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Three Dimentional Derivations of Static Plate Theories

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Encyclopedia of Continuum Mechanics

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Synonyms

Dimensional reduction; First-order shear deformation theory; Plate model or theory; Reissner or Hencky or Reissner-Mindlin thick plate theory

Definitions

  • Thin plate model: A model where the only kinematic d.o.f. is the transverse deflection. It neglects the shear energy.

  • Thick plate model: A model including also two in-plane rotation d.o.f. and including shear deflection.

Introduction

Plates are three-dimensional structures with a small dimension compared to the other two dimensions. Numerous approaches were suggested in order to replace the three-dimensional problem by a two-dimensional problem while guaranteeing the accuracy of the reconstructed three-dimensional fields. Turning the 3D problem into a 2D plate model is known as dimensional reduction.

The approaches for deriving a plate model from 3D elasticity may be separated in two main categories: axiomatic and asymptotic approaches. Axiomatic approaches start with ad hoc assumptions on the 3D field representation of the...

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References

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Author information

Authors and Affiliations

  1. Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, Université Paris-Est, Marne-la-Vallée, France

    A. Lebée & S. Brisard

Authors
  1. A. Lebée
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  2. S. Brisard
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Corresponding author

Correspondence to A. Lebée .

Editor information

Editors and Affiliations

  1. Otto-von-Guericke University Magdeburg, Chair of Engineering Mechanics, Institut, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Fakultät für Maschinenbau, Hochschule Esslingen, Esslingen am Neckar, Baden-Württemberg, Germany

    Andreas Öchsner

Section Editor information

  1. Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, Université Paris-Est, Marne-la-Vallée, France

    Karam Sab

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Lebée, A., Brisard, S. (2020). Three Dimentional Derivations of Static Plate Theories. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_132-2

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_132-2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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Chapter history

  1. Latest

    Three Dimentional Derivations of Static Plate Theories
    Published:
    11 October 2019

    DOI: https://doi.org/10.1007/978-3-662-53605-6_132-2

  2. Original

    3D Derivations of Static Plate Theories
    Published:
    28 December 2017

    DOI: https://doi.org/10.1007/978-3-662-53605-6_132-1

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