br Introduction Laminated shells of revolution are

Introduction
Laminated shells of revolution are very attractive members for structural applications, due to their high load carrying capacities. On the other hand, functionally graded materials (FGMs) have received considerable attention from researchers over the past two decades. These are advanced inhomogeneous composite materials at microscopic scale, with material compositions varying continuously within the structure. The material grading and microstructure of FGMs can be designed to obtain the desired mechanical and thermal responses for specific industrial applications. FGMs are usually made of a mixture of metal and ceramic that provides the required thermal resistance and reduction of thermal stresses. Suresh and Mortensen [1] presented a comprehensive review on the design, processing, and modeling, as well as application, of FGMs.
As manufacturing of FGMs advances, new methodologies in the structural analysis of components made of these materials have to be developed. Several numerical and analytical studies have been carried out on the thermo-mechanical behavior of FG structural members. Tornabene et al. [2] studied the vibration of functionally graded conical shells, cylindrical shells and annular plates, based on the first-order shear deformation theory, using the differential quadrature method. Tanaka et al. [3] presented a methodology for thermo-elastic design in FGMs in order to reduce their thermal stresses. They employed direct sensitivity and finite neomycin sulfate methods to reach an optimal distribution of the volume fraction of phases in the FGM. Chen and Lin [4] investigated an alternative numerical solution of thick-walled cylinders and spheres made of FGMs, using the transmission matrix method. Obata and Noda [5] investigated the thermal stresses in functionally graded hollow spheres and circular cylinders employing a perturbation approach.
Pelletier and Vel [6] analyzed the steady state response of an FG thick, simply supported, cylindrical shell subjected to thermo-mechanical loads using the power series method. Dai et al. [7] employed a direct method to solve the heat conduction problem and Navier equations of a functionally graded hollow sphere, and presented exact solutions for the one-dimensional steady-state magneto-thermo-elastic stresses. Eslami et al. [8] solved the one dimensional steady state thermo-mechanical stress problem in a hollow sphere made of functionally graded material using the direct method of solution of the corresponding Navier equation.
In recent years, piezoelectric materials have been extensively used in various smart structures as distributed sensors and actuators for active structural control purposes. Several research works have contributed towards modeling and investigating the basic structural responses of piezoelectric materials, i.e. in the pioneering research work of Tiersten [9]. Shakeri et al. [10] carried out three-dimensional elasticity analysis of laminated cylinders with a piezoelectric sensor and actuator layers, by means of trigonometric function expansion and the Galerkin finite element method. A numerical analysis of a piezoelectric strip under the effects of symmetric pressure and voltage on the upper and the lower edges, with traction free boundaries, using the generalized differential quadrature method, is presented by Hong et al. [11]. Liew et al. [12] studied the active control of functionally graded shells with piezoelectric sensors and actuators using the finite element method. Sheng and Wang [13] obtained thermo-elastic vibration and buckling characteristics of a functionally graded piezoelectric cylindrical shell, using Hamilton’s principle and the first-order shear deformation theory. Wu et al. [14] proposed an analytical solution for the thermo-electro-mechanical deformation field of a laminated cylindrical shell. Material properties of the shell were assumed to obey an identical power law in the radial direction, and exact solutions were obtained using the power series together with Fourier series expansion methods. Alibeigloo [15] obtained a thermoelastic solution for axisymmetric deformations of functionally graded cylindrical shells bonded to thin piezoelectric layers, assuming a Navier type solution for the governing equations. Akbari Alashti and Khorsand [16] carried out three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads, using the polynomial and Fourier quadrature methods.