A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory

Youcef Mokhtar , Houari Heireche , Abdelmoumen Anis Bousahla , Mohammed Sid Ahmed Houari , Abdelouahed Tounsi , S.R. Mahmoud

Abstract

In this paper, a novel simple shear deformation theory for buckling analysis of single layer graphene sheet is formulated using the nonlocal differential constitutive relations of Eringen. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the rectangular nano-plate. The equations of motion of the nonlocal theories are derived and solved via Navier\'s procedure for all edges simply supported boundary conditions. The results are verified with the known results in the literature. The influences played by Effects of nonlocal parameter, length, thickness of the graphene sheets and shear deformation effect on the critical buckling load are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

Key Words

buckling; graphene; a simple 3-unknown theory; nonlocal elasticity theory; navier type solution

Address

Youcef Mokhtar and Houari Heireche — Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria
Abdelmoumen Anis Bousahla — Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria; Centre Universitaire Ahmed Zabana de Relizane, Algeria
Mohammed Sid Ahmed Houari — Université Mustapha Stambouli de Mascara, Department of Civil Engineering, Mascara, Algeria; 4Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algeria
Abdelouahed Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Civil and Environmental Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
S.R. Mahmoud — Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

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