Exact Analysis of Simply Supported Functionally Graded Piezothermoelectric Plates

This paper presents an exact analysis of a functionally graded piezothermo-electric rectangular plate that is simply supported, electrically grounded and isothermal on its four lateral edges. The governing equations are established for an orthotropic functionally graded piezothermoelectric plate under an assumption that the mechanical, electrical, and thermal properties of the material have the same exponential dependence on the thickness-coordinate. An exact three-dimensional general solution in the form of double Fourier series is derived for arbitrary distributions of combined mechanical, electrical, and thermal loadings at the top and bottom surfaces of the plate. Numerical results are presented for three special cases of uniformly distributed loads at the top and bottom surfaces of the plate, and the effect of truncation of the series on the accuracy of the solution is discussed.