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A New Integration Algorithm for Nearly Singular BIE Kernels

  • T. A. Cruse
  • R. Aithal

Abstract

The boundary integral equation for the elasticity problem is written in terms of the boundary tractions tj and boundary displacements uj in the usual manner [1]
$$C_{ij} u_j \left( P \right) + \iint {_{ < S > } T_{ij} \left({P,Q} \right)u_j \left( Q \right)dS\left( Q \right) - \iint {_{ < S > } U_{ij} \left( {P,Q} \right)t_j \left( Q \right)dS}\left( Q \right)}$$
(1)
where < S(Q) > denotes the principal value of the integrals on the boundary surface. The points Q(y) and P(x) respectively denote the integration point and the source point, corresponding to the point of application of the point load influence function. The tractions and displacements for the point load solution are written as Tij(P,Q) and Uij(P,Q), respectively. The Cij matrix corresponds to the value of the jump in the first integral as the interior displacement evaluation point p(x) is taken to the boundary point P(x).

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References

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Copyright information

© Springer-Verlag Berlin, Heidelberg 1991

Authors and Affiliations

  • T. A. Cruse
    • 1
  • R. Aithal
    • 2
  1. 1.Vanderbilt UniversityNashvilleUSA
  2. 2.Southwest Research InstituteSan AntonioUSA

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