A three-dimensional exact state-space solution for cylindrical bending of continuously non-homogenous piezoelectric laminated plates with arbitrary gradient composition

Abstract

Most of exact solutions reported for the analysis of functionally graded piezoelectric (FGP) plates are based on the assumption, that the graded plate consists of a number of layers, where the material properties within each layer are invariant. The limited works that consider the continuous variation of electro-mechanical properties are restricted to FGP materials with the exponent-law dependence on the thickness-coordinate. In the present paper, a three-dimensional (3D) exact solution is presented for cylindrical bending of the FGP laminated plates based on the state space formalism. In contrast to the other reported solutions which are restricted to FGP materials with the exponent-law dependence on the thickness-coordinate, the present exact solution considers materials with arbitrary compositional gradient. Moreover, no assumption on displacement components and the electric potential along the thickness direction of FGP layers is introduced. Regardless of the number of layers, equations of motion, charge equation, and the boundary and interface conditions are satisfied exactly. The obtained exact solution can be used to assess the accuracy of different FGP laminated plate theories and/or for validating finite element codes.