On the Generalization of Reissner Plate Theory to Laminated Plates, Part I: 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：39-66
• 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

This is the first part of a two-part paper presenting the generalization of Reissner thick plate theory (Reissner in J. Math. Phys. 23:184–191, 1944) to laminated plates and its relation with the Bending-Gradient theory (Lebée and Sab in Int. J. Solids Struct. 48(20):2878–2888, 2011 and in Int. J. Solids Struct. 48(20):2889–2901, 2011). The original thick and homogeneous plate theory derived by Reissner (J. Math. Phys. 23:184–191, 1944) is based on the derivation of a statically compatible stress field and the application of the principle of minimum of complementary energy. The static variables of this model are the bending moment and the shear force. In the present paper, the rigorous extension of this theory to laminated plates is presented and leads to a new plate theory called Generalized-Reissner theory which involves the bending moment, its first and second gradients as static variables. When the plate is homogeneous or functionally graded, the original theory from Reissner is retrieved. In the second paper (Lebée and Sab, 2015), the Bending-Gradient theory is obtained from the Generalized-Reissner theory and comparison with an exact solution for the cylindrical bending of laminated plates is presented.