HE Ling-hui, LIM Chee-wah, LIU Ren-huai. Analysis of Elastic Layers with Dilative Eigenstrains Varying Through the Thickness[J]. Applied Mathematics and Mechanics, 2003, 24(9): 881-891.
 Citation: HE Ling-hui, LIM Chee-wah, LIU Ren-huai. Analysis of Elastic Layers with Dilative Eigenstrains Varying Through the Thickness[J]. Applied Mathematics and Mechanics, 2003, 24(9): 881-891.

# Analysis of Elastic Layers with Dilative Eigenstrains Varying Through the Thickness

• Rev Recd Date: 2003-04-22
• Publish Date: 2003-09-15
• 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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