An effective analytical method for buckling solutions of a restrained FGM nonlocal beam

Cívalek, Ömer; Uzun, Büşra; Yaylı, Mustafa Özgür

doi:10.1007/s40314-022-01761-1

Cited by 90 publications

(27 citation statements)

References 77 publications

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“…Consequently, understanding the mechanism of the dynamic behavior and mass transport of micro-sized beams under dynamic loadings could be of great significance for the optimum design of beam-like nanostructures. Some of the valuable nano and micro-structures are as follows: nano-cone [8], microbeam, nanobeam [9][10][11], functionally graded (FG) nanobeam [12][13][14], FG nanorod [15], FG microbeams [16,17], microplate, types of nanotubes like carbon nanotube, boron nitride nanotube, silicon carbide (SiC) nanotube [18][19][20][21][22], FG nanoplate [23,24], nanoshell [25], microbar, nanorod, CNT reinforced nano/micro-sized beam [26,27], reinforced composite microplate, microtubules, graphene [28], nanoplate [29,30], etc.…”

Section: Introductionmentioning

confidence: 99%

An eigenvalue solution for nonlocal vibration of guide supported perfect/imperfect functionally graded power‐law and sigmoid nanobeams on one‐parameter elastic foundation

2023

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To the best of the authors' knowledge, this study for the first time, proposes a finite element (FE) model to investigate the size-dependent vibrational responses of guide supported imperfect functionally graded (FG) nonlocal beams embedded in an elastic foundation in the context of nonlocal elasticity theory (NET). The main objective of this paper is to present a nonlocal FE solution for vibration analysis of imperfect FG nanobeams including nonlocal effect, power-law distribution function, sigmoid distribution function, even porosity model, uneven porosity model, elastic foundation parameter, and guide support condition. It is considered that perfect/imperfect FG nanobeams are made of silicon carbide (SiC) and aluminum (Al) and that beam properties vary along the height direction. In addition, the nanobeams rest on a one-parameter elastic foundation and this foundation provides the interaction between the structure and the soil with elastic springs. The frequency values of perfect/imperfect FG power-law and sigmoid nanobeams obtained by using a nonlocal FE method are shown via tables and figures.

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Section: Introductionmentioning

confidence: 99%

An eigenvalue solution for nonlocal vibration of guide supported perfect/imperfect functionally graded power‐law and sigmoid nanobeams on one‐parameter elastic foundation

2023

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“…Civalek et al. [47] presented a size‐dependent stability study of a restrained FGM nano Euler–Bernoulli beam. Hosseini Hashemi et al.…”

Section: Introductionmentioning

confidence: 99%

“…The non-linear buckling of some thermally post-buckled nanobeams made of FGMs under static and sudden mechanical loads was analysed by Salari et al [46] on the basis of the non-local elasticity theory. Civalek et al [47] presented a size-dependent stability study of a restrained FGM nano Euler-Bernoulli beam. Hosseini Hashemi et al [48] showed that the vibrational behaviour of nano plates in stationary fluid environment is different from vacuum.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the effect of viscosity and fluid flow on buckling behaviour of non‐local nanoplate with surface energy

Arpanahi,

Abdehvand,

Sheykhi

et al. 2023

The Journal of Engineering

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The buckling of a nanoplate at the bottom of a channel over which the fluid passes with a one-dimensional flow is investigated in this article. Navier-Stokes equations were used to obtain the applied force from the fluid to the nanoplate. Non-local elasticity theories and surface effects were used to consider nanoscale effects. By solving this problem using Galerkin's weighted residual method, interesting results were obtained. Applying nonlocality increases the fluid's impact on the buckling of a nanoplate. The lower modes are more noticeably affected by being placed in a fluid environment. Also, the presence of fluid and surface effects both increase the buckling capacity of the system. The obtained results are very helpful for developing and improving the performance of fluid-coupled nanostructures that have buckling potential.

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“…Fiber-reinforced [ 1 , 2 ], carbon nanotube-reinforced [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ] and graphene platelet-reinforced [ 11 , 12 , 13 , 14 , 15 ] structures can be found in the recent literature. However, other composite structures like functionally graded [ 16 , 17 , 18 , 19 , 20 ], sandwich [ 21 , 22 ] and porous functionally graded structures [ 23 , 24 , 25 , 26 , 27 , 28 ] have also attracted considerable interest. As can be seen, composite structures have attracted attention not only at a macro scale but also at nano and micro scales.…”

Section: Introductionmentioning

confidence: 99%

“…Researchers use a variety of techniques to analyze an element or structure, such as a rod, beam, plate, frame, etc., whether at the macro, nano, or micro level. Some of these techniques are: the finite element method [ 1 , 33 , 41 , 42 , 54 , 55 ], artificial neural networks [ 56 ], the Laplace transform [ 57 ], Stokes’ transformation [ 18 , 28 , 43 , 45 ], the perturbation technique [ 5 ] and the Chebyshev–Ritz method [ 19 ]. This is the first work to investigate the longitudinal vibration behavior of short-fiber-reinforced micro-/nano-rods embedded in an elastic medium via Fourier sine series with Stokes’ transformation.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Free Vibration of Embedded Short-Fiber-Reinforced Nano-/Micro-Rods with Deformable Boundary Conditions

2022

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An efficient eigenvalue algorithm is developed for the axial vibration analysis of embedded short-fiber-reinforced micro-/nano-composite rods under arbitrary boundary conditions. In the formulation, nonlocal elasticity theory is used to capture the size effect, and the deformable boundary conditions at the ends are simulated using two elastic springs in the axial direction. In addition, to determine the reinforcing effect of restrained nano-/micro-rods, a new system of linear equations with the concept of the infinite power series is presented. After performing the mathematical processes known as Fourier sine series, Stokes’ transformation and successive integration, we finally obtain a coefficient matrix in terms of infinite series for various rigid or deformable boundary conditions. Some accurate eigenvalue solutions of the free axial vibration frequencies of the short-fiber-reinforced micro-/nano-composite rods with and without being restrained by the means of elastic springs are given to show the performance of the present method. The presence of the elastic spring boundary conditions changes the axial vibration frequencies and corresponding mode shapes.

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An effective analytical method for buckling solutions of a restrained FGM nonlocal beam

Cited by 90 publications

References 77 publications

An eigenvalue solution for nonlocal vibration of guide supported perfect/imperfect functionally graded power‐law and sigmoid nanobeams on one‐parameter elastic foundation

An eigenvalue solution for nonlocal vibration of guide supported perfect/imperfect functionally graded power‐law and sigmoid nanobeams on one‐parameter elastic foundation

Investigation of the effect of viscosity and fluid flow on buckling behaviour of non‐local nanoplate with surface energy

Nonlocal Free Vibration of Embedded Short-Fiber-Reinforced Nano-/Micro-Rods with Deformable Boundary Conditions

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