Efficient and accurate multi-layered elastostatic Green's functions via the bi-material Green's function

The three-dimensional elastostatic Green's functions for multi-layered half-spaces are expressed in terms of a cylindrical system of vector functions using the propagator matrix method. To obtain efficient and accurate results near the singularity at the interface between layers, the singularity extraction method is employed in the transform domain, based on the singular solutions for the bi-material full space expressed here in vector cylindrical function form. Numerical trials demonstrate that this approach improves on previous work, which relied on singularity extraction based on the well-known singular (Kelvin) solution for the homogenous full-space. A boundary element implementation illustrates the practical potential of this work to boundary value problems.