Single- vs multilayer plate modeling 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 Journ al for Numerical Methods in Engineering,Vol. 20, 1984, pp, 1366-1368; Reiss ner, E., ''On a Mixed Variational Theorem and on a Shear Deformable Plate T heory,'' 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. Govern ing equilibrium and constitutive equations have been derived in a unified m anner. Navier-type closed-form solutions are presented for the particular c ase of cross-ply simply supported plates. Thin and thick, as well as symmet rically and asymmetrically laminated plates, have been investigated. Displa cements and transverse stresses have been evaluated and compared with avail able mixed two-dimensional results and three-dimensional solutions. The fol lowing have been concluded: 1) Reissner's mixed theorem is a very suitable tool to analyze laminated structures. 2) Multilayer modelings lead to an ex cellent agreement with exact solution for both displacement and transverse stress evaluations. Such an agreement, which has been confirmed for very th ick geometries (alh less than or equal to 4), does not depend on laminate l ayouts. 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. M ajor discrepancies have been found for very thick plate geometries with exa ct solutions. Nevertheless, their accuracy is very much subordinate to the order of the used expansion as well as to laminated layouts. Better transve rse stress evaluations are obtained upon integration of three-dimensional e quilibrium: equations a posteriori than those furnished a priori. This tren d has been confirmed for both thick and thin plates.