Justification of the Bending-Gradient Plate Model Through Asymptotic Expansions

Arthur Lebée 1 Karam Sab 1
1 MSA - Matériaux et Structures Architecturés
NAVIER UMR 8205 - Laboratoire Navier
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.
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Arthur Lebée, Karam Sab. Justification of the Bending-Gradient Plate Model Through Asymptotic Expansions. Altenbach, Holm and Forest, Samuel and Krivtsov, Anton. Generalized Continua as Models for Materials, Springer-Verlag Berlin Heidelberg, pp.217--236, 2013, ⟨10.1007/978-3-642-36394-8_12⟩. ⟨hal-00846894⟩

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