Two finite elements for general composite beams with piezoelectric actuators and sensors

Two finite elements for the static analysis of smart beams with piezoelectric sensors/actuators are presented: ad hoc smart beam element (ADSBE) and variational asymptotic smart beam element (VASBE). Both elements rely on the computation of the cross-sectional matrices associated with the electromechanical properties of the beam cross-section. ADSBE uses the Timoshenko cross-sectional stiffness matrix computed by the VABS program, and the electric field is assumed constant across the thickness of each piezoelectric layer. Taking advantage of the cross-section discretization of the beam, all the matrices related to the electric field are also computed by performing a numerical integration using the VABS program that was extended to account for these new quantities. VASBE is based on the fully coupled Timoshenko theory for smart beams constructed using the variational asymptotic method. This theory decouples the original three-dimensional electromechanical problem to a two-dimensional electromechanical cross-sectional analysis and a one-dimensional beam analysis. The cross-sectional analysis provides a one-dimensional constitutive model for the beam analysis without a priori assumptions regarding the geometry of the cross-section, the electric field distribution, and the location of smart materials. Several examples available in the literature are used to validate the accuracy of these two new elements. The numerical results obtained using ADSBE and VASBE correlated well with other published results. For structures that are out of the limits in which one structure may be modeled as a beam, the ADSBE showed considerable errors and, therefore, should not be used. Nevertheless, VASBE was able to predict the 3D results available in the literature with an error smaller than 8%. (C) 2008 Elsevier B. V. All rights reserved.