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Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates

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In a thin isotropic homogeneous three-dimensional plate of thickness h, we consider the limit passage of elastic fields as h → +0. It is assumed that the connected component Γ N of the boundary of the median cross section ω is a broken line with links of length ah, where a > 0 is a fixed parameter. We consider the Lamé equations with the Neumann condition (a free surface) on the plate bases, the Dirichlet condition (a rigidly clamped surface) on a smooth part, and some linear contact conditions on a ribbed part of the lateral surface. For the solution to the boundary value problem we obtain an asymptotic expansion with different boundary layers. In the two-dimensional model, new boundary conditions, different from the contact ones, arise on the limit smooth contour Γ0 , thereby for the spatial elasticity problem, we confirm the Babuška paradox caused by linear boundary conditions on the plate edge, but not unilateral constraints of Signorini type. Bibliography: 42 titles. Illustrations: 5 figures.

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Correspondence to S. A. Nazarov.

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Translated from Problemy Matematicheskogo Analiza 81, August 2015, pp. 55–80.

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Nazarov, S.A., Chechkin, G.A. Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates. J Math Sci 210, 399–428 (2015). https://doi.org/10.1007/s10958-015-2573-4

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