Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

3D Derivations of Static Plate Theories

  • A. LebéeEmail author
  • S. Brisard
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_132-1

Synonyms

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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Copyright information

© 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