Modeling and analysis of out-of-plane behavior of curved nanobeams based on nonlocal elasticity

Aya, Serhan Aydin; Tüfekçi, Ekrem

doi:10.1016/j.compositesb.2017.03.050

Cited by 15 publications

(5 citation statements)

References 32 publications

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“…They considered a surface stress tensor, based on the general Young–Laplace equation [ 21 ]. Other researchers modeled curved nanobeams modeling the beams as functionally-graded materials [ 22 ], while others modeled them using the non-local elasticity theory [ 23 ].…”

Section: Introductionmentioning

confidence: 99%

A Generalized Model for Curved Nanobeams Incorporating Surface Energy

Khater

2023

Micromachines

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This work presents a comprehensive model for nanobeams, incorporating beam curvature and surface energy. Gurtin–Murdoch surface stress theory is used, in conjunction with Euler–Bernoulli beam theory, to model the beams and take surface energy effects into consideration. The model was validated by contrasting its outcomes with experimental data published in the literature on the static bending of fixed–fixed and fixed–free nanobeams. The outcomes demonstrated that surface stress alters the stiffness of both fixed–fixed and fixed–free nanobeams with different behaviors in each case.

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Section: Introductionmentioning

confidence: 99%

A Generalized Model for Curved Nanobeams Incorporating Surface Energy

Khater

2023

Micromachines

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“…Eringen differential nonlocal model. Such a strategy, recently employed in (Ganapathi and Polit, 2017;Aya and Tufekci, 2017;Polit et al, 2018;Rezaiee-Pajand and Rajabzadeh-Safaei, 2018;Arefi et al, 2019), is based on the differential relation associated with the straindriven fully nonlocal integral convolution of the theory of elasticity, originally exploited by Eringen (1983) to tackle small-scale problems, defined in unbounded domains, of screw dislocation and wave propagation. Such a model has been shown to provide, in the special case of straight structures, mechanical paradoxes (Peddieson et al, 2003;Challamel and Wang, 2008;Li et al, 2015;Fernández-Sáez et al, 2016) and size-dependent responses which are of limited applicative interest.…”

Section: Introductionmentioning

confidence: 99%

On nonlocal mechanics of curved elastic beams

Barretta

Sciarra

Vaccaro

2019

International Journal of Engineering Science

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Curved beams are basic structural components of Nano-Electro-Mechanical-Sistems (NEMS) whose design requires appropriate modelling of scale effects. In the present paper, the size-dependent static behaviour of curved elastic nano-beams is investigated by stress-driven nonlocal continuum mechanics. Axial strain and flexural curvature fields are integral convolutions between equilibrated axial force and bending moment fields and an averaging kernel. The nonlocal integral methodology formulated here is the generalization to curved structures of the treatment in [Int. J. Eng. Science 115 (2017) 14-27] confined to straight beams. The corresponding nonlocal differential problem, supplemented with non-standard boundary conditions, is highlighted and shown to lead to mathematically well-posed problems of nano-engineering. The theoretical predictions, exhibiting stiffening nonlocal behaviours, are therefore appropriate to significantly model a wide range of small-scale devices of nanotechnological interest. The nonlocal approach is exploited by analytically establishing size-dependent responses of curved elastic nano-sensors and nano-actuators that are driven by the small-scale characteristic parameter.

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“…A different approach based on the sinusoidal shear deformation theory was applied by Arefi and Zenkour [21,22] for the analysis of a sandwich microbeam and nanoplate, respectively. Some additional static and dynamic analyses of curved beams at the nano-and macro-scales were presented by Aya and Tufekci [23], as well as by Hajianmaleki and Qatu [24], respectively. A nonlocal elasticity solution and wave propagation analysis of nanoplates and nanorods were proposed by Arefi and Zenkour [25,26], whereas the sinusoidal shear deformation theory was applied for the study of the transient response of curved beams [27].…”

Section: Introductionmentioning

confidence: 99%

“…Based on the available literature on the vibration and bending response of beams and plates reinforced with GPLs at the macroscale [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], as well as on the curved beams at the macroand nano-scales [18][19][20][21][22][23][24][25][26][27], here we propose a combined study of curved nanobeams reinforced with nanoplatelets. In mechanical problems of technical interest, the elastic equilibrium is generally defined in bounded structural domains, so that suitable constitutive boundary conditions have to be prescribed to ensure the equivalence between integral and differential equations [33].…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations

et al. 2019

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This paper presents a free vibration analysis of functionally graded (FG) polymer composite curved nanobeams reinforced with graphene nanoplatelets resting on a Pasternak foundation. The size-dependent governing equations of motion are derived by applying the Hamilton’s principle and the differential law consequent (but not equivalent) to Eringen’s strain-driven nonlocal integral elasticity model equipped with the special bi-exponential averaging kernel. The displacement field of the problem is here described in polar coordinates, according to the first order shear deformation theory. A large parametric investigation is performed, which includes different FG patterns, different boundary conditions, but also different geometrical parameters, number of layers, weight fractions, and Pasternak parameters.

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Modeling and analysis of out-of-plane behavior of curved nanobeams based on nonlocal elasticity

Cited by 15 publications

References 32 publications

A Generalized Model for Curved Nanobeams Incorporating Surface Energy

A Generalized Model for Curved Nanobeams Incorporating Surface Energy

On nonlocal mechanics of curved elastic beams

Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations

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