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

Journal article


Malikan, Mohammad and Nguyen, Van Bac 2018. A novel one variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on the Eringen's nonlocal differential law. World Journal of Engineering. https://doi.org/10.1108/WJE-11-2017-0357
AuthorsMalikan, Mohammad and Nguyen, Van Bac
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 resultswere 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 a symmetrical analyses. Originality/value – A formulation for FSDT was innovated by reconsidering its errors to improve the FSDT for investigation of mechanical behavior of nanoplates.

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 resultswere 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 a symmetrical analyses.
Originality/value – A formulation for FSDT was innovated by reconsidering its errors to improve the FSDT for investigation of mechanical behavior of nanoplates.

KeywordsGraphene sheets; Nonlocal; Elasticity theory; One variable FSDT
Year2018
JournalWorld Journal of Engineering
PublisherEmerald Group Publishing Limited
ISSN1708-5284
Digital Object Identifier (DOI)https://doi.org/10.1108/WJE-11-2017-0357
Web address (URL)http://hdl.handle.net/10545/623263
hdl:10545/623263
Publication dates04 Oct 2018
Publication process dates
Deposited08 Jan 2019, 11:53
Accepted05 Feb 2018
Accepted08 Feb 2018
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Archived with thanks to World Journal of Engineering

ContributorsIslamic Azad University, University of Derby, Islamic Azad University Mashhad Branch Mashhad Iran (the Islamic Republic of) and University of Derby Derbyshire United Kingdom of Great Britain and Northern Ireland
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https://repository.derby.ac.uk/item/94wx1/a-novel-one-variable-first-order-shear-deformation-theory-for-biaxial-buckling-of-a-size-dependent-plate-based-on-the-eringen-s-nonlocal-differential-law

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