Skip to main content
SpringerLink
Log in

An Overview of Integration Methods for Hypersingular Boundary Integrals

  • Chapter
Boundary Elements XIII

Abstract

Several methods of analyzing the hypersingular gradient BIE have been developed recently. This paper is a review highlighting the numerous common aspects and several differences among the methods. Significant common aspects include (a) a regularizaron of constant and linear terms, (b) analysis of integration points near rather than on the surface, and (c) analysis of the neighborhood of the singular point rather than of individual elements.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P.K. Banerjee and R. Butterfield. Boundary Element Methods in Engineering Science. McGraw Hill, 1981.

    MATH  Google Scholar 

  2. C.A. Brebbia and X.Y. Dominguez. Boundary Elements: An Introductory Course. Computational Mechanics Publications (McGraw-Hill), 1988.

    Google Scholar 

  3. G.E. Blandford, A.R. Ingraffea, and J.A. Liggett. Two dimensional stress intensity factor computations using the boundary element method. International Journal for Numerical Methods in Engineering, 17:387–404, 1981.

    Article  MATH  Google Scholar 

  4. C.A. Brebbia, J.C.F. Telles, and L.C. Wrobel. Boundary Element Techniques — Theory and Applications in Engineering. Springer-Verlag, 1984.

    MATH  Google Scholar 

  5. H.D. Bui. An integral equation for solving the problem of plane crack of arbitrary shape. J. Mech. Physics and Solids, 25:23–39, 1977.

    MathSciNet  Google Scholar 

  6. T.A. Cruse and G. Novati. Traction bie formulations and applications to non-planar and multiple cracks. In 22nd ASTM Conference on Fracture Mechanics. ASTM, 1990.

    Google Scholar 

  7. T.A. Cruse. Numerical solutions in three dimensional elastostatics. International Journal of Solids and Structures, 5:1259–1274, 1969.

    Article  MATH  Google Scholar 

  8. T.A. Cruse and W. Van Buren. Three-dimensional elastic stress analysis of a fracture specimen with an edge crack. International Journal of Fracture Mechanics, 7:1–15, 1971.

    Article  Google Scholar 

  9. A.P. Calderon and Zygmond. On the existence of certain singular integrals. Acta Mathematica, 88:85–139, 1952.

    Article  MathSciNet  MATH  Google Scholar 

  10. L.J. Gray and E.D. Lutz. On the treatment of corners in the boundary element method. Journal of Computational and Applied Mathematics, 32:369–386, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  11. N. Ghosh and S. Muhkerjee. A new boundary element method formulation for three dimensional problems in linear elasticity. Acta Medianica, 67:107–119, 1987.

    Article  MATH  Google Scholar 

  12. L.J. Gray, Luiz F. Martha, and A.R. Ingraffea. Hypersingular integrals in boundary element fracture analysis. International Journal for Numerical Methods in Engineering, 29:1135–1158, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  13. L.J. Gray. Boundary element method for regions with thin internal cavities. Engineering Analysis, 6:180–184, 1989.

    Google Scholar 

  14. N.I. Ioakimidis and M.S. Pitta. Remarks on the gaussian quadrature rule for finite-part integrals with a second-order singularity. Computer Methods in Applied Mechanics and Engineering, 69:325–343, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  15. M.A. Jaswon. Integral equation methods in potential theory, i. Proceedings of the Royal Society, 275:23–32, 1963.

    Article  MathSciNet  MATH  Google Scholar 

  16. Z.H. Jia, D.J. Shippy, and F.J. Rizzo. Boundary-element analysis of wave scattering from cracks. Communications in Applied Numerical Methods, 6:591–601, November 1990.

    Article  Google Scholar 

  17. L.W. Krishnasamy, L.W. Schmerr, T.J. Rudolphi, and F.J. Rizzo. Hypersingular boundary integral equations: Some applications in acoustic and elastic wave scattering. Journal of Applied Mechanics, 57:404–414, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  18. V.D. Kupradze. Potential Methods in the Theory of Elasticity. D. Davey, 1965.

    MATH  Google Scholar 

  19. E.D. Lutz. Numerical Methods for Hypersingular and Near-Singular Boundary Integrals in Fracture Mechanics. PhD thesis, Cornell University, Ithaca, NY, USA, 1991.

    Google Scholar 

  20. J.C. Lachet and J.O. Watson. Effictive numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics. International Journal for Numerical Methods in Engineering, 10:991–1005, 1976.

    Article  Google Scholar 

  21. S.G. Mikhlin. Multidimensional Singular Integrals and Singular Integral Equations. Pergamon Press, 1965.

    MATH  Google Scholar 

  22. S.G. Mikhlin and S. Proessdorf. Singular Integral Operators. Springer-Verlag, 1980.

    Google Scholar 

  23. E.Z. Polch, T.A. Cruse, and C.-J. Huang. Traction bie solutions for flat cracks. Computational Mechanics, 2:253–267, 1987.

    Article  MATH  Google Scholar 

  24. M. Rezayat and T. Burton. A boundary-integral formulation for complex three-dimensional geometries. International Journal for Numerical Methods in Engineering, 29:263–273, 1990.

    Article  MATH  Google Scholar 

  25. F.J. Rizzo. An integral equation approach to boundary value problems of classical elastostatics. Quarterly of Applied Mathemathics, 25:83–95, 1969.

    Google Scholar 

  26. J. Weaver. Three dimensionial crack analysis. International Journal of Solids and Structures, 13:321–330, 1977.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 486 Engineering and Theory Center, Cornell University, Ithaca, NY, 14850, USA

    E. Lutz

  2. Mathematical Sciences Section, Oak Ridge National Labs, Oak Ridge, TN, 37831, USA

    L. J. Gray

  3. Cornell University, 317 Hollister Hall, Ithaca, NY, 14850, USA

    A. R. Ingraffea

Authors
  1. E. Lutz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. J. Gray
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. R. Ingraffea
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Wessex Institute of Technology, Ashurst Lodge, Ashurst, Southampton, SO4 2AA, UK

    C. A. Brebbia

  2. School of Civil Engineering, Oklahoma State University, 314 Engineering South, Stillwater, OK, 74078, USA

    G. S. Gipson

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Computational Mechanics Publications

About this chapter

Cite this chapter

Lutz, E., Gray, L.J., Ingraffea, A.R. (1991). An Overview of Integration Methods for Hypersingular Boundary Integrals. In: Brebbia, C.A., Gipson, G.S. (eds) Boundary Elements XIII. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3696-9_72

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3696-9_72

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-85166-696-6

  • Online ISBN: 978-94-011-3696-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation