Eur. Phys. J. Plus (2019) 134: 555
https://doi.org/10.1140/epjp/i2019-12912-7

Regular Article

A comparison for the non-classical plate model based on axial buckling of single-layered graphene sheets

¹ Department of Mechanical Engineering Science, Faculty of Engineering and Built Environment, University of Johannesburg, 2006, Johannesburg, South Africa
² Department of Mechanical Engineering, Tsinghua University, 100084, Beijing, China

^* e-mail: afattahi@uj.ac.za

Received: 5 February 2019
Accepted: 27 July 2019
Published online: 8 November 2019

Abstract

In this study, the size effect on the axial buckling behavior of single-layered graphene sheets embedded in elastic foundation is studied. Eringen’s non-local elasticity equations are incorporated into first-order shear deformation, higher-order shear deformation, and classical plate theories. Values of Winkler and Pasternak moduli parameters, side lengths of square SLGSs, non-local parameter and mode numbers are obtained from different non-local plate theories. It is shown that the axial buckling behavior is strongly dependent on non-local parameters and moduli which are different for different numbers and side lengths. Furthermore, we find that non-locality is more influential in first-order shear deformation than other non-local plate theories, especially in certain ranges of non-local parameters. Sensitivity indices are determined based on the Sobol method in their corresponding physical ranges.