Open AccessBending, buckling and Vibrations Analysis of the graphene nanoplate using the modified couple stress theory
Author(s) -
Majid Eskandari Shahraki,
Mahmoud Shariati,
Naser Asiaban,
Jafar Eskandari Jam
Publication year - 2021
Publication title -
mechanika
Language(s) - English
Resource type - Journals
eISSN - 2029-6983
pISSN - 1392-1207
DOI - 10.5755/j02.mech.25298
Subject(s) - buckling , cauchy stress tensor , boundary value problem , bending , curvature , materials science , infinitesimal strain theory , tensor (intrinsic definition) , vibration , stress (linguistics) , pure bending , structural engineering , work (physics) , strain energy , graphene , mechanics , mathematical analysis , geometry , mathematics , composite material , finite element method , physics , engineering , thermodynamics , nanotechnology , linguistics , philosophy , quantum mechanics
In this paper using the modified couple stress theory, to study the bending, buckling and vibration characteristics of the rectangular Mindlin's nanoplates with graphene material was investigated. With the aim of considering the effects of small scales, the modified couple stress theory, which has only one parameter of length scale and also was presented by Yang in 2002, was used. In the modified couple stress theory; the strain energy density is a function of the components of the strain tensor, curvature tensor, stress tensor and the symmetric part of the couple stress tensor. After obtaining the strain energy, external work, and buckling equation and placing them in the Hamilton's equation, the basic and auxiliary equations of the nanoplates were obtained. Then, by applying boundary and force conditions in the governing equations, the bending, buckling and vibration of the rectangular graphene nanoplates with thickness h and simply-supported conditions were explored. Also, the solution method was the Navier's solution.