Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory

Li, Xiaobai; Li, Li; Hu, Yujin; Ding, Zhe; Deng, Weiming

doi:10.1016/j.compstruct.2017.01.032

Cited by 276 publications

(63 citation statements)

References 83 publications

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“…In addition, the nonlocal elasticity has been utilised to explore the size-dependent bending behaviour of non-homogeneous nanobeams [124,125]. More recently, a NSGT-based beam model has been proposed by Li et al [126] for the mechanical behaviour of non-homogeneous nanoscale beams. Figure 11 indicates the maximum deflection of a non-homogeneous nanobeam with simply supported boundary conditions subject to sinusoidal applied load in the transverse direction.…”

Section: 3a Nonlocal Beam Modelmentioning

confidence: 99%

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A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

210

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Understanding the mechanical behaviour of nanostructures is of great importance due to their applications in nanodevices such as in nanomechanical resonators, nanoscale mass sensors, electromechanical nanoactuators and nanogenerators. Due to the difficulties of performing accurate experimental measurements at nanoscales and the high computational costs associated with the molecular dynamics simulations, the continuum modelling of nanostructures has attracted a considerable amount of attention. Since size influences have a crucial role in the mechanics of structures at nanoscale levels, classical continuum-based theories have been modified to incorporate these effects. Among various modified continuum-based theories, the nonlocal elasticity and the nonlocal strain gradient elasticity have been employed to estimate the mechanical behaviour of nanostructures. In this review paper, first these two modified elasticity theories are briefly explained. Then, the nonlocal motion equations for different nanostructures including nanorods, nanorings, nanobeams, nanoplates and nanoshells are derived. Several papers which reported on the size-dependent mechanical behaviour of nanostructures using modified continuum models are reviewed. Furthermore, important results reported on the vibration, bending and buckling of nanostructures as well as the results of size-dependent wave propagation analyses are discussed.

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Section: 3a Nonlocal Beam Modelmentioning

confidence: 99%

“…More recently, NSGT-based continuum models have been introduced for the vibration of nanobeams [82,126,183,[186][187][188][189]. Various modified theories of elasticity are compared in Fig.…”

Section: 3d Size-dependent Vibration Of Nanobeamsmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

210

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“…It is well established that the local elasticity theory cannot be adopted to capture mechanical responses of nano-continua, and consequently, a variety of size-dependent elasticity models are available in literature. Analysis and assessment of size-effects in nano-structures is currently a topic of major interest in the scientific community [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Torsional deformations can frequently occur in structural elements of NEMS, and therefore, various size-dependent elasticity theories have been exploited in literature [21][22][23][24][25][26][27][28][29][30][31][32], as comprehensively discussed in review contributions [33,34].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

et al. 2019

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Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems.In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation.The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest.Both elastostatic torsional responses and torsional free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviours of structures involved in modern Nano-Electro-Mechanical-Systems (NEMS). KeywordsTorsion; nano-beams; nonlocal strain gradient model; strain gradient elasticity; integral elasticity; size effects; analytical modelling; NEMS. d J J dx J J dx J

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“…For example, Tadi et al studied the free vibration of FG nanoshells and the effects of different parameters on frequency was shown as well [2]. The bending, buckling and vibration behaviors of axially FG nanobeams were investigated by Li et al and the critical buckling force and natural frequency were shown size dependent [3]. Ebrahimi et al examined the wave propagation of FG nanoplate under nonlinear thermal loading and the influence of different parameters such as gradient index, temperature distribution and length scale parameter on the wave dispersion was presented [4].…”

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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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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Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory

Cited by 276 publications

References 83 publications

A review on the mechanics of nanostructures

A review on the mechanics of nanostructures

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

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

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