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Journal of Elasticity

, Volume 126, Issue 1, pp 67–94 | Cite as

On the Generalization of Reissner Plate Theory to Laminated Plates, Part II: Comparison with the Bending-Gradient Theory

  • Arthur LebéeEmail author
  • Karam Sab
Article

Abstract

In the first part of this two-part paper (Lebée and Sab in On the generalization of Reissner plate theory to laminated plates, Part I: theory, doi: 10.1007/s10659-016-9581-6, 2015), the original thick plate theory derived by Reissner (J. Math. Phys. 23:184–191, 1944) was rigorously extended to the case of laminated plates. This led to a new plate theory called Generalized-Reissner theory which involves the bending moment, its first and second gradients as static variables. In this second paper, the Bending-Gradient theory (Lebée and Sab in Int. J. Solids Struct. 48(20):2878–2888, 2011 and 2889–2901, 2011) is obtained from the Generalized-Reissner theory and several projections as a Reissner–Mindlin theory are introduced. A comparison with an exact solution for the cylindrical bending of laminated plates is presented. It is observed that the Generalized-Reissner theory converges faster than the Kirchhoff theory for thin plates in terms of deflection. The Bending-Gradient theory does not converge faster but improves considerably the error estimate.

Keywords

Thick plate theory Higher-order models Laminated plates Functionally graded plates Sandwich panels 

Mathematics Subject Classification (2010)

74G65 74K20 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Laboratoire Navier, UMR 8205, École des Ponts ParisTech, IFSTTAR, CNRS, UPEÉcole Nationale des Ponts et ChausséesMarne-la-Vallée cedex 2France

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