A bending-gradient model for thick plates, I : theory

Arthur Lebée (1) , Karam Sab (1)

1 msa - Matériaux et Structures Architecturés

This is the first part of a two-part paper dedicated to a new plate theory for out-of-plane loaded thick plates where the static unknowns are those of the Kirchhoff-Love theory (3 in-plane stresses and 3 bending moments), to which six components are added representing the gradient of the bending moment. The new theory, called the Bending-Gradient plate theory is described in the present paper. It is an extension to arbitrarily layered plates of the Reissner-Mindlin plate theory which appears as a special case of the Bending-Gradient plate theory when the plate is homogeneous. However, we demonstrate also that, in the general case, the Bending-Gradient model cannot be reduced to a Reissner-Mindlin model. In part two (Lebee and Sab, 2010a), the Bending-Gradient theory is applied to multilayered plates and its predictions are compared to those of the Reissner-Mindlin theory and to full 3D Pagano's exact solutions. The main conclusion of the second part is that the Bending-Gradient gives good predictions of both deflection and shear stress distributions in any material configuration. Moreover, under some symmetry conditions, the Bending-Gradient model coincides with the second-order approximation of the exact solution as the slenderness ratio L/h goes to infinity.

Mots clés: Plate Theory; Higher-order Models; Laminated Plates; Composite Plates

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Arthur Lebée, Karam Sab. A bending-gradient model for thick plates, I : theory. International Journal of Solids and Structures, 2011, 48, pp.2878-2888. ⟨10.1016/j.ijsolstr.2011.06.006⟩. ⟨hal-00661326⟩