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Journal of Elasticity

, Volume 103, Issue 1, pp 53–71 | Cite as

On the Justification of Plate Models

  • Dietrich Braess
  • Stefan Sauter
  • Christoph SchwabEmail author
Article

Abstract

In this paper, we will consider the modelling of problems in linear elasticity on thin plates by the models of Kirchhoff–Love and Reissner–Mindlin. A fundamental investigation for the Kirchhoff plate goes back to Morgenstern (Arch. Ration. Mech. Anal. 4:145–152, 1959) and is based on the two-energies principle of Prager and Synge. This was half a century ago.

We will derive the Kirchhoff–Love model based on Morgenstern’s ideas in a rigorous way (including the proper treatment of boundary conditions). Our derivation provides insights (a) into the relation of the (1,1,0)-model with the (1,1,2)-model which differs by a quadratic term in the ansatz for the third component of the displacement field and (b) into the rôle of the shear correction factor. A further advantage of the approach by the two-energies principle is that the extension to the Reissner–Mindlin plate model becomes very transparent and easy. Our study includes plates with reentrant corners with any interior opening angle <2π.

Keywords

Plate models Justification Hypercircle inequality Prager–Synge Shear correction factor Reissner–Mindlin model 

Mathematics Subject Classification (2000)

74K20 35Q74 74B05 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Dietrich Braess
    • 1
  • Stefan Sauter
    • 2
  • Christoph Schwab
    • 3
    Email author
  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  2. 2.Institut für MathematikUniversität ZürichZürichSwitzerland
  3. 3.ETH ZürichZurichSwitzerland

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