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Exact solutions are presented for the static behavior of laminated piezoelectric plates with simple support. The upper and lower surfaces of the laminate can be subjected to a number of applied loadings, confined in this study to an applied transverse load or a specified surface potential. Each layer of the laminate can be piezoelectric, elastic/dielectric, or conducting, with perfect bonding assumed between each interface. Expressions are obtained for the components of displacement, stress, electric displacement, and potential through the thickness of the laminate. Representative examples are shown to demonstrate the fundamental behavior, and the influence of the piezoelectric coefficients and internal electrodes are discussed.
Paul R. Heyliger (Sun,) studied this question.