On non-linear behaviour of spherical shallow shells bonded with piezoelectric actuators by the differential quadrature element method (DQEM)

The static behaviour of spherical shallow shells bonded with piezoelectric actuators and subjected to electrical loading are studied in this paper by using the di6erential quadrature element method (DQEM). Geometrical non-linear e6ects are considered. Detailed formulations for the DQ circular spherical shallow shell element and the DQ annular spherical shallow shell element are given for the >rst time. Numerical studies are performed to evaluate the e6ects of actuator size, thickness and boundary conditions. Very accurate results are obtained by the DQEM. Based on the results reported in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions for smart materials and structures exhibiting geometric non-linear behaviours. Thickness e6ects cannot be neglected when the actuator thickness is comparableto that of thebasemate rial. Snap-through may occur when theapplie d voltage reaches a critical value even without mechanical loading for certain geometric con>gurations