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BEM analysis of wave scattering in transversely isotropic solids. (English) Zbl 0932.74075
We develop a boundary element approach for wave propagation problems in transversely isotropic solids. The procedure is based on the well-known formulation for time-harmonic elasticity and a new version of a fundamental solution for transversely isotropic media. The fundamental solution is transformed to obtain new expressions which can be efficiently evaluated at any point. This fact allows for a drastic reduction of the computation time and makes possible the implementation of a general purpose three-dimensional quadratic element code. To show the simplicity and accuracy of the approach, the diffraction of waves by a spherical cavity and the interaction between two cavities in a boundless domain are studied.

74S15 Boundary element methods applied to problems in solid mechanics
74J20 Wave scattering in solid mechanics
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[1] and Diffraction of Elastic Waves in Dynamic Stress Concentrations, Crane-Russak, New York, 1973.
[2] and Boundary Element Methods in Elastodynamics, Unwin-Hyman, London, 1988.
[3] Boundary Elements in Dynamics, CMP and Elsevier Applied Science, Southampton and London, 1993.
[4] Graffi, Mem. Accad. Sci. Bologna 10 pp 103– (1946)
[5] Wheeler, Arch. Rational Mech. Anal. 31 pp 51– (1968)
[6] Buchwald, Proc. Roy. Soc. London A253 pp 563– (1959) · Zbl 0092.42304
[7] Lighthill, Philos. Trans. Roy. Soc. London A252 pp 397– (1960) · Zbl 0097.20806
[8] ?Elastic waves in anisotropic media?, in and (eds.), Progress in Solid Mechanics, vol. 2, North-Holland Publishing Company, Amsterdam, 1961, pp. 64-85.
[9] Crystal Acoustics, Holden-Day Inc., San Francisco, 1970.
[10] Elastic Wave Propagation in Transversely Isotropic Media, Martinus Nijhoff Publishers, The Hague, 1983.
[11] Tsvanskin, Izvestiya. Earth Phys. 25 pp 528– (1989)
[12] Burridge, Proc. Roy. Soc. London A440 pp 655– (1993) · Zbl 0793.73020
[13] Kazi-Aoual, Geophys. J. 39 pp 587– (1988)
[14] Zhu, J. Appl. Mech. 59 pp 587– (1992) · Zbl 0760.73006
[15] Wang, Proc. Roy. Soc. London A449 pp 441– (1995) · Zbl 0852.73011
[16] and ?3-D elastodynamic Green’s functions for BEM applications to anisotropic solids?, in and (eds.), Proc. IUTAM Symp. on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics, Kluwer Academic Publisher, The Netherlands, 1995, pp. 307-320. · Zbl 0882.73022
[17] Pan, J. Appl. Mech. 43 pp 608– (1976) · Zbl 0352.73016
[18] Wilson, Int. J. Numer. Meth. Engng. 12 pp 1383– (1978) · Zbl 0377.73054
[19] Application of the boundary element method to anisotropic crack problems, in and (eds.), Advances in Boundary Element Methods for Fracture Mechanics, CMP and Elsevier, Southampton and London, 1990, pp. 269-292.
[20] ?Numerical analysis of elastodynamic problems in transversely isotropic materials?, Ph.D. Thesis, Escuela Superior de Ingenieros, Universidad de Sevilla, Spain 1997.
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