Computationally efficient representation for elastostatic and elastodynamic Green’s functions for anisotropic solids

Abstract

A computationally efficient representation of the three-dimensional elastostatic and elastodynamic Green’s functions for anisotropic solids is derived by solving the Christoffel equation in terms of delta functions. The representation is also applicable to other wave equations. The method is applied to calculate the transient and the static displacement field due to a point source in infinite and semi-infinite anisotropic cubic solids. For elastodynamic calculations in anisotropic solids, our representation saves the computational time by a factor of about 1000 over the conventional Fourier-Laplace representation. In the elastostatic case, the computational efficiency of our method is much more than the conventional Fourier representation but comparable to the methods of Barnett and Barnett and Lothe in specific cases.