The elasticity of generalized plane strain is written in terms of a first-order matrix differential equation in six variables (the components of the displacement and the stress function vector). The approach holds for general elastic anisotropy and provides a unified analytical description of elastic fields in layered, stratified, or graded media. The theory is formulated in terms of a propagator matrix. An analysis of its general properties is presented. In particular, the decomposition of this matrix into two parts with different behavior at ±∞ in Fourier space is explicitly found. This allows one to obtain analytically the Green's functions for a series of boundary-value problems in anisotropic inhomogeneous media of infinite extent.
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