On the Generalization of Reissner Plate Theory to Laminated Plates, Part II: Comparison with the Bending-Gradient Theory

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• 作者：Arthur Lebée ; Karam Sab
• 关键词：Thick plate theory ; Higher ; order models ; Laminated plates ; Functionally graded plates ; Sandwich panels
• 刊名：Journal of Elasticity
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：126
• 期：1
• 页码：67-94
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-2681
• 卷排序：126

文摘

In the first part of this two-part paper (Lebée and Sab in On the generalization of Reissner plate theory to laminated plates, Part I: theory, doi:10.1007/s10659-016-9581-6, 2015), the original thick plate theory derived by Reissner (J. Math. Phys. 23:184–191, 1944) was rigorously extended to the case of laminated plates. This led to a new plate theory called Generalized-Reissner theory which involves the bending moment, its first and second gradients as static variables. In this second paper, the Bending-Gradient theory (Lebée and Sab in Int. J. Solids Struct. 48(20):2878–2888, 2011 and 2889–2901, 2011) is obtained from the Generalized-Reissner theory and several projections as a Reissner–Mindlin theory are introduced. A comparison with an exact solution for the cylindrical bending of laminated plates is presented. It is observed that the Generalized-Reissner theory converges faster than the Kirchhoff theory for thin plates in terms of deflection. The Bending-Gradient theory does not converge faster but improves considerably the error estimate.