Abstract
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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Contributed by LIU Ren-huai
Biographies: HE Ling-hui (1964}), Professor, Doctor (E-mail: lhhe@ustc.edu.cn); LIU Ren-huai (1940}), Professor, Academician of Chinese Academy of Engineering (E-mail: lrh@jnu.edu.cn)
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Ling-hui, H., Chee-wah, L. & Ren-huai, L. Analysis of elastic layers with dilative eigenstrains varying through the thickness. Appl Math Mech 24, 997–1008 (2003). https://doi.org/10.1007/BF02437632
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DOI: https://doi.org/10.1007/BF02437632