Evaluation of Mechanical Behaviors of Single-Walled Carbon Nanotubes by Finite Element Analysis

2010 ◽  
Author(s):  
Xiaoxing Lu ◽  
Zhong Hu
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Cross Section ◽  
Plane Deformation ◽  
Element Model ◽  
Element Analysis ◽  
Elliptical Cross ◽  
Beam Elements ◽  
Young’S Moduli ◽  
Walled Carbon Nanotubes

Based on molecular mechanics, a three-dimensional finite element model for armchair, zigzag and chiral single-walled carbon nanotubes (SWCNTs) has been developed, in which the carbon nanotubes (CNTs), when subjected to load, behave like space-frame structures. The bending stiffness of the graphite layer has been considered. The potentials associated with the atomic interactions within a CNT were evaluated by the strain energies of beam elements which serve as structural substitutions of covalent bonds. The out-of-plane deformation (inversion) of the bonds was distinguished from the in-plane deformation by considering an elliptical cross-section for the beam elements. The elastic moduli of beam elements are determined by using a linkage between molecular and continuum mechanics. A closed form solution of the sectional properties of the beam element was derived analytically and verified through the analysis of rolling a graphite sheet into a carbon nanotube. This method was validated by its application to a graphene model, and Young’s modulus of the model was found, showing agreement with the known values of graphite. Modeling of the elastic deformation of SWCNTs reveals that Young’s moduli and the shear modulus of CNTs vary with the tube diameter and are affected by their helicity. With increasing tube diameter, Young’s moduli of both armchair and zigzag CNTs are increasing monotonically and approaching to the Young’s modulus of graphite, which are in agreement with the existing theoretical and experimental results. The rolling energy per atom was computed by finite element analysis. By comparing mechanical properties with circular cross section models, it is found that the computational results of the proposed elliptical cross-section model are closer to the results from the atomistic computations. The proposed model is valid for problems where the effect of local bending of the graphite layer in a CNT is significant. This research work shows that the proposed finite element model may provide a valuable tool for studying the mechanical behaviors of CNTs and their integration in nano-composites.

Support-Condition Analyses of Rotating Beams Under Distributed Imbalance Loading

2011 ◽  
Author(s):  
Kai Jokinen ◽  
Erno Keskinen ◽  
Marko Jorkama ◽  
Wolfgang Seemann
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Constant Cross Section ◽  
Support Condition ◽  
Beam Elements

In roll balancing the behaviour of the roll can be studied either experimentally with trial weights or, if the roll dimensions are known, analytically by forming a model of the roll to solve response to imbalance. Essential focus in roll balancing is to find the correct amount and placing for the balancing mass or masses. If this selection is done analytically the roll model used in calculations has significant effect to the balancing result. In this paper three different analytic methods are compared. In first method the mode shapes of the roll are defined piece wisely. The roll is divided in to five parts having different cross sections, two shafts, two roll ends and a shell tube of the roll. Two boundary conditions are found for both supports of the roll and four combining equations are written to the interfaces of different roll parts. Totally 20 equations are established to solve the natural frequencies and to form the mode shapes of the non-uniform roll. In second model the flexibility of shafts and the stiffness of the roll ends are added to the support stiffness as serial springs and the roll is modelled as a one flexibly supported beam having constant cross section. Finally the responses to imbalance of previous models are compared to finite element model using beam elements. Benefits and limitations of each three model are then discussed.

scholarly journals Vibrational Characteristics of Zigzag, Armchair and Chiral Cantilever Single-Walled Carbon Nanotubes

2013 ◽  
Vol 22 (6) ◽  
pp. 096369351302200
Author(s):  
S.K. Jalan ◽  
B. Nageswara Rao ◽  
S. Gopalakrishnan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Single Walled Carbon Nanotubes ◽  
Finite Element Models ◽  
Element Analysis ◽  
Single Walled Carbon ◽  
Empirical Relations ◽  
Vibrational Characteristics ◽  
Walled Carbon Nanotubes

Finite element analysis has been performed to study vibrational characteristics of cantilever single walled carbon nanotubes. Finite element models are generated by specifying the C-C bond rigidities, which are estimated by equating energies from molecular mechanics and continuum mechanics. Bending, torsion, and axial modes are identified based on effective mass for armchair, zigzag and chiral cantilever single walled carbon nanotubes, whose Young's modulus is evaluated from the bending frequency. Empirical relations are provided for frequencies of bending, torsion, and axial modes.

scholarly journals Numerical Studies on the Stiffness of Arc Elliptical Cross-section Helical Spring Subjected to Circumference Force

Mechanika ◽  
2021 ◽  
Vol 27 (4) ◽  
pp. 327-334
Author(s):  
Yuan WANG ◽  
Qingchun WANG ◽  
Zehao SU
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cross Section ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Helical Spring ◽  
Element Analysis ◽  
Elliptical Cross ◽  
Stiffness Property ◽  
Regression Formula

 Due to its excellent properties, elliptical cross-section helical spring has been widely used in automobile industry, such as valve spring, arc spring used in Dual Mass Flywheel and so on. Existing stiffness formulae of helical spring remain to be tested, and stiffness property of elliptical cross-section arc spring has been little studied. Hence, study on the stiffness of elliptical cross-section helical spring is significant in the development of elliptical cross-section helical spring. This paper proposes a method to study the stiffness property of elliptical cross-section helical spring that the experiment design method is adopted with finite element analysis. Firstly, the finite element analysis method was used to verify the cylindrical (circular cross-section and elliptical cross-section) springs. Then, the regression formula was designed and derived compared with the reference springs’ stiffness formulae by experimental design. Last, regression formula was verified with existing experiment data. The novelty in this paper is that simulation technology of arc spring was investigated and a stiffness regression equation of arc elliptical cross-section spring was obtained using orthogonal regression design, with significance in wide use of the arc elliptical cross-section helical spring promotion. 

scholarly journals Development of Empirical Relations for the Transversely Isotropic Properties of Zigzag, Armchair and Chiral Single-Walled Carbon Nanotubes

2012 ◽  
Vol 21 (4) ◽  
pp. 096369351202100 ◽  
Author(s):  
S.K. Jalan ◽  
B. Nageswara Rao ◽  
S. Gopalakrishnan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Transversely Isotropic ◽  
Single Walled Carbon Nanotubes ◽  
Element Analysis ◽  
Single Walled Carbon ◽  
Empirical Relations ◽  
Pure Extension ◽  
Walled Carbon Nanotubes ◽  
Walled Cylinder

Finite element analysis has been performed to evaluate transversely isotropic properties of the single walled carbon nanotubes (SWCNTs). Finite element models of SWCNTs are generated by specifying the C-C bond rigidities (which are arrived by equating the energies from molecular mechanics and continuum mechanics). The five independent transversely isotropic properties for different chiralities are evaluated using the stress fields of thick-walled cylinders and the elastic deformations of SWCNTs subjected to pure extension, internal pressure and pure torsion loads. The adequacy of the elastic properties is demonstrated through modelling of an equivalent overall orthotropic hollow thick-walled cylinder under different loading conditions. Empirical relations are provided for the five independent elastic constants useful for armchair, zigzag and chiral zigzag SWCNTs.

LENGTH AND WIDTH EFFECTS OF METAL FILMS ON STRESS-INDUCED BENDING OF SURFACE MICROMACHINED CANTILEVER CURVED GRATING

2012 ◽  
Vol 19 (01) ◽  
pp. 1250001 ◽  
Author(s):  
JU-NAN KUO
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Plane Deformation ◽  
Beam Theory ◽  
Element Model ◽  
Metal Films ◽  
Width Ratio ◽  
Element Analysis ◽  
Close Relationship ◽  
Out Of Plane

In this study, the length and width effects of metal films on the stress-induced bending of a surface micromachined cantilever curved grating are systematically investigated. A characterization of cantilever curved gratings with various lengths and widths was conducted to observe out-of-plane deformation. A finite element model was established to analyze the deformation. Finite element analysis and experimental results indicate that the commonly used beam theory formula for predicting the deformation of surface micromachined cantilever curved gratings is not valid for these devices. Experiments show that the shape of a cantilever curved grating and residual stress have a close relationship. As the length increases, the residual stress of the metal increases, resulting in a larger out-of-plane deformation of the cantilever curved grating. The tip deflection gradually decreases as the length-to-width ratio of the cantilever curved grating increases. A more reliable shape design of metal films on the stress-induced bending of surface micromachined cantilever curved gratings can thus be achieved.

scholarly journals Finite Element Analysis and Optimization of Steel Girders with External Prestressing

2018 ◽  
Vol 4 (7) ◽  
pp. 1490 ◽  
Author(s):  
Ali Laftah Abbas ◽  
Abbas Haraj Mohammed ◽  
Raad Dheyab Khalaf ◽  
Khattab Saleem Abdul-Razzaq
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Element Model ◽  
Bottom Flange ◽  
Element Analysis ◽  
Steel Girder ◽  
Finite Element Software ◽  
External Prestressing ◽  
Design Variables ◽  
The Web

Optimization is a process through which the best possible values of design variables are achieved under the given of constraints and in accordance to a selected optimization objective function. Steel I-girders have been used widely in different fields, which are generally fabricated by connecting two plate flanges, a flat web and a series of longitudinal or transverse stiffeners together. The use of steel girder with external prestressing has been used in many countries as a means of strengthening bridges. The purpose of this paper is to develop a finite element model for the optimization of a steel girder with external prestressing. The ANSYS finite element software package was used to find the optimum cross section dimension for the steel girder. Two objective functions are considered in this study there are optimization of the strain energy and total volume of the girder. The design variables are the width of top flange, the thickness of top flange, the width of bottom flange, the thickness of bottom flange, the height of the web, the width of the web and area of prestressing tendons. Two type of steel girder are considered there are steel girder without prestressing and steel girder with prestressing. The results for volume minimization shows that the optimum cross section for steel girder with prestressing smaller than for steel girder without prestressing.

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