Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Buckling and Post-buckling of Plates

  • Basile AudolyEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_134-1

Synonyms

Definition

An elastic plate is a thin, quasi two-dimensional elastic body, whose dimension in one direction (thickness) is much smaller than its dimensions in the perpendicular directions. By definition, and contrary to elastic shells, elastic plates are naturally planar i.e., do not bend out of their midplane. When subject to in-plane loading, plates can give rise to non-planar solutions by a symmetry-breaking bifurcation called buckling. Buckling and post-buckling analyses are concerned with the derivation of buckled solutions to plate theories in the neighborhood of a bifurcation point, using expansion methods.

Overview

Owing to their geometry, thin elastic plates can easily bend and are prone to rotations of moderate to large amplitude, even when subjected to relatively small loads. Linear elasticity theory is unable to...

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References

  1. Audoly B, Pomeau Y (2000) Elasticity and geometry. In: Kaiser R, Montaldi J (eds) Peyresq lecture notes on nonlinear phenomena, chap 1. World Scientific, New York, pp 1–35Google Scholar
  2. Everall PR, Hunt GW (2000) Mode jumping in the buckling of struts and plates: a comparative study. Int J Non Linear Mech 35:1067–1079CrossRefGoogle Scholar
  3. Green AE (1936) The equilibrium and elastic stability of a thin twisted strip. Proc R Soc A Math Phys Eng Sci 154:430–455CrossRefGoogle Scholar
  4. Green AE (1937) The elastic stability of a thin twisted strip. II. Proc R Soc Lond A 161:197–220CrossRefGoogle Scholar
  5. Korte AP, Starostin EL, van der Heijden GHM (2011) Triangular buckling patterns of twisted inextensible strips. Proc R Soc Lond A 467:285–303MathSciNetCrossRefGoogle Scholar
  6. Landau LD, Lifshitz EM (1981) Theory of elasticity, 2nd edn. Course of theoretical physics. Pergamon Press, Oxford/TorontozbMATHGoogle Scholar
  7. Mockensturm EM (2001) The elastic stability of twisted plates. J Appl Mech 68(4):561–567CrossRefGoogle Scholar
  8. Schaeffer D, Golubitsky M (1979) Boundary conditions and mode jumping in the buckling of a rectangular plate. Commun Math Phys V69(3):209–236MathSciNetCrossRefGoogle Scholar
  9. Timoshenko S, Gere JM (1961) Theory of elastic stability, 2nd edn. MacGraw Hill, New YorkGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.Laboratoire de mécanique des solides, CNRS and École PolytechniquePalaiseauFrance

Section editors and affiliations

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