On the justification of plate theories in linear elasticity theory using exponential decay estimates
type: Item
instance of: scholarly article
title: On the justification of plate theories in linear elasticity theory using exponential decay estimates
zbMATH Open document ID: 0830.73035
DOI: 10.1007/BF00042497
author: Alexander Mielke
published in: Journal of Elasticity
publication date: 1995-10-18T00:00:00Z
review text: This investigation is based on an (not necessarily homogeneous) infinite isotropic elastic layer. Its aim is the deduction and mathematical justification of two-dimensional plate theories. For the corresponding reduction process, the Fourier transform method in connection with the asymptotic expansion approach is used, the lateral boundaries being pushed away via a rescaling of the length. The solution of the \(F\)- transformed Navier's equations for an infinite, surface- and volume loaded layer is shown to consist of a singular and a holomorphic part, the latter one giving rise to an exponentially decay (boundary layer effect). The relations to laterally bounded domains and to St.-Venant's principle are worked out, and existence and convergence results as well as decay estimates are established. In the limit as the thickness tends to zero, the Kirchhoff's plate equation arises.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 797089
zbMATH Keywords: boundary layer effect
zbMATH Keywords: infinite isotropic elastic layer
zbMATH Keywords: Fourier transform method
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: Navier's equations
zbMATH Keywords: St.-Venant's principle
zbMATH Keywords: existence
zbMATH Keywords: convergence
zbMATH Keywords: Kirchhoff's plate equation
reviewed by: Hans Bufler
MaRDI profile type: Publication
Wikidata QID: Q59902117
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description: scientific article; zbMATH DE number 797089