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 Forced Vibration Numerical Analysis of Reticulate Systems by Dynamic Finite Element Method

2019 ◽  
Vol 13 (4) ◽  
pp. 24
Author(s):  
Olivier A. Passoli ◽  
Emmanuel E. T. Olodo ◽  
Valery K. Doko ◽  
Georges Ale ◽  
Edmond C. Adjovi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Forced Vibration ◽  
Excitation Frequency ◽  
Dynamic Finite Element ◽  
Dynamic Rigidity ◽  
Simple Systems ◽  
Element Method

This work is devoted to forced vibration numerical analysis of reticulate bar systems. The dynamic finite element method was used for determination of frequencies, displacement amplitudes, rotation angles and the dynamic effort factors. By this method the components of the dynamic rigidity matrix and inertia matrix depend on applied external excitation frequency. Obtained results are compared with those calculated by the classical finite element method as well as by analytical method. It is shown that the dynamic finite element allows for exact solutions to the problems in forced vibration of structures. Accuracy of dynamic finite element solution is verified through obtaining analytical solutions on simple systems. In case of complex systems where analytical calculations are complicated the dynamic finite element can become a universal tool for dynamic analysis.

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.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

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