Finite Element Analysis of Functionally Graded Piezoelectric Beams

In this paper, the static bending, free vibration, and dynamic response of functionally graded piezoelectric beams have been carried out by nite element method under different sets of mechanical, thermal, and electrical loadings. The beam with functionally graded piezoelectric material (FGPM) is assumed to be graded across the thickness with a simple power law distribution in terms of the volume fractions of the constituents. The electric potential is assumed linear across the FGPM beam thickness. The temperature eld is assumed to be of uniform distribution over the beam surface and through the beam thickness. The governing equations are obtained using potential energy and Hamilton s principle based on the Euler-Bernoulli beam theory that includes thermo-piezoelectric effects. The nite element model is derived based on the constitutive equation of piezoelectric material accounting for coupling between the elasticity and the electric effect by two nodes Hermitian beam element. The present nite element is modelled with displacement components and electric potential as nodal degrees of freedom. The temperature eld is calculated by post-computation through the constitutive equation. Results are presented for two-constituent FGPM beam under different mechanical boundary conditions. Numerical results include the in uence of the different power law indexes, the effect of mechanical, thermal, and electrical loadings and the type of in-plane boundary conditions on the de ection, stress, natural frequencies, and dynamic response. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.