A Refined Sinus Finite Element Model for the Analysis of Piezoelectric-Laminated Beams

A three-nodded beam finite element is developed for the analysis of composite-laminated beams with distributed piezoelectric sensor/actuator layers. The mechanical part of the proposed element is based on the refined sinus model. This element does not require shear correction factor and ensures continuity conditions for displacements, transverse shear stresses as well as boundary conditions on the upper and lower surfaces of the beam. This conforming finite element is totally free of shear locking, and the number of mechanical unknowns is independent of the number of layers. For each piezoelectric layer, a high-order electrical potential field is considered. The virtual work principle leads to a derivation that could include dynamic analysis. However, in this study, only static problems have been considered. Comparison of numerical results obtained from this formulation with previous works shows that the present finite element is suitable for predicting fully coupled behaviors of both thick and thin smart-laminated beams under mechanical and electrical loadings.