Green's Function for Anisotropic-Isotropic Materials Using Stroh Formalism

Abstract

In the present paper, the three-dimensional and two-dimensional Green's functions due to point and line forces in anisotropic-isotropic elastic bimaterials are derived by using generalized Stroh formalism and two-dimensional Fourier transforms. When the Stroh formalism is applied to isotropic materials, the eigen matrix derived from equilibrium equations yields a triple root of i (i : imaginary unit), and then an independent eigen vector corresponding to the eigen value can not be determined. In the present paper, the eigen vectors for the triple root are determined and general expressions for displacement and stress are derived. The unknown vectors involved in the expressions are determined using boundary conditions for an interface and at a loading point. Numerical examples are given to demonstrate the validity of the present formulation of three-dimensional point-force Green's functions. The Green's functions include the Kelvin solutions for isotropic materials in two- and three- dimensional infinite domains and Mindlin solutions for isotropic material in three-dimensional half-domain.