A Modified Couple Stress Theory for Postbuckling Analysis of Timoshenko and Reddy-Levinson Single-Walled Carbon Nanobeams

Abstract

The novelty of this study is presentation of an exact solution for prediction of postbuckling<br><br>behavior of shear deformable micro- and nano-scale beams based on modified couple<br><br>stress theory and using principle of minimum potential energy. Timoshenko and Reddy-<br><br>Levinson beam theories are applied to consider the shear deformation effect and Von<br><br>Karman nonlinear kinematics is used to describe the nonlinear behavior of the<br><br>postbuckling, and the Poisson's effect is also considered in stress-strain relation. Also, the<br><br>size effect is exposed by introducing a material length scale parameter. Finally, the<br><br>influences of shear deformation, Poisson's ratio and variations of length and thickness are<br><br>investigated. The results indicate that the classical theory exaggerates the postbuckling<br><br>amplitude of the nanobeam and overstates the effect of shear deformation on the<br><br>postbuckling response of the nanobeam.