Elastic layers with varying dilative eigenstrains through the thickness were concerned. A general procedure was proposed for the analysis of such layers under arbitrary loads. The study is based on the state_space method and an asymptotic expansion technique. When the external loads are uniform, the expansion terminates after some leading terms, and an explicit representation for the mechanical field in a layer is obtained. This representation relies only on the displacement components of the mid_plane, which are governed by a set of two_dimensional differential equations similar to those in the classical plate theory. Consequently, obtaining the solution to the two_dimensional equations immediately gives the three_dimensional responses of the layer. As an illustrative example, a clamped elliptical layer under a uniformly distributed transverse load is analyzed in detail.
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