Modified Nonlocal Strain Gradient Elasticity for Nano-Rods and Application to Carbon Nanotubes

Nowadays, the modified nonlocal strain gradient theory provides a mathematically well-posed and technically reliable methodology to assess scale effects in inflected nano-structures. Such an approach is extended in this paper to investigate the extensional behavior of nano-rods. The considered integral elasticity model, involving axial force and strain fields, is conveniently shown to be equivalent to a nonlocal differential problem equipped with constitutive boundary conditions. Unlike treatments in the literature, no higher-order boundary conditions are required to close the nonlocal problem. Closed-form solutions of elastic nano-rods under selected loadings and kinematic boundary conditions are provided. As an innovative implication, Young’s moduli of Single-Walled Carbon Nanotubes (SWCNT) weare assessed and compared with predictions of Molecular Dynamics (MD). New benchmarks for numerical analyses were also detected.

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Buckling and vibration analysis of FG-CNT-reinforced composite rectangular thick nanoplates resting on Kerr foundation based on nonlocal strain gradient theory

Journal of Vibration and Control ◽

10.1177/1077546319878976 ◽

2019 ◽

Vol 26 (5-6) ◽

pp. 277-305

Author(s):

Hosein Shahraki ◽

Hossein Tajmir Riahi ◽

Mohsen Izadinia ◽

Sayed Behzad Talaeitaba

Keyword(s):

Carbon Nanotubes ◽

Free Vibration ◽

Boundary Conditions ◽

Strain Gradient ◽

Vibration Analysis ◽

Strain Gradient Theory ◽

Gradient Theory ◽

Length Scale ◽

Reinforced Composite ◽

Nonlocal Strain Gradient

This paper investigates the buckling and free vibration analysis of functionally graded carbon nanotube-reinforced composite thick rectangular nanoplates resting on a Kerr foundation under different boundary conditions. Quasi-three-dimensional hyperbolic shear deformation theory is employed to study the effects of transverse shear deformation and thickness stretching. To capture the small-size effects of nanoscale dimensions, the nonlocal strain gradient theory is used, which includes nonlocal parameters and length scale of the material. In this study, rectangular nanocomposite plates are reinforced by carbon nanotubes which are assumed to be graded through the thickness direction with four types of distributions, namely, uniformly, FG-O, FG-V, and FG-X. The governing equations and boundary conditions are extracted within Hamilton’s principle. They are discretized and numerically solved by utilizing a generalized differential quadrature method. The critical buckling loads and natural frequencies are determined by solving the eigenvalue problem. The accuracy of present results is validated with those available in the literature. Also, the effect of various factors, such as aspect ratio, length-to-thickness ratio, in-plane loading factor, length scale parameter, nonlocal parameter, volume fraction and dispersion profile of carbon nanotubes, elastic foundation coefficients, and different boundary conditions, on the buckling behavior and free vibration of nanoplates is investigated.

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

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x20924828 ◽

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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Torsional Vibration Analysis of Carbon Nanotubes Based on the Strain Gradient Theory and Molecular Dynamic Simulations

Journal of Vibration and Acoustics ◽

10.1115/1.4024208 ◽

2013 ◽

Vol 135 (5) ◽

Cited By ~ 23

Author(s):

R. Ansari ◽

R. Gholami ◽

S. Ajori

Keyword(s):

Carbon Nanotubes ◽

Boundary Conditions ◽

Molecular Dynamic ◽

Strain Gradient ◽

Torsional Vibration ◽

Strain Gradient Theory ◽

Gradient Theory ◽

Length Scale ◽

Molecular Dynamic Simulations ◽

Dynamic Simulations

In the current study, the torsional vibration of carbon nanotubes is examined using the strain gradient theory and molecular dynamic simulations. The model developed based on this gradient theory enables us to interpret size effect through introducing material length scale parameters. The model accommodates the modified couple stress and classical models when two or all material length scale parameters are set to zero, respectively. Using Hamilton's principle, the governing equation and higher-order boundary conditions of carbon nanotubes are obtained. The generalized differential quadrature method is utilized to discretize the governing differential equation of the present model along with two boundary conditions. Then, molecular dynamic simulations are performed for a series of carbon nanotubes with different aspect ratios and boundary conditions, the results of which are matched with those of the present strain gradient model to extract the appropriate value of the length scale parameter. It is found that the present model with properly calibrated value of length scale parameter has a good capability to predict the torsional vibration behavior of carbon nanotubes.

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