Single- vs Multilayer Plate Modelings on the Basis of Reissner's Mixed Theorem

The use of Reissner's mixed variational theorem (Reissner, E., On a Certain Mixed Variational Theory and a Proposed Applications, International Journal for Numerical Methods in Engineering, Vol. 20, 1984, pp. 1366-1368; Reissner, E.,On a Mixed Variational Theorem and on a Shear Deformable Plate Theory, International Journal of Numerical Methods in Engineering, Vol. 23, 1986, pp. 193-198) to analyze laminated plate structures is examined. The two cases of single-layer and multilayer models have been compared. Governing equilibrium and constitutive equations have been derived in a unified manner. Navier-type closed-form solutions are presented for the particular case of cross-ply simply supported plates. Thin and thick, as well as symmetrically and asymmetrically laminated plates, have been investigated. Displacements and transverse stresses have been evaluated and compared with available mixed two-dimensional results and three-dimensional solutions. The following have been concluded: 1) Reissner's mixed theorem is a very suitable tool to analyze laminated structures. 2) Multilayer modelings lead to an excellent agreement with exact solution for both displacement and transverse stress evaluations. Such an agreement, which has been confirmed for very thick geometries (a/h ≤ 4), does not depend on laminate layouts. No remarkable differences have been found for stresses evaluated a priori by the assumed model with respect to exact results. 3) Single-layer analyses lead to an accurate description of the response of thick plates. Major discrepancies have been found for very thick plate geometries with exact solutions. Nevertheless, their accuracy is very much subordinate to the order of the used expansion as well as to laminated layouts. Better transverse stress evaluations are obtained upon integration of three-dimensional equilibrium equations a posteriori than those furnished a priori. This trend has been confirmed for both thick and thin plates.

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