Piezoelectric shell theories with a priori continuous transverse electromechanical variables

This paper addresses the static analysis of multilayer shells with embedded piezoelectric materials. The Reissner Mixed Variational Theorem is used to obtain transverse electromechanical variables (transverse shear and normal stresses, plus normal electrical displacement) which are a priori continuous at each layer-interface. The governing differential equations of doubly curved shells are derived by referring to the Unified Formulation in terms of a few fundamental nuclei. Formulation with discord interface continuity of transverse stresses and/or electrical displacements are discussed for comparison purpose. We address both equivalent single-layer models and layerwise models; up to fourth-order expansions in the thickness coordinate have been implemented. Numerical analysis has been restricted to closed-form solutions. Plates and simply supported cylindrical shells with orthotropic layers have been investigated. Both sensor and actuator configuration have been analyzed. The results obtained demonstrate the superiority of the proposed approach with respect to the other formulations considered, and its ability to furnish a priori interlaminar continuous transverse electrical displacement.