Equivalent single-layer Mindlin theory of laminated piezoelectric plates and application

Based on the Mindlin first-order shear deformation theory, this paper proposes an equivalent single layer (ESL) plate theory to analyze the electro-mechanical coupling problem of laminated piezoelectric plates (LPPs). The main features of the proposed approach are: (i) It assumes that the electric potential across the thickness is a polynomial function, ensuring its continuity at the interface. (ii) The electric displacements are continuous at the interface, in line with the interface continuity condition between laminated plates. The theoretical solutions for the deformation and electric potential of LPPs are obtained. The validity and accuracy of the theoretical solutions are confirmed through comparison with results of two- and four-layer LPPs obtained from the three-dimensional finite element method (FEM). The numerical results discuss the influence of different series expansions and emphasize the necessity of high-order expansion. Meanwhile, the range of application of three-dimensional FEM is discussed. It is expected that such a new analytical method can be instructive to the optimal design of piezoelectric device.