Three-Dimensional Green's Functions of Steady-State Motion in Anisotropic Half-Spaces and Bimaterials
B. Yang, E Pan, Vinod Tewary
Three-dimensional Green's functions (GFs) of steady-motion in linear anisotropic elastic half-space and bimaterials are derived within the framework of generalized Stroh formalism and two-dimensional Fourier transforms. While the methodology may be extened to cope with arbitrary velocity, the present formulation is limited to the subsonic case where the sextic equation has six complex eigenvalues. If the source and field points reside in the same material, the GF is expresed in two parts: a singular part that corresponds to the infinite-space GF, and a complementary part that corresponds to the reflective effect of the interface in the bimaterial case and of the free surface in the half-space case. The singular part in the physical domain is calculated analytically by applying the Radon transform and the residue theorem. If the source and field points reside in different materials (in the bimaterial case), the GF is a one-term solution. The physical counter parts of the complementary part in te half-space case of the one-term solution in the bimaterial case are derived as a one-dimensional integral by analytically carrying out the integration along the radial direction in the Fourier-inverse transform. When the source and field points are both on the interface in the bimaterial case on the surface in the half-space case, singularities appear in the Fourier-inverse transform of the GF. These singularities are treated explicitly using a method proposed recently by the authors. Numerical examples are presented to demonstrate the signicant influence of the wave velocity on the stress fields, which could be of interests to various engineering problems related to steady-state motion. Furthermore, these GFs are required in the steady-state boundary-integral equations where material anisotropy is significant.
anisotropy, elastodynamics, generalized Stroh formalism, steady-state motion, three-dimensional Green's function
, Pan, E.
and Tewary, V.
Three-Dimensional Green's Functions of Steady-State Motion in Anisotropic Half-Spaces and Bimaterials, Engineering Analysis With Boundary Elements, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=851343
(Accessed May 30, 2023)