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On axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets

  • Gao, Yang (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Xiao, Wan-shen (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Zhu, Haiping (School of Computing, Engineering and Mathematics, Western Sydney University)
  • Received : 2019.05.11
  • Accepted : 2019.10.01
  • Published : 2019.10.25

Abstract

The main objective of this paper is to study the axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets (GSs) under in-plane loading in the theoretical framework of the nonlocal strain gradient theory. To begin with, a graphene sheet is modeled by a two-dimensional plate subjected to simply supported ends, and supposed to have a small initial curvature. Then according to the Hamilton's principle, the nonlinear governing equations are derived with the aid of the classical plate theory and the von-karman nonlinearity theory. Subsequently, for providing a more accurate physical assessment with respect to the influence of respective parameters on the mechanical performances, the approximate analytical solutions are acquired via using a two-step perturbation method. Finally, the authors perform a detailed parametric study based on the solutions, including geometric imperfection, nonlocal parameters, strain gradient parameters and wave mode numbers, and then reaching a significant conclusion that both the size-dependent effect and a geometrical imperfection can't be ignored in analyzing GSs.

Keywords

geometric imperfection;perturbation method;graphene sheets;nonlocal strain gradient theory

Acknowledgement

Supported by : Hunan Provincial Innovation Foundation