Three-dimensional Green's functions in anisotropic trimaterials

Abstract

In this paper, three-dimensional Green’s functions for anisotropic bimaterials are studied based on Stroh formalism and two-dimensional Fourier transforms. Although the Green’s functions can be expressed exactly in the Fourier transform domain, it is diAcult to obtain the explicit expressions of the Green’s functions in the physical domain due to the general anisotropy of the material and a geometry plane involved. Utilizing Fourier inverse transform in the polar coordinate and combining with Mindlin’s superposition method, the physical-domain bimaterial Green’s functions are derived as a sum of a full-space Green’s function and a complementary part. While the full-space Green’s function is in an explicit form, the complementary part is expressed in terms of simple regular line-integrals over [0, 2pa that are suitable for standard numerical integration. Furthermore, the present bimaterial Green’s functions can be reduced to the special cases such as half-space, surface, interfacial, and full-space Green’s functions. Numerical examples are given for both half-space and bimaterial cases with isotropic, transversely isotropic, and anisotropic material properties to verify the applicability of the technique. For the half-space case with isotropic or transversely isotropic material properties, the Green’s function solutions are in excellent agreement with the existing analytical solutions. For anisotropic half-space and bimaterial cases, numerical results show the strong dependence of the Green’s functions on the material properties. 7 2000 Elsevier Science Ltd. All rights reserved.