Keywords: functionally graded material, first order shear deformation shell theory, cylindrical shell, finite element method, static and dynamic analysis, free vibration.

Several research works have been completed for the analysis of the behaviour of functionally graded (FG) and piezoelectric materials in recent years. For example, Tarn [1] studied the thermo mechanical states of functionally graded material (FGM) cylinders under various loadings. Exact solution for thermoelastic deformations and stress fields are obtained in this paper. In another paper, Yang and Shen [2] investigated the free vibration and dynamic instability of functionally graded cylindrical panels subjected to static and periodic axial forces in a thermal environment. A semi-analytical approach is employed to determine the natural frequencies and the unstable regions of the panel. With a three-dimensional piezoelectricity, Wu and Syu [3] present asymptotic formulations of FG piezoelectric cylindrical shells under cylindrical bending type of electromechanical loads by using the method of perturbation. The coupled electro-elastic effects on the structural behavior of FG piezoelectric shells are evaluated. The influence of the material property gradient index on the variables of electric and mechanical fields is studied.

In this paper the analysis of the static bending, free vibration, and dynamic response of a FG panel with two piezoelectric layers has been carried out by using finite element method under different sets of mechanical and electrical loadings. The shell with FGM is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. The electric potential is assumed linear across the FGM shell thickness. The governing equations are obtained using potential energy and Hamilton's principle based on the first order shear deformation shell theory (FSDT) that includes piezoelectric effect. The finite element model is derived based on a constitutive equation of the piezoelectric material accounting for coupling between the elasticity and electric effects using four node elements. The finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGM shells under different mechanical boundary conditions. Numerical results for the FGM shell are given in both dimensionless tabular and graphical forms. The effects of material composition and boundary conditions on static bending, free vibration and dynamic response are also studied. The numerical results obtained using the present model are in good agreement with the available solutions reported in the literature.

1

J.Q. Tarn, "Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads", Int. J. Solids and Structures, 38, 8189-8206, 2001. doi:10.1016/S0020-7683(01)00182-2

2

J. Yang, H.S. Shen, "Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels", J. of Sound and Vibration, 261, 871-893, 2003. doi:10.1016/S0022-460X(02)01015-5

3

C.P. Wu, Y.S. Syu, "Exact solutions of functionally graded piezoelectric shells under cylindrical bending", Int. J. of Solids and Structures, 44, 6450-6472, 2007. doi:10.1016/j.ijsolstr.2007.02.037

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