Static Analysis of a Functionally Graded Piezoelectric Beam Using Finite Element Method

In this study static analysis of functionally graded piezoelectric material (FGPM) beams is performed using finite element modeling. First order shear deformation beam theory (Timoshenko beam theory) with the assumption of linear strain-displacement relations is used for modeling of displacement and strain fields in the beam. Theoretical formulations are derived employing Hamilton’s principle using linear constitutive relations of piezoelectric materials and including the effect of transverse shear deformation. Finite element method with one dimensional linear continuum isoparametric element, three displacement mechanical degrees of freedom, and one electric potential degree of freedom assigned to each node is then used to investigate the bending behavior of FGPM beam actuator under thermo-electro-mechanical loads. Consequently, a parametric study of the bending behavior of an FGPM beam is performed. The effects of slenderness ratio and fraction of volume of constituent materials, on the thermo-electro-mechanical characteristics are studied. It is shown that under electrical loading the beam represents the so-called non-intermediate behavior.