Rayleigh–Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions

Ansari, R.; Sahmani, S.; Rouhi, H.

doi:10.1016/j.physleta.2011.01.046

Cited by 106 publications

(38 citation statements)

References 49 publications

(55 reference statements)

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“…Darvizeh et al [82] developed a mathematical modeling for generally laminated plates based on generalized differential quadrature rule and Rayleigh-Ritz method. Ansari et al [83] studied the axial buckling of single-walled carbon nanotubes (SWCNTs) with arbitrary boundary conditions by using the Rayleigh-Ritz solution technique and molecular dynamics simulations.…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Rahmani

Jandaghian

2015

Appl. Phys. A

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In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. A detailed derivation of the equations of motion based on Eringen nonlocal theory using Hamilton's principle is presented, and a closedform solution is derived for buckling behavior of the new model with various boundary conditions. The nonlocal elasticity theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The proposed model is efficient in predicting the shear effect in FG nanobeams by applying third-order shear deformation theory. The proposed approach is validated by comparing the obtained results with benchmark results available in the literature. In the following, a parametric study is conducted to investigate the influences of the length scale parameter, gradient index, and length-to-thickness ratio on the buckling of FG nanobeams and the improvement on nonlocal third-order shear deformation theory comparing with the classical (local) beam model has been shown. It is found out that length scale parameter is crucial in studying the stability behavior of the nanobeams.

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Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Rahmani

Jandaghian

2015

Appl. Phys. A

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“…In this work, the results of present nonlocal elastic beam models are matched with those of molecular dynamics simulations conducted by Ansari et al [34] for a series of singlewalled carbon nanotubes with different boundary conditions. Through using a nonlinear least square fitting procedure, the Euclidean norm of the difference between the two series of results is minimized in which the value of nonlocal parameter is set as the optimization variable to obtain the consistent values of it corresponding to each type of nonlocal beam model and boundary conditions.…”

Section: Appropriate Values Of Nonlocal Parametermentioning

confidence: 52%

Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions

Sahmani

Ansari

2011

J Mech Sci Technol

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Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen's equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions.analysis.

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“…The vibration and buckling aspects of carbon nanotubes using nonlocal Donnell shell theory was examined by Ansari et al [22,23].…”

Section: Introductionmentioning

confidence: 99%

Vibrational Behavior of Single-Walled Carbon Nanotubes Based on Donnell Shell Theory Using Wave Propagation Approach

Hussain¹

2018

Novel Nanomaterials - Synthesis and Applications

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This chapter is concerned with the vibration analysis of single-walled carbon nanotubes (SWCNTs). This analysis is based on the Donnell thin shell theory. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in SWCNTs. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. Vibration frequency spectra are gained and evaluated for physical parameter like length-to-diameter ratios. The dimensionless frequency is also investigated in armchair and zigzag SWCNTs with in-plane rigidity and mass density per unit lateral area for armchair and zigzag SWCNTs. These frequencies of the SWCNTs are computed with the aid of the computer software MATLAB. These results are compared with those obtained using molecular dynamics (MD) simulation and the results are somewhat in agreement.

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Rayleigh–Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions

Cited by 106 publications

References 49 publications

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions

Vibrational Behavior of Single-Walled Carbon Nanotubes Based on Donnell Shell Theory Using Wave Propagation Approach

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