On the Finite Element Modelling and Simulation of Carbon Nanotubes

2014 ◽  
Vol 607 ◽  
pp. 55-61 ◽  
Author(s):  
Ghasem Ghadyani ◽  
Mojtaba Akbarzade ◽  
Andreas Öchsner
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Beam Theory ◽  
Elastic Stiffness ◽  
Buckling Load ◽  
Timoshenko Beams ◽  
Bernoulli Beam ◽  
Critical Buckling Load ◽  
Beam Elements ◽  
Mesh Density

In this paper, two different beam elements (i.e. according to the Bernoulli beam and Timoshenko beam theory) for the modeling of the behavior of carbon nanotubes are applied. Finite element models are developed for this study with variation of chirality for both zig-zag and armchair configurations of CNTs. The deformations from the finite element simulations are subsequently used to predict the elastic stiffness and the critical buckling load in terms of material and geometric parameters. Furthermore, the dependence of mechanical properties on the kind of beam element and the mesh density is also compared. Based on the obtained results, Youngs modulus and critical buckling load of structures using Timoshenko beams are clearly lower than the Bernoulli beam approach for all chiralities.

Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory

2020 ◽  
Vol 62 ◽  
pp. 108-119
Author(s):  
Tayeb Bensattalah ◽  
Ahmed Hamidi ◽  
Khaled Bouakkaz ◽  
Mohamed Zidour ◽  
Tahar Hassaine Daouadji
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Axial Compression ◽  
Buckling Load ◽  
Small Scale ◽  
Beam Model ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Nonlocal Continuum Theory ◽  
Walled Carbon Nanotubes

The present paper investigates the nonlocal buckling of Zigzag Triple-walled carbon nanotubes (TWCNTs) under axial compression with both chirality and small scale effects. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling loads under axial compression are obtained. The TWCNTs are considered as three nanotube shells coupled through the van der Waals interaction between them. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, a significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed, and these are then compared with: A single-walled carbon nanotubes (SWCNTs); and Double-walled carbon nanotubes (DWCNTs). These findings are important in mechanical design considerations and reinforcement of devices that use carbon nanotubes.

Analytical Solution of Sidewise Buckling of Two-Hinged Circular Arch under Concentrated Force

2013 ◽  
Vol 676 ◽  
pp. 170-174
Author(s):  
Ju Tao Kuang ◽  
Ai Rong Liu ◽  
Qi Ca Yu ◽  
Jiang Dong Deng
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Lateral Displacement ◽  
Displacement Function ◽  
Buckling Load ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Critical Buckling Load ◽  
Circular Arch ◽  
Good Agreement

By the setting torsional and lateral displacement function of sidewise buckling of two-hinged circular arch under concentrated force, the single-arch structure's bending, torsional deformation and external force potential can be constructed. An analytical solution for the lateral critical buckling load of two-hinged arch is first deduced by using the energy method; the results are also compared and analyzed by the finite element method. The results show that the analytical solution of single arch’s lateral critical buckling load is in good agreement with the finite element numerical solution, and the validity of the formula is proven.

Developing a beam formulation for semi-crystalline two-way shape memory polymers

2020 ◽  
Vol 31 (12) ◽  
pp. 1465-1476
Author(s):  
Mohammad-Ali Maleki-Bigdeli ◽  
Majid Baniassadi ◽  
Kui Wang ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Shape Memory ◽  
Shape Memory Polymer ◽  
Beam Theory ◽  
Shape Memory Polymers ◽  
Bernoulli Beam ◽  
Von Karman ◽  
Von Kármán ◽  
Euler Bernoulli Beam ◽  
Beam Theories

In this research, the bending of a two-way shape memory polymer beam is examined implementing a one-dimensional phenomenological macroscopic constitutive model into Euler–Bernoulli and von-Karman beam theories. Since bending loading is a fundamental problem in engineering applications, a combination of bending problem and two-way shape memory effect capable of switching between two temporary shapes can be used in different applications, for example, thermally activated sensors and actuators. Shape memory polymers as a branch of soft materials can undergo large deformation. Hence, Euler–Bernoulli beam theory does not apply to the bending of a shape memory polymer beam where moderate rotations may occur. To overcome this limitation, von-Karman beam theory accounting for the mid-plane stretching as well as moderate rotations can be employed. To investigate the difference between the two beam theories, the deflection and rotating angles of a shape memory polymer cantilever beam are analyzed under small and moderate deflections and rotations. A semi-analytical approach is used to inspect Euler–Bernoulli beam theory, while finite-element method is employed to study von-Karman beam theory. In the following, a smart structure is analyzed using a prepared user-defined subroutine, VUMAT, in finite-element package, ABAQUS/EXPLICIT. Utilizing generated user-defined subroutine, smart structures composed of shape memory polymer material can be analyzed under complex loading circumstances through the two-way shape memory effect.

Buckling of laminated composite cylindrical skew panels

2015 ◽  
Vol 30 (9) ◽  
pp. 1175-1199
Author(s):  
Srinivasa Venkateshappa Chikkol ◽  
Prema Kumar Puttiah Wooday ◽  
Suresh Jayadevappa Yelaburgi
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Laminated Composite ◽  
Buckling Load ◽  
Finite Element Solution ◽  
Element Solution ◽  
Skew Angle ◽  
Critical Buckling Load ◽  
Aluminum 7075 ◽  
Experimental Values

Experimental studies were made on isotropic cylindrical skew panels made of Aluminum 7075-T6 and laminated composite cylindrical skew panels under uniaxial compression. The experimental values of the critical buckling load ( Pcr) were determined using five different methods. The values of Pcr were also determined using MSC/Nastran and CQUAD8 finite element. The experimental values of the Pcr obtained by different methods were compared with the finite element solution. The effects of the skew angle and aspect ratio on the critical buckling load of isotropic cylindrical skew panels made of Aluminum 7075-T6 were studied. The effects of the skew angle, aspect ratio, and the laminate stacking sequence on the critical buckling load of laminated composite cylindrical skew panels were also studied. It is found that the method IV (based on a plot of applied load ( P) vs. average axial strain) yields the highest value for Pcr and method III (based on a plot of P vs. square of out-of-plane-deflection) the lowest value for Pcr. The experimental values given by method IV are seen to be closest to the finite element solution, the discrepancy being in the range of 5–23% for laminated composite cylindrical skew panels. For isotropic panels, it is found that the value Pcr initially increases with an increase in the skew angle and later decreases as the skew angle increases beyond 15°. For laminated composite panels, the Pcr value decreases as the aspect ratio increases for all laminate stacking sequences.

Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler–Bernoulli beam theory

2012 ◽  
Vol 24 (2) ◽  
pp. 226-239 ◽  
Author(s):  
Gang Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Energy Harvesters ◽  
Bernoulli Beam Theory ◽  
Spectral Finite Element ◽  
Euler Bernoulli Beam ◽  
Element Method

Single-degree-of-freedom lumped parameter model, conventional finite element method, and distributed parameter model have been developed to design, analyze, and predict the performance of piezoelectric energy harvesters with reasonable accuracy. In this article, a spectral finite element method for bimorph piezoelectric beam energy harvesters is developed based on the Timoshenko beam theory and the Euler–Bernoulli beam theory. Linear piezoelectric constitutive and linear elastic stress/strain models are assumed. Both beam theories are considered in order to examine the validation and applicability of each beam theory for a range of harvester sizes. Using spectral finite element method, a minimum number of elements is required because accurate shape functions are derived using the coupled electromechanical governing equations. Numerical simulations are conducted and validated using existing experimental data from the literature. In addition, parametric studies are carried out to predict the performance of a range of harvester sizes using each beam theory. It is concluded that the Euler–Bernoulli beam theory is sufficient enough to predict the performance of slender piezoelectric beams (slenderness ratio > 20, that is, length over thickness ratio > 20). In contrast, the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, must be used for short piezoelectric beams (slenderness ratio < 5).

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.

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