New finite-element formulations are developed for the analysis of a plate having thin piezoelectric actuators bonded on its upper and/or lower surfaces. The proposed finite elements are two-dimensional, quadrangular, four-node, Mindlin-type, locking-free, and have five degrees of freedom per node. These 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-element formulations is shown by studying some case problems, whose analytical solutions are available.
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