method employed for the elastostatic fundamental solution can also be applied to the elastodynamic analysis.

原文English
頁(從 - 到)128-143
頁數16
期刊Applied Mathematical Modelling
81
DOIs
出版狀態Published - 2020 五月

    指紋

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

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