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3-D elastodynamic Green’s functions for BEM applications to anisotropic solids. (English) Zbl 0882.73022
Parker, D. F. (ed.) et al., IUTAM symposium on anisotropy, inhomogeneity and nonlinearity in solid mechanics. Proceedings of the IUTAM-ISIMM symposium, Nottingham, UK, August 30 - September 3, 1994. Dordrecht: Kluwer Academic Publishers. Solid Mech. Appl. 39, 307-320 (1995).
The paper deals with the BEM formulation for solution of three-dimensional elastodynamic problems for anisotropic solids using the Green’s function. General anisotropic but linearly elastic solids are considered. The authors obtain the Green’s functions in time domain by the use of Radon transform; solutions in the frequency domain follow directly by a subsequent application of Fourier transform. The Green’s functions are expressed in terms of surface integrals over a unit sphere, and a boundary integral equation for scattering of elastic waves is given with numerical implementation. The fundamental tractions are decomposed into static singular part (analytical expression) and dynamic regular part (with the need to carry out numerical integrations). Then the Cauchy principal value integrals together with free coefficients are eliminated from the formulation by using the Lachat-Watson technique. Numerical examples concern the scattering of elastic waves on a spherical cavity in an unbounded solid.
For the entire collection see [Zbl 0839.00015].

74J20 Wave scattering in solid mechanics
74S15 Boundary element methods applied to problems in solid mechanics
74E10 Anisotropy in solid mechanics