A Bending-Gradient model for thick plates, Part II: Closed-form solutions for cylindrical bending of laminates

Abstract

In the first part (Lebée and Sab, 2010a) of this two-part paper we have presented a new plate theory for out-of-plane loaded thick plates where the static unknowns are those of the Kirchhoff-Love theory (3 inplane stresses and 3 bending moments), to which six components are added representing the gradient of the bending moment. The new theory, called Bending-Gradient plate theory is an extension to arbitrarily layered plates of the Reissner-Mindlin plate theory which appears as a special case when the plate is homogeneous. Moreover, we demonstrated that, in the general case, the Bending-Gradient model cannot be reduced to a Reissner-Mindlin model. In this paper, the Bending-Gradient theory is applied to laminated plates and its predictions are compared to those of Reissner-Mindlin theory and to full 3D Pagano’s exact solutions. The main conclusion is that the Bending-Gradient gives good predictions of deflection, shear stress distributions and in-plane displacement 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.

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Cite this paper

@inproceedings{Lebe2011ABM, title={A Bending-Gradient model for thick plates, Part II: Closed-form solutions for cylindrical bending of laminates}, author={A Leb{\'e}e and K. Sab}, year={2011} }