Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Abstract

In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. A detailed derivation of the equations of motion based on Eringen nonlocal theory using Hamilton's principle is presented, and a closedform solution is derived for buckling behavior of the new model with various boundary conditions. The nonlocal elasticity theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The proposed model is efficient in predicting the shear effect in FG nanobeams by applying third-order shear deformation theory. The proposed approach is validated by comparing the obtained results with benchmark results available in the literature. In the following, a parametric study is conducted to investigate the influences of the length scale parameter, gradient index, and length-to-thickness ratio on the buckling of FG nanobeams and the improvement on nonlocal third-order shear deformation theory comparing with the classical (local) beam model has been shown. It is found out that length scale parameter is crucial in studying the stability behavior of the nanobeams.

Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium

“…(16) and integrating Eqs. (19)(20)(21)(22), over the beam's cross-section area, the force-strain and the momentstrain of the nonlocal third-order Reddy FGP beam theory can be obtained as follows:…”

“…An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory in presented by Ansari et al [18]. Recently, Rahmani and Jandaghian [19] presented buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory. Also, mechanical behavior of functionally graded nanoscale beams using a refined shear deformation beam theory examined by Zemri et al [20].…”

Nonlocal vibration analysis of circular double-layered graphene sheets resting on an elastic foundation subjected to thermal loading

“…In other words, the mechanical behavior of nanostructures is size-dependent. Since the classic continuum models cannot capture the size effect, some higher-order continuum theories such as the modified couple stress theory [6,7], the strain gradient theory [8,9], the surface stress theory [10][11][12][13], and the nonlocal elasticity theory [14][15][16][17] can be employed for the analysis of small-scale systems. In addition, Peddieson et al [18] indicated that the nonlocal elasticity theory can be appropriately applied to nanotechnology applications.…”

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

“…Most recently, Ebrahimi et al [23] examined the applicability of differential transformation method in investigations on vibrational characteristics of FG size-dependent nanobeams. Recently, Rahmani and Jandaghian [24] presented Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory. Also, nonlinear free vibration of axially FG Euler-Bernoulli microbeams with immovable ends is studied by Simsek [25], using the MCST.…”