scholarly journals Buckling Analysis of Vacancy-Defected Graphene Sheets by the Stochastic Finite Element Method

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1545 ◽  
Author(s):  
Liu Chu ◽  
Jiajia Shi ◽  
Shujun Ben
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Probability Density Distribution ◽  
Graphene Sheets ◽  
Stochastic Finite Element ◽  
Vacancy Defects ◽  
Buckling Behavior ◽  
Element Method ◽  
Defected Graphene

Vacancy defects are unavoidable in graphene sheets, and the random distribution of vacancy defects has a significant influence on the mechanical properties of graphene. This leads to a crucial issue in the research on nanomaterials. Previous methods, including the molecular dynamics theory and the continuous medium mechanics, have limitations in solving this problem. In this study, the Monte Carlo-based finite element method, one of the stochastic finite element methods, is proposed and simulated to analyze the buckling behavior of vacancy-defected graphene. The critical buckling stress of vacancy-defected graphene sheets deviated within a certain range. The histogram and regression graphs of the probability density distribution are also presented. Strengthening effects on the mechanical properties by vacancy defects were detected. For high-order buckling modes, the regularity and geometrical symmetry in the displacement of graphene were damaged because of a large amount of randomly dispersed vacancy defects.

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

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Liu Chu ◽  
Jiajia Shi ◽  
Eduardo Souza de Cursi ◽  
Xunqian Xu ◽  
Yazhou Qin ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Natural Frequencies ◽  
Vacancy Defect ◽  
Honeycomb Lattice ◽  
Graphene Sheets ◽  
Pristine Graphene ◽  
Vacancy Defects ◽  
Element Method

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.

scholarly journals A New Approach of Mathematical Analysis of Structure of Graphene as a Potential Material for Composites

Materials ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 3918
Author(s):  
Mieczysław Jaroniek ◽  
Leszek Czechowski ◽  
Łukasz Kaczmarek ◽  
Tomasz Warga ◽  
Tomasz Kubiak
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Graphene Sheets ◽  
Superposition Method ◽  
Plane Model ◽  
New Approach ◽  
Element Method

The new analysis of a simplified plane model of single-layered graphene is presented in this work as a potential material for reinforcement in ultralight and durable composites. However, owing to the clear literature discrepancies regarding the mechanical properties of graphene, it is extremely difficult to conduct any numerical analysis to design parts of machines and devices made of composites. Therefore, it is necessary to first systemize the analytical and finite element method (FEM) calculations, which will synergize mathematical models, used in the analysis of mechanical properties of graphene sheets, with the very nature of the chemical bond. For this reason, the considered model is a hexagonal mesh simulating the bonds between carbon atoms in graphene. The determination of mechanical properties of graphene was solved using the superposition method and finite element method. The calculation of the graphene tension was performed for two main directions of the graphene arrangement: armchair and zigzag. The computed results were verified and referred to articles and papers in the accessible literature. It was stated that in unloaded flake of graphene, the equilibrium of forces exists; however, owing to changes of inter-atom distance, the inner forces occur, which are responsible for the appearance of strains.

scholarly journals Elastic modulus of defected graphene sheets

2021 ◽  
Vol 1199 (1) ◽  
pp. 012021
Author(s):  
J Bocko ◽  
P Lengvarský
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Modulus ◽  
Graphene Sheets ◽  
The Finite Element Method ◽  
Beam Elements ◽  
Element Method ◽  
Defected Graphene

Abstract In this paper, the elastic modulus of single-layered graphene sheets (SLGSs) with and without defects is investigated using the finite element method. The SLGSs with two chiralities (armchair and zigzag) are modeled by beam elements. At first, the SLGSs without defects are investigated then the carbon atoms and corresponding beam elements are removed and the elastic modulus of SLGSs is determined. The increasing number of defects apparently decreased the elastic modulus of graphene sheets.

Modal properties of macaw palm fruit-rachilla system: An approach by the stochastic finite element method (SFEM)

2021 ◽  
Vol 184 ◽  
pp. 106099
Author(s):  
Fábio Lúcio Santos ◽  
Francisco Scinocca ◽  
Deisenara de Siqueira Marques ◽  
Nara Silveira Velloso ◽  
Flora Maria de Melo Villar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stochastic Finite Element Method ◽  
Stochastic Finite Element ◽  
Palm Fruit ◽  
Modal Properties ◽  
Macaw Palm ◽  
Element Method
Sign in / Sign up

Export Citation Format

Share Document