Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Classical Plate Problems

  • Sébastien BrisardEmail author
Living reference work entry

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DOI: https://doi.org/10.1007/978-3-662-53605-6_133-2



Bending of plates refers to internal states of stress such that the membrane stress resultants vanish. From the kinematic point of view, it means that the in-plane displacements of the material points of the plate are null. In other words, the degrees of freedom of plates in bending are the out-of-plane displacement (thick and thin plates), together with the two material rotations (thick plates only) – see article “Direct Derivation of Plate Theories”.

The out-of-plane displacement is usually called deflection of the plate.


This article discusses a few classical, closed-form solutions of plate problems. It is restricted to bending problems of isotropic, homogeneous, linearly elastic plates subjected to distributed forces only (no distributed couples).

The general field equations that govern the bending of such plates (both thick and thin) were...
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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