An equivalent classical plate model of corrugated structures is derived using the variational asymptotic method. Starting from a thin shell theory, we carry out an asymptotic analysis of the strain energy in terms of the smallness of a single corrugation with respect to the characteristic length of macroscopic deformation of the corrugated structure. We obtained the complete set of analytical formulas for effective plate stiffnesses valid for both shallow and deep corrugations. These formulas can reproduce the well-known classical plate stiffnesses when the corrugated structure is degenerated to a ﬂat plate. The extension-bending coupling stiffnesses are obtained the first time. The complete set of relations are also derived for recovering the local ﬁelds of corrugated structures.
This paper gives the complete set of correct constants and recovery relations corresponding to the classical plate model for corrugated structures made of isotropic materials, concluding around 100 years of rich history on plate modeling of corrugated structures. Attached is a submitted version. The published version can be found at:
Ye, Z.; Berdichevsky, V.; and Yu, W.: "An Equivalent Plate Modeling of Corrugated Structures," International Journal of Solids and Structures,vol. 51, 2014, pp. 2073-2083.
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