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Journal of Nanomaterials
Volume 2018, Article ID 3037063, 12 pages
Research Article

Monte Carlo-Based Finite Element Method for the Study of Randomly Distributed Vacancy Defects in Graphene Sheets

1School of Transportation, Nantong University, Nantong, China
2Département Mécanique, Institut National des Sciences Appliquées de Rouen, Rouen, France

Correspondence should be addressed to Jiajia Shi; nc.ude.utn@jjihs

Received 20 January 2018; Revised 4 June 2018; Accepted 29 July 2018; Published 10 October 2018

Academic Editor: Giuseppe Compagnini

Copyright © 2018 Liu Chu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposed an effective stochastic finite element method for the study of randomly distributed vacancy defects in graphene sheets. The honeycomb lattice of graphene is represented by beam finite elements. The simulation results of the pristine graphene are in accordance with literatures. The randomly dispersed vacancies are propagated and performed in graphene by integrating Monte Carlo simulation (MCS) with the beam finite element model (FEM). The results present that the natural frequencies of different vibration modes decrease with the augment of the vacancy defect amount. When the vacancy defect reaches 5%, the regularity and geometrical symmetry of displacement and rotation in vibration behavior are obviously damaged. In addition, with the raise of vacancy defects, the random dispersion position of vacancy defects increases the variance in natural frequencies. The probability density distributions of natural frequencies are close to the Gaussian and Weibull distributions.