Simplified theory and analytical solutions for functionally graded piezoelectric circular plate

Simplified theory and analytical solutions for afunctionally graded piezoelectric circular plate subjected to axisymmetricloading was presented with some assumptions, such as Kirchhoff assumption,Reissner-Mindlin assumption, and the assumption that material propertiesvary exponentially across the thickness of the plate. We derived thesolution of the rotation angle of the normal line of the neutral layer andthe solution of the electric potential in the plate expressed byFourier-Bessel series, in the cases that the edges of the plate was fixed orsimply supported and grounded. The presented solutions were obviously simplecompared with some exact analytical solutions and easy to perform thenumerical analysis. The numerical results for the edge-fixed/grounded platewere applied to validate the simplified theory presented in the paper.