Eur. Phys. J. Plus (2017) 132: 231
https://doi.org/10.1140/epjp/i2017-11497-5

Regular Article

Nonlocal size dependency in nonlinear instability of axially loaded exponential shear deformable FG-CNT reinforced nanoshells under heat conduction

¹ Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
² Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran

^* e-mail: a.fattahi@iaut.ac.ir

Received: 10 February 2017
Accepted: 7 April 2017
Published online: 25 May 2017

Abstract

The present study deals with size-dependent nonlinear instability characteristics of functionally graded carbon nanotube (FG-CNT) reinforced composite shells at nanoscale subjected to axial compression combined with through-thickness heat conduction. To take size dependency into account, Eringen’s nonlocal continuum elasticity is incorporated to a novel shear deformation shell theory including a refined exponential distribution for transverse shear strain. In addition to the uniform distribution (UD) of CNT reinforcements, three FG patterns are also considered, namely FG-A, FG-V and FG-X. Also, on the basis of polynomial series, the temperature variation due to the through-thickness heat conduction is estimated. Via a perturbation-based boundary layer-type solving procedure, explicit expressions for nonlocal equilibrium curves are proposed relevant to the prebuckling and postbuckling regimes of FG-CNT exponential shear deformable nanoshells with temperature-dependent and temperature-independent material properties. It is observed that by taking the nonlocality size effect into consideration, the influence of the through-thickness heat conduction on the nonlinear axial instability response of FG-CNT reinforced nanoshells becomes more significant.