Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Direct Derivation of Plate Theories

  • Sébastien BrisardEmail author
  • Arthur Lebée
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_131-1



A shell is a solid body with one dimension (the thickness) small in comparison with the others. The thickness of a shell is measured with respect to a reference surface. A plate is a particular case of shell with flat reference surface.


This article provides an overview of elementary plate models. It starts in section “Equilibrium of Plates” with the definition of the internal state of stress of plates and the derivation of the equilibrium equations governing the corresponding stress-resultants and stress-couples. These equilibrium equations must be complemented with constitutive relations; this is addressed within the framework of elasticity in sections “The Thick Plate Model” and “The Thin Plate Model.”

Throughout this article, the so-called direct approach is adopted (see Naghdi, 1973; Altenbach and Eremeyev, 2009; Altenbach et al, 2010, and references therein). In other words,...

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© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTARUniversité Paris-EstMarne-la-ValléeFrance

Section editors and affiliations

  • Karam Sab
    • 1
  1. 1.Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTARUniversité Paris-EstMarne-la-ValléeFrance