Assessment of Third‌-order Shear Deformation Graphene Nanoplate Response under Static Loading Using Modified Couple Stress Theory

الموضوعات :

Majid Eskandari Shahraki ¹ (Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran)
Mahmoud Shariati ² (Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran)
Naser Asiaban ³ (Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran)
Ali Davar ⁴ (Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran)
Mohsen Heydari Beni ⁵ (Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran)
Jafar Eskandari Jam ⁶ (Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran)

تاريخ الإرسال : 19 الثلاثاء , شعبان, 1443 تاريخ التأكيد : 08 الإثنين , شوال, 1443 تاريخ الإصدار : 29 الثلاثاء , جمادى الثانية, 1443

الکلمات المفتاحية: Bending, Buckling, Navier Solution Method, Modified couple-stress theory, Third-order Nano-plate,

ملخص المقالة :

In this paper bending and buckling characteristics of third-order shear, and deformation nanoplates were investigated using the modified couple stress theory and Navier type solution. It can be useful for designing and manufacturing micro-electromechanical and nano-electromechanical systems. The modified couple stress theory was applied to provide the possibility of considering the effects of small scales that have only one material length scale parameter. In this theory, the strain energy density is a function of the strain tensor components, curvature tensor, stress tensor, and the symmetric part of the couple stress tensor. After obtaining the strain energy, external work, and buckling equations, the Hamilton principle is employed to derive the governing equations. Furthermore, by applying boundary and loading conditions in the governing equations, the bending and buckling of a third-order shear deformation nanoplate with simply-supported bearings are obtained and the Navier’s solution is used to solve the equations. The results indicate that the third-order nanoplate subjected to sinusoidal loading yields smaller values of dimensionless bending than it does while subjected to uniform surface traction. It was also found that by increasing the length to thickness ratio, the value of the dimensionless bending of nanoplate decreases but by increasing the aspect ratio of the plate, this value increases. Furthermore, it was shown that the critical buckling load of the third-order nanoplate under uniaxial loading increases by increasing the ratio of the length scale parameter to the thickness of the nanoplate but it decreases by increasing the length to thickness ratio of the nanoplate.

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