Application of sinusoidal shear deformation theory and physical neutral surface to analysis of functionally graded piezoelectric plate

The concept of neutral surface for a Functionally Graded Piezoelectric (FGP) plate is developed in this paper. The electro-elastic analysis of a FGP plate resting on Winkler-Pasternak foundation is performed in the theoretical framework provided by a two-variable sinusoidal shear deformation theory, including the aforementioned concept of neutral surface. First, the location of neutral surface is defined with respect to the position of the middle surface and then the governing bending equations are derived using the principle of virtual work. An analytical method is presented to investigate the variation of the displacement and stress components in terms of the main parameters of the model, which are volume fraction exponent of the constituents, the electric potential and foundation parameters. The numerical results are validated through the comparison with available references. The numerical results prove that the value of transverse bending deflection is greater than the corresponding shear deflection. In addition, it can be observed that the volume fraction exponent has peculiar influence on the distribution of displacements and stresses.