Size-Dependent Stress Analysis of Single-Wall Carbon Nanotube Based on Strain Gradient Theory

2017 ◽  
Vol 09 (06) ◽  
pp. 1750087 ◽  
Author(s):  
Mohammad Hosseini ◽  
Hamid Haghshenas Gorgani ◽  
Mohammad Shishesaz ◽  
Amin Hadi
Keyword(s):  
Differential Equation ◽  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Strain Gradient ◽  
Numerical Results ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Classical Elasticity ◽  
Size Dependent ◽  
Governing Differential Equation

This paper studies stress distribution in a single-walled carbon nanotube (SWCNT) under internal pressure with various chirality. Strain gradient theory is used to capture the size-dependent behavior of the SWCNT. Minimum total potential energy principle is successfully applied to derive the governing differential equation and its associated boundary conditions. Due to complexity of the governing differential equation and boundary conditions, numerical scheme is used to solve the problem. Comparing the results based on strain gradient theory and that of classical elasticity shows a major difference between these two methods. However, a close examination of the results indicates that both theories predict the same trend for variations in the radial displacement along the SWCNT radius. Numerical results also indicate that the proposed model can lead into the classical elasticity model, provided the material length scale parameters are taken to be zero. Additionally, for plane strain condition, the radial displacements predicted by strain gradient theory are lower than those predicted by classical elasticity theory. Moreover, numerical results show that in a SWCNT, the non-dimensional radial and circumferential stresses along the wall thickness of the SWCNT increase as the radius is increased. The opposite behavior is true for non-dimensional high-order stresses.

On the size-dependent vibration of the embedded double-walled carbon nanotube conveying fluid using shell model

2018 ◽  
pp. 66-77
Author(s):  
Yaghoub Tadi Beni
Keyword(s):  
Carbon Nanotube ◽  
Size Effect ◽  
Boundary Conditions ◽  
Strain Gradient ◽  
Shell Theory ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Pasternak Foundation ◽  
Modified Strain Gradient Theory ◽  
Conveying Fluid

In this paper, the vibration and instability of double-walled carbon nanotube (DWCNT) conveying fluid were investigated by using the modified strain gradient theory. The Donnell's shell theory was used by taking into consideration the three size effects and simply-supported boundary conditions. The effect of van der Waals force between the two intended walls and the surroundings of the DWCNT was modelled as visco-Pasternak foundation. The governing equations of the problem and boundary conditions were derived from Hamilton’s principle. Also, Navier procedure was used to solve the vibration problem. To verify the results, a comparison was drawn between the results of this study and those of the references. According to the findings, the effects of fluid velocity, stiffness and damping of visco-Pasternak foundation, length of DWCNT and size effect are more considerable in the modified strain gradient theory than in the modified couple stress theory and classical theory. Keywords: Modified strain gradient theory, Donnell’s shell theory, DWCNT, size effect, shell vibration.

A novel model and solution on the bending problem of arbitrary shaped magnetoelectroelastic plates based on the modified strain gradient theory

2021 ◽  
pp. 1045389X2110411
Author(s):  
Yating Han ◽  
Zhen Yan ◽  
Ji Lin ◽  
Wenjie Feng
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Magnetic Coupling ◽  
Current Method ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
General Applicability ◽  
Modified Strain Gradient Theory ◽  
Size Dependent ◽  
Novel Model

A size-dependent magnetoelectroelastic (MEE) plate bending model is established where the governing equations and concrete forms of three different mechanical boundary conditions under modified strain gradient theory are derived by the variational principle. Then, the meshless method of polynomial particular solutions is further developed to solve this bending problem. Finally, the influences of size effect, mechanical-electric-magnetic coupling loads, and Pasternak foundation on the bending properties of MEE plates are detailed discussed by some typical numerical examples. Of importance, by virtue of the general applicability and superior flexibility of current method, the bending analyses of MEE plates under different mechanical boundary conditions and geometrical shapes can be carried out, and some novel conclusions are concluded.

On wave dispersion characteristics of fluid-conveying smart nanotubes considering surface elasticity and flexoelectricity approach

2020 ◽  
pp. 095440622096561
Author(s):  
Amir-Reza Asghari Ardalani ◽  
Ahad Amiri ◽  
Roohollah Talebitooti ◽  
Mir Saeed Safizadeh
Keyword(s):  
Wave Propagation ◽  
Strain Gradient ◽  
Surface Elasticity ◽  
Shear Deformation Theory ◽  
Wave Dispersion ◽  
Strain Gradient Theory ◽  
Wave Number ◽  
Gradient Theory ◽  
Specific Domain ◽  
Size Dependent

Wave dispersion response of a fluid-carrying piezoelectric nanotube is studied in this paper utilizing an improved model for piezoelectric materials which capture a new effect known as flexoelectricity in conjunction with the surface elasticity. For this aim, a higher order shear deformation theory is employed to model the problem. Furthermore, strain gradient effect as well as nonlocal effect is taken into consideration throughout using the nonlocal strain gradient theory (NSGT). Surface elasticity is also considered to make an accurate size-dependent formulation. Additionally, a non-compressible and non-viscous fluid is taken into consideration to model the flow effect. The wave propagation solution is then implemented to the governing equations obtained by Hamiltonian’s approach. The phase velocity and group velocity of the nanotube is determined for three wave modes (i.e. shear, longitudinal and bending waves) to study the influence of various involved factors including strain gradient, nonlocality, flexoelectricity and surface elasticity and flow velocity on the wave dispersion curves. Results reveal a considerable effect of the flexoelectric phenomenon on the wave propagation properties especially at a specific domain of the wave number. The size-dependency of this effect is disclosed. Overall, it is found that the flexoelectricity exhibits a substantial influence on wave dispersion properties of the smart fluid-conveying systems. Hence, such size-dependent effect should be considered to achieve exact and accurate knowledge on wave propagation characteristics of the system.

USE OF STRAIN GRADIENT THEORY FOR MODELING THE SIZE-DEPENDENT PULL-IN OF ROTATIONAL NANO-MIRROR IN THE PRESENCE OF MOLECULAR FORCE

2013 ◽  
Vol 27 (18) ◽  
pp. 1350083 ◽  
Author(s):  
Y. TADI BENI ◽  
M. ABADYAN
Keyword(s):  
Strain Gradient ◽  
Continuum Theory ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Cross Sectional ◽  
Size Dependent ◽  
Proposed Model ◽  
Molecular Force ◽  
Intrinsic Material Length ◽  
Material Length

Experiments reveal that mechanical behavior of nanostructures is size-dependent. Herein, the size dependent pull-in instability of torsional nano-mirror is investigated using strain gradient nonclassic continuum theory. The governing equation of the mirror is derived taking the effect of electrostatic Coulomb and molecular van der Waals (vdW) forces into account. Variation of the rotation angle of the mirror as a function of the applied voltage is obtained and the instability parameters i.e., pull-in voltage and pull-in angle are determined. Nano-mirrors with square and circular cross-sectional beams are investigated as case studies. It is found that when the thickness of the torsional nano-beam is comparable with the intrinsic material length scales, size effect can substantially increase the instability parameters of the rotational mirror. Moreover, the effect of vdW forces on the size-dependent pull-in instability of the system is discussed. The proposed model is able to predict the experimental results more accurately than the previous classic models and reduce the gap between experiment and previous theories.

Free nonlinear vibration analysis of nano-truncated conical shells based on modified strain gradient theory

2021 ◽  
pp. 146442072110419
Author(s):  
Alireza Sheykhi ◽  
Shahrokh Hosseini-Hashemi ◽  
Adel Maghsoudpour ◽  
Shahram E Haghighi
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Couple Stress ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Conical Shells ◽  
Modified Couple Stress

In this study, the nonlinear free vibrations behaviour of nano-truncated conical shells was analysed, using the first-order shear deformable shell model. The analysis took into account the structure size through modified strain gradient theory, and differential quadrature and Fréchet derivative methods in von Kármán-Donnell-type approach to kinematic nonlinearity. The governing equations were obtained, utilizing Hamilton's principle. Partial differential equations plus the non-classical and classical boundary conditions were used to obtain the shells’ equations of motion. Discretizing the boundary conditions and equations of motion were performed based on a generalized differential quadrature analogy. The eigenvalue system was considered based on the harmonic balance technique. The Galerkin and Fréchet derivative approaches were used to determine the nonlinear free vibration behaviour of the carbon nano-cone, which was modelled in the simply- and clamped-supported boundary conditions. Comparisons were made between the findings from the new model versus the couple and classical stress theories, indicating that the classical and modified couple stress theories are distinct representations of modified strain gradient theory. The results also revealed that the degree of hardening of nano-truncated conical shells in the modified strain gradient theory is less than that of modified couple stress and classical theories. This led to a rise in the non-dimensional amplitude and frequency ratios. This study investigated the effect of size on free nonlinear vibrations of nano-truncated conical shells for various apex angles and lengths. Finally, we evaluated and compared our findings versus those reported by previous studies, which confirmed the precision and accuracy of our results.

A nonlocal strain gradient theory for rotating thermo-mechanical characteristics on magnetically actuated viscoelastic functionally graded nanoshell

2020 ◽  
Vol 31 (12) ◽  
pp. 1511-1523
Author(s):  
Mohammad Mahinzare ◽  
Hossein Akhavan ◽  
Majid Ghadiri
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Smart Structure ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Nonlocal Strain Gradient Theory ◽  
Nonlocal Strain Gradient

In this article, a first-order shear deformable model is expanded based on the nonlocal strain gradient theory to vibration analysis of smart nanostructures under different boundary conditions. The governing equations of motion of rotating magneto-viscoelastic functionally graded cylindrical nanoshell in the magnetic field and corresponding boundary conditions are obtained using Hamilton’s principle. To discretize the equations of motion, the generalized differential quadrature method is applied. The aim of this work is to investigate the effects of the temperature changes, nonlocal parameter, material length scale, viscoelastic coefficient, various boundary conditions, and the rotational speed of this smart structure on natural frequencies of rotating cylindrical nanoshell made of magneto-viscoelastic functionally graded material.

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