Exact solutions for static electro-mechanical response of doubly curved smart laminated shells

This paper deals with the derivation of the exact solutions for the static electro-mechanical response of a simply-supported doubly curved (DC) smart shell, composed of a piezoelectric fiber reinforced composite (PFRC) placed over a laminated substrate. These responses are evaluated when the system is subjected to distributed electrical and mechanical loads. The electro-mechanical governing equations and the associated boundary conditions have been derived here for the curvilinear coordinate system using the variational principle. Closed-form expressions for the mechanical displacement and the electrical potential have been obtained by solving these governing differential equations and simultaneously satisfying the derived boundary conditions. Numerical results have been presented for different shell geometries. The effect of the curvature and the geometric parameters of the PFRC layer over its performance as an actuator are studied and compared for these shells. Also, the effect of varying geometric parameters of the PFRC over its performance as a sensor is studied. Optimal dimensions of the PFRC for use as an actuator and sensor/harvester have been proposed. This study may be considered as a benchmark for use in the numerical and experimental studies involving smart shells.