A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams

Thai, Huu‐Tai; Vo, Thuc P.

doi:10.1016/j.ijengsci.2012.01.009

Cited by 198 publications

(61 citation statements)

References 29 publications

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“…Based on the nonlocal theory of Eringen, a number of studies have been published trying to develop nonlocal continuum models and apply them to analyze the general behavior of nanostructures [37][38][39][40][41][42][43][44][45][46][47][48]. Also the nonlocal continuum mechanics have been used by many researchers in the study of the buckling of nanotubes [49][50][51][52][53][54][55][56], nanobeams [57,58], and graphene sheets [59][60][61].…”

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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“…CBT overestimates the fundamental frequency and critical buckling load; in addition, it underestimates the bending de ection of a beam [59,60]. So, HSDTs can predict these parameters more precisely as compared to the classic beam theory by considering the e ect of transverse shear strain on the thickness of a beam.…”

Section: Parametric Resultsmentioning

confidence: 99%

An analytical solution for bending, buckling, and free vibration of FG nanobeam lying on Winkler-Pasternak elastic foundation using different nonlocal higher order shear deformation beam theories

2017

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Abstract. In the present study, various Higher-order Shear Deformation beam Theories (HSDTs) are applied in order to achieve the exact analytical solution to bending, buckling, and free vibration of Functionally Graded (FG) nanobeam lying on the Winkler and Pasternak elastic foundations. HSDTs are those in which the e ect of transverse shear strain is included. The displacement eld of these theories involves a quadratic variation of transverse shear strains and stresses; hence, this hypothesis leads to the diminishing of transverse shear stresses at the top and bottom surfaces of a beam. Thus, necessarily, there is no need to use a shear correction factor in the HSDTs. Nanobeam has been made of FG materials in which the properties of these materials are changed through the thickness direction of nanobeam according to the power-law distribution. Hamilton's principle is used to derive the equation of motions and the related boundary conditions of simply supported nanobeam. The present study shows that the stability and vibration behaviors of FG nanobeam are extremely dependent on the Winkler and Pasternak elastic foundation, gradient index, aspect ratio, and nonlocal parameter. The obtained results of the present study might be useful in the advanced eld of micro/nano electromechanical systems.

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“…Ansari et al [18] derived the governing partial differential equation for a uniform rotating beam incorporating the nonlocal scale effects. Thai and Vo [19] applied a sinusoidal theory of non-local shear deformation. Eltaher et al [20] studied the free vibration nanobeams using the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Functionally Graded Nanobeams Based on Different Order Beam Theories Using Ritz Method

Elmeiche¹,

Megueni

Lousdad

2016

Period. Polytech. Mech. Eng.

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A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams

Cited by 198 publications

References 29 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

An analytical solution for bending, buckling, and free vibration of FG nanobeam lying on Winkler-Pasternak elastic foundation using different nonlocal higher order shear deformation beam theories

Free Vibration Analysis of Functionally Graded Nanobeams Based on Different Order Beam Theories Using Ritz Method

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