Elasticity of multilayers: Properties of the propagator matrix and some applications

The elasticity of generalized plane strain is written in terms of a first-o rder matrix differential equation in six variables (the components of the d isplacement and the stress function vector). The approach holds for general elastic anisotropy and provides a unified analytical description of elasti c fields in layered, stratified, or graded media. The theory is formulated in terms of a propagator matrix. An analysis of its general properties is p resented. In particular, the decomposition of this matrix into two parts wi th different behavior at too in Fourier space is explicitly found. This all ows one to obtain analytically the Green's functions for a series of bounda ry-value problems in anisotropic inhomogeneous media of infinite extent.