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A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law

Mohammad Malikan (Faculty of Engineering, Department of Mechanical Engineering, Islamic Azad University, Mashhad Branch, Mashhad, Iran)
Van Bac Nguyen (College of Engineering and Technology, Department of Mechanical Engineering and the Built Environment, University of Derby, Derbyshire, UK)

World Journal of Engineering

ISSN: 1708-5284

Article publication date: 1 October 2018

Abstract

Purpose

This paper aims to present a new one-variable first-order shear deformation theory (OVFSDT) using nonlocal elasticity concepts for buckling of graphene sheets.

Design/methodology/approach

The FSDT had errors in its assumptions owing to the assumption of constant shear stress distribution along the thickness of the plate, even though by using the shear correction factor (SCF), it has been slightly corrected, the errors have been remained owing to the fact that the exact value of SCF has not already been accurately identified. By using two-variable first-order shear deformation theories, these errors decreased further by removing the SCF. To consider nanoscale effects on the plate, Eringen’s nonlocal elasticity theory was adopted. The critical buckling loads were computed by Navier’s approach. The obtained numerical results were then compared with previous studies’ results using molecular dynamics simulations and other plate theories for validation which also showed the accuracy and simplicity of the proposed theory.

Findings

In comparing the biaxial buckling results of the proposed theory with the two-variable shear deformation theories and exact results, it revealed that the two-variable plate theories were not appropriate for the investigation of asymmetrical analyses.

Originality/value

A formulation for FSDT was innovated by reconsidering its errors to improve the FSDT for investigation of mechanical behavior of nanoplates.

Keywords

Acknowledgements

The authors wish to express their sincere thanks to the reviewers for their valuable suggestions for improving the paper.

Citation

Malikan, M. and Nguyen, V.B. (2018), "A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law", World Journal of Engineering, Vol. 15 No. 5, pp. 633-645. https://doi.org/10.1108/WJE-11-2017-0357

Publisher

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Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited