A New Integration Algorithm for Nearly Singular BIE Kernels

  • T. A. Cruse
  • R. Aithal


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]
$$C_{ij} u_j \left( P \right) + \iint {_{ < S > } T_{ij} \left({P,Q} \right)u_j \left( Q \right)dS\left( Q \right) - \iint {_{ < S > } U_{ij} \left( {P,Q} \right)t_j \left( Q \right)dS}\left( Q \right)}$$
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).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cruse, T. A., Boundary Element Analysis in Computational Fracture Mechanics, Kluwer Academic Publishers, The Netherlands (1988).MATHCrossRefGoogle Scholar
  2. 2.
    F. J. Rizzo and D. J. Shippy, An Advanced Boundary Integral Equation Method for Three-Dimensional Thermoelasticity, Int. J. Num. Meth. Eng. 11, 1753–1768 (1977).MATHCrossRefGoogle Scholar
  3. 3.
    Meng H. Lean and A. Wexler, Accurate Numerical Integration of Singular Boundary Element Kernels over Boundaries with Curvature, Int. J. Numer. Meth. Eng., 21, 211–228 (1985).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    M. H. Aliabadi, W. S. Hall, and T. G. Phemister, Taylor Expansions for Singular Kernels in the Boundary Element Method, Int. J. Numer. Meth. Eng., 21, 2221–2236 (1985).MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    M. Guiggiani and A. Gigante, A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method, submitted for publication.Google Scholar
  6. 6.
    T. A. Cruse, An Improved Boundary-Integral Equation Method for Three Dimensional Elastic Stress Analysis, Comp. & Struct., 4, 741–754 (1974).CrossRefGoogle Scholar
  7. 7.
    T. A. Cruse, Three-Dimensional Elastic Stress Analysis of a Fracture Specimen with an Edge Crack, Int. J. Fract. Mech., 7, 1–15 (1971).Google Scholar

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

Personalised recommendations