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Numerical integration of singularities in meshless implementation of local boundary integral equations

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Abstract

 The necessity of a special treatment of the numerical integration of the boundary integrals with singular kernels is revealed for meshless implementation of the local boundary integral equations in linear elasticity. Combining the direct limit approach for Cauchy principal value integrals with an optimal transformation of the integration variable, the singular integrands are recasted into smooth functions, which can be integrated by standard quadratures of the numerical integration with sufficient accuracy. The proposed technique exhibits numerical stability in contrast to the direct integration by standard Gauss quadrature.

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Authors and Affiliations

  1. Institute of Construction and Architecture, Slovak Academy of Sciences, 842 20 Bratislava, Slovak Republic, , , , ,

    V. Sladek & J. Sladek

  2. Center for Aerospace Research & Education, 48-121, Engineering IV, University of California at Los Angeles, Los Angeles, CA 90024, USA, , , , , , US

    S. N. Atluri

  3. Department of Mathematical Analysis, University of Gent, Galglaan 2, B – 9000 Gent, Belgium, , , , , , BE

    R. Van Keer

Authors
  1. V. Sladek
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  2. J. Sladek
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  3. S. N. Atluri
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  4. R. Van Keer
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Received 12 August 1999

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Sladek, V., Sladek, J., Atluri, S. et al. Numerical integration of singularities in meshless implementation of local boundary integral equations. Computational Mechanics 25, 394–403 (2000). https://doi.org/10.1007/s004660050486

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  • DOI: https://doi.org/10.1007/s004660050486

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