Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell

Mehralian, Fahimeh; Beni, Yaghoub Tadi; Ansari, R.

doi:10.1016/j.compstruct.2016.05.024

Cited by 89 publications

(18 citation statements)

References 79 publications

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“…Based on the nonlocal strain gradient theory proposed by Lim et al the strain energy is given by [9]:…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…Modified continuum theories, which are developed as analytical methods producing more accurate results as such being comparable to those of atomistic models, are utilized in many studies. For example, Mehralian et al studied the buckling of FG piezoelectric nanoshell under pressure based on the new modified couple stress theory and the critical buckling pressure was shown significantly size dependent by increase in thickness and decrease in length [9]. Size-dependent first order shear deformable shell model on the basis of modified strain gradient theory was utilized by Gholami et al to study the axial buckling of functionally graded cylindrical shell [10].…”

Section: Introductionmentioning

confidence: 99%

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A Nonlocal Strain Gradient Shell Model for Free Vibration Analysis of Functionally Graded Shear Deformable Nanotubes

Beni¹,

Mehralian²

2017

International Journal of Engineering &Amp; Applied Sciences

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In the current study, the size dependent free vibration of shear deformable functionally graded (FG) nanotubes is investigated. The nanotube is modeled as cylindrical shell which contains small scale effects by using the nonlocal strain gradient theory. Material properties of the FG nanotube are assumed to be variable along thickness direction according to power law distribution. The Hamilton's principle is implemented to derive the governing equations and boundary conditions. The numerical results are presented for simply supported FG nanotube and the influence of different parameters, such as nonlocal parameter, length scale parameter, length, thickness and power law index on frequency of FG nanotube are extensively studied. The results reveal that the frequency is significantly size dependent.

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“…Based on the nonlocal strain gradient theory proposed by Lim et al the strain energy is given by [9]:…”

Section: Theoretical Developmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Nonlocal Strain Gradient Shell Model for Free Vibration Analysis of Functionally Graded Shear Deformable Nanotubes

Beni¹,

Mehralian²

2017

International Journal of Engineering &Amp; Applied Sciences

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“…The result also indicates that the deformation magnitude of piezoelectric plates is smaller than that of plates without piezoelectricity, due to the well-known piezoelectric stiffening effect.With the increasing application of functionally-graded piezoelectric materials, precise characterization of their mechanical properties is urgently needed. A great deal of research has been done on the mechanical properties of functionally-graded piezoelectric materials and structures: for example, FGPM cantilever beams [8][9][10][11][12], FGPM plates [13][14][15][16][17], and FGPM shells [18][19][20][21]. At the same time, the generation of new problems also puts forward greater requirements for the corresponding solving methods.…”

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confidence: 99%

Application of Multi-Parameter Perturbation Method to Functionally-Graded, Thin, Circular Piezoelectric Plates

Yang

et al. 2020

Mathematics

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In this study, a multi-parameter perturbation method is used for the solution of a functionally-graded, thin, circular piezoelectric plate. First, by assuming that elastic, piezoelectric, and dielectric coefficients of the functionally-graded materials vary in the form of the same exponential function, the basic equation expressed in terms of two stress functions and one electrical potential function are established in cylindrical coordinate system. Three piezoelectric coefficients are selected as perturbation parameters, and the established equations are solved by the multi-parameter perturbation method, thus obtaining up to first-order perturbation solutions. The validity of the perturbation solution obtained is verified by numerical simulations, based on layer-wise theory. The perturbation process indicates that adopting three piezoelectric coefficients as perturbation parameters follows the basic idea of perturbation theory—i.e., if the piezoelectricity may be regarded as a kind of introduced disturbance, the zero-order solution of the disturbance system corresponds exactly to the solution of functionally-graded plates without piezoelectricity. The result also indicates that the deformation magnitude of piezoelectric plates is smaller than that of plates without piezoelectricity, due to the well-known piezoelectric stiffening effect.

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“…The second approach is use of molecular dynamics methods which include heavy, complicated, and costly calculations. [21][22][23][24][25][26][27][28][29][30][31][32][33][34] The third method is using the higher order continuum theories. These theories utilize material length scale parameters in their constitutive relations and thus help the results to be more accurate.…”

Section: Introductionmentioning

confidence: 99%

“…Elements for modeling nanostructures include nano-beams, nano-discs, and nano-shells. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] Carbon nanotube (CNT) is one of the most commonly used elements in nanostructures which are used in a variety of composite materials and nano systems. CNTs are hollow cylinder made of the convolution of graphene sheets around an axis.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

Beni

Mehralian

Zeverdejani

2017

Journal of Low Frequency Noise, Vibration and Active Control

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In the present work, using the couple stress theory, a new model is provided for vibrating behavior of anisotropic carbon nanotubes. Carbon nanotubes have many applications, and careful analysis of their behavior is important. So far, using the isotropic models, several studies have been conducted on carbon nanotube vibration. According to the arrangement of carbon atoms on the nanotube walls, their properties will be different in various directions. Therefore, the behavior of carbon nanotubes must be considered as anisotropic materials. In this article, initially, using the Hamilton's principle, motion equations, and boundary conditions of carbon nanotubes are extracted based on couple stress theory. Afterwards, the equations are solved using the analytical solution method. In the results section, the effect of different parameters, particularly the anisotropic effect, on the carbon nanotube natural frequency is investigated.

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Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell

Cited by 89 publications

References 79 publications

A Nonlocal Strain Gradient Shell Model for Free Vibration Analysis of Functionally Graded Shear Deformable Nanotubes

A Nonlocal Strain Gradient Shell Model for Free Vibration Analysis of Functionally Graded Shear Deformable Nanotubes

Application of Multi-Parameter Perturbation Method to Functionally-Graded, Thin, Circular Piezoelectric Plates

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

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