Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Homogenization of Thin Periodic Plates

  • Karam Sab
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_137-1

Synonyms

Definitions

Homogenization is the operation that approximates the solution of a boundary value problem involving heterogeneous material properties by the solution of another boundary value problem involving homogeneous material properties which are so-called the homogenized one.

Introduction

Taking advantage of the fact that a plate has a small dimension compared to the other two dimensions, the purpose of plate theories is to replace the three-dimensional problem by a two-dimensional problem while guaranteeing the accuracy of the three-dimensional fields.

This so-called dimensional reduction was initially operated on isotropic homogeneous plates and then extended to arbitrary laminated plates. Adapting to elastic thin periodic plates, the homogenizing techniques initially developed for 3D composites, it was possible since the beginning of the 1980s to homogenize such plates which...

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References

  1. Caillerie D (1984) Thin elastic and periodic plates. Math Methods Appl Sci 6(1):159–191MathSciNetCrossRefMATHGoogle Scholar
  2. Lewiński T, Telega JJ (2000) Plates, laminates and shells: asymptotics analysis and homogenization. World Scientific, Singapore/New Jersey/London [etc.]Google Scholar
  3. Sab K, Lebée A (2015) Homogenization of Thick and Heterogeneous Plates. Wiley-ISTE, HobokenCrossRefMATHGoogle Scholar

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