An extension of Reissner Mixed Variational Theorem to piezoelectric laminates

This paper presents a technique to consistently extend the Reissner Mixed Variational Theorem (RMVT) to problems involving multiple fields. In particular, a new partially mixed formulation is presented for multilayered structures embedding piezoelectric layers. The formulation satisfies a priori the interlaminar continuity of the transverse stresses. Following Reissner, the constitutive equations for the coupled linear electromechanical behavior associated to the partially mixed variational statement are derived from a modified internal energy function by means of partial Legendre transformations. As a result, the mechanical displacements, the electric potential, as well as the transverse stresses, can be independently assumed. The resulting three-field formulation has been applied to an established axiomatic modelling technique for multilayered structures. An implementation and assessment of a large number of laminate theories, including "layerwise" and "equivalent single layer" descriptions, is performed. Numerical results are given within a closed-form solution technique for two exemplary case studies, for which an exact three-dimensional solution is available in open literature.