In the present work, new mixed variational formulations for a first-order shear deformation laminate theory are proposed. The out-of-plane stresses are considered as primary variables of the problem. In particular, the shear stress profile is represented either by independent piecewise quadratic functions in the thickness or by satisfying the three-dimensional equilibrium equations written in terms of midplane strains and curvatures. The developed formulations are characterized by several advantages: They do not require the use of shear correction factors as well as the out-of-plane shear stresses can be derived without post-processing procedures. Some numerical applications are presented in order to verify the effectiveness of the proposed formulations. In particular, analytical solutions obtained using the developed models are compared with the exact three-dimensional solution, with other classical laminate analytical solutions and with finite element results. Finally, we note that the proposed formulations may represent a rational base for the development of effective finite elements for composite laminates.

*Finite Element Analysis of Composite Laminates*, Kluwer, Dordrecht, The Netherlands.

*Mechanics of Laminated Composite Plates, Theory and Analysis*, CRC Press, Boca Raton, FL.

*Theory of Anisotropic Plates*, Technomic, Lancaster, PA.

**5**, pp. 451–466.