The refined theory of piezoelectric thick plates

Based on linear piezoelasticity theory, without requirement of any ad hoc assumptions concerning the deformation or the stress state, various two-dimensional equations have been deduced systematically and directly from the three-dimensional theory of thick rectangular plates by using the general solution of transversely isotropic piezoelasticity and the Lur´e method, and they construct the refined theory of plates. It is shown that the displacements and stresses of plates can be represented by the displacements and electric potential of the mid-plane. In the case of homogeneous boundary conditions, the refined plate theory is exact in the sense that a solution of the theory satisfies all the equations in the piezoelasticity theory and consists of three parts: the biharmonic part, the shear part, the transcendental part.