The cylindrical bending of composite plates with piezoelectric and SMA layers

Abstract

A laminated plate with orthotropic piezoelectric layers undergoing cylindrical bending under the application of electromechanical loading is considered. A known elasticity solution is extended to the coupled electroelastic field case by introducing, in addition to an Airy stress function, the electric potential for every layer. The validity of the way electric boundary conditions are applied in classical beam or plate theories is discussed. The electroelastic solution is applied to the non-linear case of a hybrid composite plate with piezoelectric layers attached to shape memory alloy (SMA) thin strips. An incremental piecewise elastic formation of the problem incorporates both stiffness changes and transformation strains in the SMA layers. The study of a laminated plate with PZT layers attached on both sides of an NiTi SMA layer shows that a full loading-unloading cycle in the applied electric field leads to energy dissipation in the laminated plate due to the dissipative process of stress induced martensitic phase transformation.