The refined theory of piezoelectric thick plates

摘要

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.