Nonlinear bending and thermal post-buckling behavior of functionally graded piezoelectric nanosize beams using a refined model

We in this paper analyze the problem of the nonlinear bending, thermal buckling and post-buckling of functionally graded piezoelectric material nanobeams based on Eringen's nonlocal elasticity theory. The beams with immovable clamped ends are exposed to the external electric voltages, a uniform transverse load as well as uniform temperature change. A refined beam model which can transform the Reddy beam model into the Timoshenko beam model is introduced into this study so that we can distinguish the role of transverse shear deformation in complicated stress field. The governing equations are induced by using the generalized variation principle, and then the approximate analytical solution of the FGP material nanobeams for nonlinear, thermal buckling, post-buckling are obtained by using a two-step perturbation method. Subsequently, detailed parametric studies are carried out to get an insight into the effects of different physical parameters, including the slenderness ratio, small scale parameter, volume fraction index and external electric voltages.