Journal of Mathematical Sciences

, Volume 210, Issue 4, pp 399–428 | Cite as

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


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.


Dirichlet Condition Unilateral Constraint Rigid Displacement Asymptotic Term Limit Passage 
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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.St. Petersburg State University St. Petersburg State Polytechnical University, Institute for Problems in Mechanical Engineering RASSt. PetersburgRussia
  2. 2.Lomonosov Moscow State UniversityMoscowRussia

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