Time-Harmonic Elastic-Wave Scattering: The Role of Hypersingular Boundary Integral Equations

  • G. Krishnasamy
  • F. J. Rizzo
Conference paper

Summary

Some numerical data for scattering of elastic waves from cracks are presented using a hypersingular boundary integral formula. Then it is shown how the appropriate hypersingular formulas, needed for a formulation for elastodynamic scattering from any void shape, valid at all frequencies, may be derived from the hypersingular formula for cracks.

Keywords

Elastic Wave Boundary Element Method Boundary Integral Equation Penny Shaped Crack Void Model 
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References

  1. 1.
    Cruse, T. A., Van Buren, W.: Three-dimensional elastic stress analysis of fracture specimen with an edge crack. Int. J. Fracture Mech. 7 (1971) 1–15.Google Scholar
  2. 2.
    Rizzo, F. J., Shippy, D. J., Rezayat, M.: A boundary integral equation method for radiation and scattering of elastic waves in three dimensions. International Journal for Numerical Methods in Engineering 21 (1985) 115–129.ADSCrossRefGoogle Scholar
  3. 3.
    Schafbuch, P. J., Thompson, R. Bruce, Rizzo, F. J.: Application of the boundary element method to elastic wave scattering by irregular defects. To appear in J. of Nondestructive Evaluation.Google Scholar
  4. 4.
    Krishnasamy, G., Schmerr, L. W., Rudolphi, T. J., Rizzo, F.J.: Hypersingular boundary integral equations: Some applications in acoustic and elastic wave scattering. ASME J. of Appl. Mech. 57 (1990) 404–414.MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Gray, L. J., Martha, Luiz F., Ingraffea, A. R.: Hypersingular integrals in boundary element fracture analysis. Int. J. of Num. Meth. in Engg. 29 (1990) 1135–1158.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Polch, E. Z., Cruse, T. A., Huang, C. J.: Traction BIE solutions for flat cracks. Comput. Mech. 2 (1987) 253–267.MATHCrossRefGoogle Scholar
  7. 7.
    Burton, A. J., Miller, G. F.: The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proc. Roy. Soc. Lond. A 323 (1971) 201–210.MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    Martin, P. A.: Identification of irregular frequencies in simple direct integral-equation methods for scattering by homogeneous inclusions. To appear in Wave Motion (1989).Google Scholar
  9. 9.
    Gonsalves, I. R., Shippy, D. J., Rizzo, F. J.: The direct boundary integral equation method for the three-dimensional elastodynamic transmission problem. To appear in Computers and Mathematics with Applications.Google Scholar
  10. 10.
    Kutt, H. R.: The numerical evaluation of principal value integrals by finite-part integration. Numer. Math. 24 (1975) 20–210.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Chien, C. C., Rajiyah, H., Atluri, S. N.: An effective method for solving the hypersingular integral equations in 3-D acoustics. J. Acoust. Soc. Am. 88(2) (1990) 918–936.MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Liu, Y., Rudolphi, T. J.: Some identities for fundamental solutions and their applications to non-singular boundary element formulations. To appear in J. Engg. Analysis.Google Scholar
  13. 13.
    Jones, D. S.: Boundary integrals in elastodynamics, IMA J. Appl. Math. 34(1) (1985) 83–97.MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Budreck, D. E., Achenbach, J. D.: Scattering from three-dimensional planar cracks by the boundary integral equation method. ASME J. of Appl. Mech. 55 (1988) 405–411.ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1991

Authors and Affiliations

  • G. Krishnasamy
    • 1
  • F. J. Rizzo
    • 1
  1. 1.Department of Theoretical and Applied MechanicsUniversity of IllinoisUrbanaUSA

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