Nonlocal static analysis of a functionally graded material curved nanobeam

Rezaiee‐Pajand, Mohammad; Rajabzadeh-Safaei, Niloofar

doi:10.1080/15376494.2017.1285463

Cited by 26 publications

(4 citation statements)

References 38 publications

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“…Based on Timoshenko beam model in the curvilinear coordinates, Rahmani et al [56] illustrated the buckling and frequency of temperature-dependent FGM curved microbeam employing the strain-gradient theory. Rezaiee-Pajand and Rajabzadeh-Safaei [57] employed the nonlocal elasticity theory to analyze the bending response of FGM-curved nanobeam. In accordance with Euler-Bernoulli theory, the deflection of bi-directional FGM curved beam was studied by Pydah and Sabale [58].…”

Section: Introductionmentioning

confidence: 99%

Differential quadrature method for magneto-hygrothermal bending of functionally graded graphene/Al sandwich-curved beams with honeycomb core via a new higher-order theory

Sobhy

2020

Jnl of Sandwich Structures & Materials

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Based on the differential quadrature method (DQM), the bending of sandwich-curved beams with graphene platelets/aluminum (GPLs/Al) nanocomposite face sheets and aluminum honeycomb core is investigated using a new shear and normal deformations curved beam theory. The present new model is resting on elastic foundation and subjected to a circumferential magnetic field, thermal load, and humid conditions. The face sheets are made of several bonded composite layers with randomly oriented and uniformly distributed graphene platelets in each layer. The mechanical and hygrothermal properties of the faces are assumed to be functionally graded (FG) using a piece-wise law by varying the weight fraction of the GPLs in the face thickness direction. Four governing differential equations are derived based on a novel four-variable curved beam theory taking into account the thickness stretching effect. The governing equations are solved for various boundary conditions on the basis of the DQM.

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Section: Introductionmentioning

confidence: 99%

Differential quadrature method for magneto-hygrothermal bending of functionally graded graphene/Al sandwich-curved beams with honeycomb core via a new higher-order theory

Sobhy

2020

Jnl of Sandwich Structures & Materials

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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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“…The functionally graded (FG) curved beams are generally used as structural elements of light-weight and heavy load-bearing components, and they are used to satisfy the design obligations of stiffness in industrial designs. [32][33][34][35][36][37][38] Due to the extensive application of FG curved beams in several engineering areas, a deeper comprehension of the mechanical behavior of similar beams is required. The concept of FGM can be utilized for the management of microstructure of a material so that bending, buckling, and vibration behaviors of a nanobeam structure can be improved.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal strain gradient theory for bending, buckling, and vibration of viscoelastic functionally graded curved nanobeam embedded in an elastic medium

Allam

Radwan

2019

Advances in Mechanical Engineering

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This article investigates bending, buckling, and vibration analysis in viscoelastic functionally graded curved nanobeam embedded in an elastic medium under different boundary conditions. The stresses can be calculated based on not only the nonlocal stress field but also the strain gradient stress field according to the nonlocal strain gradient elasticity theory. The present higher order refined curved nanobeam theory which captures shear deformation influence does not need any shear correction factors. Two power-law models are used to describe the continuous variation of material properties of viscoelastic functionally graded curved nanobeam. Governing equations of nonlocal strain gradient viscoelastic functionally graded curved nanobeam are obtained using Hamilton's principle. To establish the present model, the results are compared with those of functionally graded curved nanobeams. The effects of nonlocal parameter, length scale parameter, viscoelastic damping coefficient, spring stiffness, boundary conditions, and power-law exponent on the bending, buckling, and vibration responses of viscoelastic functionally graded curved nanobeam are discussed.

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Nonlocal static analysis of a functionally graded material curved nanobeam

Cited by 26 publications

References 38 publications

Differential quadrature method for magneto-hygrothermal bending of functionally graded graphene/Al sandwich-curved beams with honeycomb core via a new higher-order theory

Differential quadrature method for magneto-hygrothermal bending of functionally graded graphene/Al sandwich-curved beams with honeycomb core via a new higher-order theory

On nonlocal mechanics of curved elastic beams

Nonlocal strain gradient theory for bending, buckling, and vibration of viscoelastic functionally graded curved nanobeam embedded in an elastic medium

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