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

Abstract

A piezoelectric multilamina shell FE developed to model thin walled structures with piezoelectric fibre composites polarized with interdigitated electrodes (PFCPIE) is proposed 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 the poling direction. Each piezoelectric lamina admits an arbitrary poling direction. Based on Reissner-Mindlin assumptions and a multilaminate approach, the element employs a single layer assumption for the mechanical displacements and a layerwise constant electric potential. An MITC strategy is used to avoid shear locking. Two static examples are presented. The first is a cantilever piezoactuated beam and the second a single cell closed box beam with piezoelectric actuators. The results obtained for the cantilever beam with the present formulation are compared with those obtained with native ABAQUS plane stress elements and an analytical solution. For the closed box beam the numerical results were compared with experimental results 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 state space model (SS). Based on the SS model, the design of the control system and the assessment of the system performance are carried out. Important systems characteristics are captured by the model, i.e.attenuation levels, frequency response and control voltage levels. This reveals that the proposed FE can be used to model and assess structural behaviour in a relatively simple and efficient way.