Justification of the Bending-Gradient Theory Through Asymptotic Expansions

  • Arthur Lebée
  • Karam Sab
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 22)


In a recent work, a new plate theory for thick plates was suggested where the static unknowns are those of the Kirchhoff-Love theory, to which six components are added representing the gradient of the bending moment [1]. This theory, called the Bending-Gradient theory, is the extension to multilayered plates of the Reissner-Mindlin theory which appears as a special case when the plate is homogeneous. This theory was derived following the ideas from Reissner [2] without assuming a homogeneous plate. However, it is also possible to give a justification through asymptotic expansions. In the present paper, the latter are applied one order higher than the leading order to a laminated plate following monoclinic symmetry. Using variational arguments, it is possible to derive the Bending-Gradient theory. This could explain the convergence when the thickness is small of the Bending-Gradient theory to the exact solution illustrated in [3]. However, the question of the edge-effects and boundary conditions remains open.


Asymptotic Expansion Transverse Shear Laminate Plate Plate Model Transverse Shear Stress 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Laboratoire Navier (ENPC–IFSTTAR–CNRS), École des Ponts ParisTechUniversité Paris-EstMarne-la-ValléeFrance

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