Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties

Rahmani, O.; Hosseini, Seyyed Amirhosein; Ghoytasi, I.; Golmohammadi, H.

doi:10.1007/s00339-016-0591-9

Cited by 30 publications

(8 citation statements)

References 71 publications

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“…There have been several excellent properties of nano/micro-sized structures such as large surface area, high sensitivity and enhanced mechanical stability [18][19][20]. Consequently, several researches have been performed to study the stability, dynamic and static characteristics of these structures in recent decades [21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Winkler‐Pasternak foundation effect on the buckling loads of arbitrarily rigid or restrained supported nonlocal beams made of different FGM and porosity distributions

Uzun,

Yaylı

2023

Z Angew Math Mech

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The present research investigates lateral stability of a functionally graded nanobeam using Eringen's differential nonlocal elasticity model under rigid (clamped, pinned, free) and deformable (lateral, rotational restraints) boundary conditions. Sigmoid and power law have been employed as grading laws to study the influence of the material distribution on the snap‐buckling analysis of a nanobeam with arbitrary boundary conditions. Moreover, Fourier sine series with Stokes’ transformation are employed to investigate the effects of boundary conditions on the stability response of nanobeams embedded in a Pasternak foundation. A parametric study has been performed to investigate the effect of deformable boundaries, Pasternak foundation and small‐scale parameters on the stability response of the nanobeam and the results have been presented in a series of tables and figures. It has been observed that consideration of the small‐scale parameter, Pasternak foundation, deformable boundaries and functionally grading index (of sigmoid and power‐law) are essential while analyzing the static stability response. The obtained analytical results may be used as benchmarks in future researches of functionally graded nanobeams embedded in an elastic medium.

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Section: Introductionmentioning

confidence: 99%

Winkler‐Pasternak foundation effect on the buckling loads of arbitrarily rigid or restrained supported nonlocal beams made of different FGM and porosity distributions

Uzun,

Yaylı

2023

Z Angew Math Mech

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“…Thermal buckling and free vibration of temperature-dependent FGM curved nanobeams were investigated by Hosseini and Rahmani [55] employing Euler-Bernoulli beam theory. 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.…”

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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“…In numerical examples, the effects of temperature‐dependent material property and several parameters such as mode number, temperature change, opening angle and nonlocal parameter on frequency and critical temperature are studied. Rahmani investigated the influences of a thermomechanical loading in buckling and free vibration of shallow curved nanobeam using strain gradient theory. Differential governing equations and associated boundary conditions are developed based on Hamilton's principle.…”

Section: Introductionmentioning

confidence: 99%

Theoretical analysis for static bending of circular Euler–Bernoulli beam using local and Eringen's nonlocal integral mixed model

2019

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Many studies have shown that Eringen's differential nonlocal model leads to some inconsistencies for the cantilever beams, which indicates the necessity to adopt the original integral nonlocal model. In this paper, Eringen's two‐phase local/nonlocal model is applied to capture the size effect in the curved Euler‐Bernoulli beam. The governing equations of equilibrium and boundary conditions are derived on the basis of Hamilton's principle. The Fredholm type integral governing equations are transformed to Volterra integral equations of the second kind through simply adjusting the limit of integrals, and solved uniquely through the Laplace transformation with several unknown constants, which are determined through the boundary conditions and extra constrained equations. The Exact solutions for a curved microbeam bending are derived explicitly for different boundary conditions. The present model is validated against the straight Euler beam for large radius circular case. The numerical results from current model show that the consistent softening effect of the two parameters on the bending deflection of the microbeams is observed for all boundary conditions.

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Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties

Cited by 30 publications

References 71 publications

Winkler‐Pasternak foundation effect on the buckling loads of arbitrarily rigid or restrained supported nonlocal beams made of different FGM and porosity distributions

Winkler‐Pasternak foundation effect on the buckling loads of arbitrarily rigid or restrained supported nonlocal beams made of different FGM and porosity distributions

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

Theoretical analysis for static bending of circular Euler–Bernoulli beam using local and Eringen's nonlocal integral mixed model

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