On the generalization of Reissner plate theory to laminated plates. I: Theory. (English) Zbl 1364.74041
Summary: This is the first part of a two-part paper presenting the generalization of E. Reissner thick plate theory [J. Math. Phys., Mass. Inst. Techn. 23, 184–191 (1944; Zbl 0061.42501)] to laminated plates and its relation with the Bending-Gradient theory [the authors, “A Bending-Gradient model for thick plates. I: Theory”, Int. J. Solids Struct. 48, No. 20, 2878–2888 (2011; doi:10.1016/j.ijsolstr.2011.06.006); “A Bending-Gradient model for thick plates. II: Closed-form solutions for cylindrical bending of laminates”, ibid. 48, No. 20, 2889–2901 (2011; doi:10.1016/j.ijsolstr.2011.06.005)]. The original thick and homogeneous plate theory derived by Reissner [loc. cit.] 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 [the authors, ibid. 126, No. 1, 67–94 (2017; Zbl 1364.74042)], 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.
Keywords:
thick plate theory; higher-order models; laminated plates; functionally graded plates; sandwich panelsReferences:
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