Piezoelectric shell FE for the static and dynamic analysis of piezoelectric fibre compositelaminates

Abstract

A piezoelectric multilamina shell FE developed to model thin walled structures withpiezoelectric fibre composites polarized with interdigitated electrodes (PFCPIE) isproposed in this paper. A new scheme for the interpolation of the electric field is presented.The electric field in each lamina lies parallel to the lamina plane and coincides with thepoling direction. Each piezoelectric lamina admits an arbitrary poling direction. Basedon Reissner–Mindlin assumptions and a multilaminate approach, the elementemploys a single layer assumption for the mechanical displacements and a layerwiseconstant electric potential. An MITC strategy is used to avoid shear locking.Two static examples are presented. The first is a cantilever piezoactuated beam and thesecond a single cell closed box beam with piezoelectric actuators.The results obtained for the cantilever beam with the present formulation are comparedwith those obtained with native ABAQUS plane stress elements and an analytical solution.For the closed box beam the numerical results were compared with experimentalresults from the literature. Very encouraging results are obtained in both cases.Finally, for the piezoactuated closed box beam, the FE model is used to obtain a statespace model (SS). Based on the SS model, the design of the control system andthe assessment of the system performance are carried out. Important systemscharacteristics are captured by the model, i.e. attenuation levels, frequency responseand control voltage levels. This reveals that the proposed FE can be used tomodel and assess structural behaviour in a relatively simple and efficient way.