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Elastic Potentials in BIE Formulations

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Time-dependent and Vibration Problems

Part of the book series: Topics in Boundary Element Research ((TBOU,volume 2))

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Abstract

This chapter is an expansion of a paper, Shaw [1], given at a recent BEM meeting. The aim of this work is to examine some of the several boundary integral equation formulations available for problems of linear elasticity. In particular, emphasis will be placed on a comparison of the advantages and disadvantages of the widely used displacement-traction formulation, e.g. Cruse and Rizzo [2], based on reciprocity theorems of elasticity and the displacement potential formulations, e.g. Banaugh and Goldsmith [3], which are actually introduced earlier, at least for elastodynamic problems.

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References

  1. Shaw, R.P., Alternative solution methods in elastic BIE problems. Presented at the 6th BEM conference, Q.E.II, July, 1984

    Google Scholar 

  2. Cruse, T.A. and Rizzo, F.J., A direct formulation and numerical solution of the general transient elastodynamic problem, I. J. Math. Anal. Appl. 22, 244–259, 1968

    Article  MATH  Google Scholar 

  3. Banaugh, R.P. and Goldsmith, W., Diffraction of steady elastic waves by surfaces of arbitrary shape. J. Appl. Mech. 30, 589–597, 1963

    Article  ADS  MATH  Google Scholar 

  4. Friedman, M.B. and Shaw, R.P., Diffraction of a plane shock wave by an arbitrary rigid obstacle. J. Appl. Mech. 29, 40–46, 1962

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Cole, D.M., Kosloff, D.D., and Minster, J.B., A numerical boundary integral equation for elastodynamics, I. Bull. Seis. Soc. Amer. 68, 1331–1357, 1978

    Google Scholar 

  6. Miklowitz, J., The Theory of Elastic Waves and Waveguides. North-Holland Press, N.Y., 1978

    Google Scholar 

  7. Achenbach, J.D., Wave Propagation in Elastic Solids. North-Holland Press, N.Y., 1975

    Google Scholar 

  8. Karabalis, D.L. and Beskos, D.E., Dynamic response of 3D rigid surface foundations by the time domain boundary element method. Earth Engr. Struc. Dyn. 12, 73–94, 1984

    Article  Google Scholar 

  9. Manolis, G.D. and Beskos, D.E., Dynamic stress concentration studies by the integral equation method. Proc. 2nd Int. Symp. Innovative Num. Anal., ed. Shaw, R.P., et al., Univ. of Va. Press, 459–463, 1980

    Google Scholar 

  10. Kobayashi, S. and Nishimura, N., Transient analysis of tunnels and caverns of arbitrary shape due to travelling waves. Developments in Boundary Element Methods. 2, ed. Banerjee, P.K. and Shaw, R.P., Chap. 7, App. Sci. Pub., London, 1982

    Google Scholar 

  11. Love, A.E.H., The Mathematical Theory of Elasticity. 4th ed., Dover Pub., N.Y., 1944

    MATH  Google Scholar 

  12. Shaw, R.P., Boundary integral equation methods applied to wave problems. Develop-ments in Boundary Element Methods. 1, ed. Banerjee, P.K. and Butterfield, R., Chap. 6, App. Sci. Pub., London, 1980

    Google Scholar 

  13. Banaugh, R.P., Application of integral representations of displacement potentials in elastodynamics. Bull. Seis. Soc. Amer. 54, 1073–1086, 1964

    Google Scholar 

  14. Brebbia, C.A., The Boundary Element Method for Engineers. Pentech Press, London, 1978

    Google Scholar 

  15. Sternberg, E., On the integration of the equations of motion in the classical theory of elasticity. Arch. Rat. Mech. Anal. 6, 34–50, 1960

    Article  MathSciNet  MATH  Google Scholar 

  16. Kircher, T.A. and Kaul, R.K., On the concept of generalized potentials in the classical theory of elasticity. FEAS Rep. No. DA8325075, SUNY at Buffalo, 1983

    Google Scholar 

  17. Ghorieshi, A.J. and Kaul, R.K., On the exact solution of problems in elastostatic in terms of harmonic functions. FEAS Rep. (unnumbered ), SUNY at Buffalo, 1984

    Google Scholar 

  18. Saada, A.S., Elasticity; Theory and Applications. Pergamon Press, N.Y., 1974

    MATH  Google Scholar 

  19. Shaw, R.P. and Kaul, R.K., The use of harmonic potentials in elastostatic BIE formulations. In preparation, 1985

    Google Scholar 

  20. Chertock, G., Convergence of iterative solutions to integral equations for sound radiation. Quar. Appl. Math. 26, 268–271, 1968

    MATH  Google Scholar 

  21. Shaw, R.P., Time harmonic acoustic radiation from a submerged elastic shell defined by nonconcentric circular cylinders. J. Acous. Soc. Amer. 64, 311–317, 1978

    Article  ADS  MATH  Google Scholar 

  22. Shaw, R.P., Elastic plate vibrations by boundary integral equations; part I — Infinite plates. Res. Mech. 4, 83–88, 1982

    Google Scholar 

  23. Sharma, D.L., Scattering of steady elastic waves by surfaces of arbitrary shape. Bull. Seis. Soc. Amer. 57, 795–812, 1967

    Google Scholar 

  24. Manolis, G.D., A comparative study on three boundary element method approaches to problems in elastodynamics. Int. J. Num. Meth. Eng. 19, 73–91, 1983

    Article  MATH  Google Scholar 

  25. BEASY — A Boundary Element Method Code. Computational Mechanics Centre, Ashurst Lodge, Ashurst, U.K

    Google Scholar 

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© 1985 Springer-Verlag Berlin Heidelberg

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Shaw, R.P. (1985). Elastic Potentials in BIE Formulations. In: Brebbia, C.A. (eds) Time-dependent and Vibration Problems. Topics in Boundary Element Research, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-29651-6_2

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  • DOI: https://doi.org/10.1007/978-3-662-29651-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-28142-0

  • Online ISBN: 978-3-662-29651-6

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