Mindlin-type finite elements for piezoelectric sandwich plates

New finite-element formulations are developed for the analysis of a plate h aving thin piezoelectric actuators bonded on its upper and/or lower surface s. The proposed finite elements are two-dimensional, quadrangular, four-nod e, Mindlin-type, locking-free, and have five degrees of freedom per node. T hese are the deflection of the middle plane of the plate, the rotations of the fibers normal to the middle plane and the actuation electric potentials of the piezoelectric actuators. The effectiveness of the proposed finite-e lement formulations is shown by studying some case problems, whose analytic al solutions are available.