A Bending-Gradient model for thick plates. Part I: Theory

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:48

Article

Lebee, A.¹  Sab, K.¹ 

[1] Univ Paris Est, Lab Navier, Ecole Ponts ParisTech, IFSTTAR,CNRS, F-77455 Marne La Vallee, France

关键词: Plate theory;    Higher-order models;    Laminated plates;    Composite plates;   

DOI  :  10.1016/j.ijsolstr.2011.06.006

来源: Elsevier

【 摘 要 】

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, 2011), 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. (C) 2011 Elsevier Ltd. All rights reserved.

【 授权许可】

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