scholarly journals Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment

2021 ◽  
Vol 11 (7) ◽  
pp. 3250
Author(s):  
Ahmed Amine Daikh ◽  
Mohammed Sid Ahmed Houari ◽  
Behrouz Karami ◽  
Mohamed A. Eltaher ◽  
Rossana Dimitri ◽  
...  
Keyword(s):  
Thermal Environment ◽  
Numerical Study ◽  
Slenderness Ratio ◽  
Higher Order ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Scale Size ◽  
Proposed Model ◽  
Reinforcement Material

This paper presents a mathematical continuum model to investigate the static stability buckling of cross-ply single-walled (SW) carbon nanotube reinforced composite (CNTRC) curved sandwich nanobeams in thermal environment, based on a novel quasi-3D higher-order shear deformation theory. The study considers possible nano-scale size effects in agreement with a nonlocal strain gradient theory, including a higher-order nonlocal parameter (material scale) and gradient length scale (size scale), to account for size-dependent properties. Several types of reinforcement material distributions are assumed, namely a uniform distribution (UD) as well as X- and O- functionally graded (FG) distributions. The material properties are also assumed to be temperature-dependent in agreement with the Touloukian principle. The problem is solved in closed form by applying the Galerkin method, where a numerical study is performed systematically to validate the proposed model, and check for the effects of several factors on the buckling response of CNTRC curved sandwich nanobeams, including the reinforcement material distributions, boundary conditions, length scale and nonlocal parameters, together with some geometry properties, such as the opening angle and slenderness ratio. The proposed model is verified to be an effective theoretical tool to treat the thermal buckling response of curved CNTRC sandwich nanobeams, ranging from macroscale to nanoscale, whose examples could be of great interest for the design of many nanostructural components in different engineering applications.

scholarly journals Hygro-Magnetic Vibration of the Single-Walled Carbon Nanotube with Nonlinear Temperature Distribution Based on a Modified Beam Theory and Nonlocal Strain Gradient Model

2020 ◽  
Vol 12 (05) ◽  
pp. 2050054 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty ◽  
Mohammad Malikan ◽  
Hamid Mohammad-Sedighi
Keyword(s):  
Shear Deformation ◽  
Strain Gradient ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Beam Theory ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Single Walled Carbon Nanotube ◽  
Proposed Model ◽  
Nonlocal Strain Gradient

In this study, vibration analysis of single-walled carbon nanotube (SWCNT) has been carried out by using a refined beam theory, namely one variable shear deformation beam theory. This approach has one variable lesser than a contractual shear deformation theory such as first-order shear deformation theory (FSDT) and acts like classical beam approach but with considering shear deformations. The SWCNT has been placed in an axial or longitudinal magnetic field which is also exposed to both the hygroscopic as well as thermal environments. The thermal environment is considered as nonlinear thermal stress field based on the Murnaghan’s model whereas the hygroscopic environment is assumed as a linear stress field. The size effect of the SWCNT has been captured by both the nonlocal and gradient parameters by employing the Nonlocal Strain Gradient Theory (NSGT). Governing equation of motion of the proposed model has been developed by utilizing the extended Hamilton’s principle and the non-dimensional frequency parameters have been computed by incorporating the Navier’s approach for Hinged–Hinged (HH) boundary condition. The proposed model is validated with the existing model in special cases, by comparing the non-dimensional frequency parameters, displaying an excellent agreement. Further, a parametric study has been conducted to analyze the impact of nonlocal parameter, gradient parameter, thermal environment, hygroscopic environment, and magnetic field intensity on the non-dimensional frequency parameters. Also, results for some other theories like Classical Elasticity Theory (CET), Nonlocal Elasticity Theory (NET), and Strain Gradient Theory (SGT) have been presented along with the NSGT.

scholarly journals A Method to Determine Material Length Scale Parameters in Elastic Strain Gradient Theory

2019 ◽  
Vol 87 (3) ◽  
Author(s):  
Jingru Song ◽  
Yueguang Wei
Keyword(s):  
Strain Gradient ◽  
Size Effects ◽  
Elastic Strain ◽  
Higher Order ◽  
Experimental Results ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Face Centered Cubic ◽  
Scale Parameters

Abstract With specimen size decrease for advanced structural materials, the measured mechanics behaviors display the strong size effects. In order to characterize the size effects, several higher-order theories have been presented in the past several decades, such as the strain gradient theories and the micro-polar theories, etc. However, in each higher-order theory, there are several length scale parameters included, which are usually taken as the material parameters and are determined by using the corresponding theoretical predictions to fit experimental results. Since such kind of experimental approaches needs high techniques, it is very difficult to be performed; therefore, the obtained experimental results are very few until now; in addition, the physical meanings of the parameters still need to be investigated. In the present research, an equivalent linkage method is used to simply determine the elastic length parameters appeared in the elastic strain gradient theory for a series of typical metal materials. We use both the elastic strain gradient theory and the higher-order Cauchy-Born rule to model the materials mechanics behaviors by means of a spherical expanding model and then make a linkage for both kinds of results according to the equivalence of strain energy densities. The values of the materials length parameters are obtained for a series of typical metal systems, such as the face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) metals.

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.

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

2013 ◽  
Vol 135 (5) ◽  
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.

Higher order nonlocal viscoelastic strain gradient theory for dynamic buckling analysis of carbon nanocones

2020 ◽  
Vol 107 ◽  
pp. 106259
Author(s):  
M.S.H. Al-Furjan ◽  
Ahmad Farrokhian ◽  
Behrooz Keshtegar ◽  
Reza Kolahchi ◽  
Nguyen-Thoi Trung
Keyword(s):  
Strain Gradient ◽  
Higher Order ◽  
Buckling Analysis ◽  
Dynamic Buckling ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Carbon Nanocones ◽  
Viscoelastic Strain
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