A nonlinear piezoelectric shell model: Theoretical and numerical considerations

A nonlinear piezoelectric shell model capable of accurately expressing the direct and the converse piezoelectric effect is discussed here with the support of numerical simulations. The theory under investigation is meant to be able to encompass a complete coupling between the mechanical and the electrical fields in the frame of geometrically exact shell formulations. To this aim, warping functions characterized by an ad hoc polynomial expansion in the shell through-the-thickness coordinate are considered to describe the shear and the extensional deformability of transverse fibers. The governing equations of motion are numerically implemented for the cases of a rectangular semi-cylinder and for a multilayered 90° rectangular cylinder. Numerical results show the effects of key geometric parameters and of the nature of the loading on the system response, evidencing that significant misrepresentations of the system behavior are possible if lower-order kinematics are taken into account.