# Justification of the Bending-Gradient Theory Through Asymptotic Expansions

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

## Abstract

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.

## Keywords

Asymptotic Expansion Transverse Shear Laminate Plate Plate Model Transverse Shear Stress
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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