Eur. Phys. J. Plus (2018) 133: 196
https://doi.org/10.1140/epjp/i2018-12014-2

Regular Article

Nonlocal elasticity and shear deformation effects on thermal buckling of a CNT embedded in a viscoelastic medium

¹ Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia
² Department of Mathematics, Faculty of Science, Kafrelsheikh University, 33516, Kafrelsheikh, Egypt

^* e-mail: zenkour@sci.kfs.edu.eg

Received: 2 December 2017
Accepted: 16 April 2018
Published online: 24 May 2018

Abstract

The thermal buckling analysis of carbon nanotubes embedded in a visco-Pasternak’s medium is investigated. The Eringen’s nonlocal elasticity theory, in conjunction with the first-order Donnell’s shell theory, is used for this purpose. The surrounding medium is considered as a three-parameter viscoelastic foundation model, Winkler-Pasternak’s model as well as a viscous damping coefficient. The governing equilibrium equations are obtained and solved for carbon nanotubes subjected to different thermal and mechanical loads. The effects of nonlocal parameter, radius and length of nanotube, and the three foundation parameters on the thermal buckling of the nanotube are studied. Sample critical buckling loads are reported and graphically illustrated to check the validity of the present results and to present benchmarks for future comparisons.