Size-dependent buckling and vibration analyses of GNP reinforced microplates based on the quasi-3D sinusoidal shear deformation theory

Afshari, Hassan; Adab, Niloufar

doi:10.1080/15397734.2020.1713158

Cited by 58 publications

(22 citation statements)

References 53 publications

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“…2, five linear types of GNPs distribution patterns are considered in this paper. Mass fraction of GNPs for these patterns can be stated as [4] in which g * GNP is total mass fraction of GNPs. It should be noted that in order to have a fair comparison between (7)…”

Section: Governing Equationsmentioning

confidence: 99%

“…distribution patterns, Eq. (10) is regulated to have same total mass fraction of GNPs for all patterns [4]. The set of the governing equations can be derived using Hamilton's principle as [10] where [t 1 ,t 2 ] is a desired time interval, δ stands for variational operator, T indicates to kinetic energy, W n.c. is work done by non-conservative loads, U e stands for the strain energy of the shell and U h indicates the strain energy generated by initial hoop tension.…”

Section: Governing Equationsmentioning

confidence: 99%

“…They confirmed that stability of the porous arch can be enhanced by using symmetrically non-uniform porosity distribution and the addition of a small amount of GNPs. Afshari and Adab [4] presented exact solutions for size-dependent buckling and vibration analyses of GNP-reinforced rectangular microplates. It was shown by them that in order to have a better reinforcing effect, GNPs with larger surface area and fewer monolayer graphene sheets should be used.…”

Section: Introductionmentioning

confidence: 99%

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Effect of graphene nanoplatelet reinforcements on the dynamics of rotating truncated conical shells

Afshari

2020

J Braz. Soc. Mech. Sci. Eng.

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In this paper, a parametric study is presented for free vibration analysis of rotating truncated conical shells reinforced with graphene nanoplatelets (GNPs). The composite shell is considered to be composed of epoxy as the matrix and the GNPs which are distributed along the thickness direction based on the various distribution patterns. The shell is modeled based on the first-order shear deformation theory (FSDT), and effective material properties are calculated based on the Halpin-Tsai model and the rule of mixture. Incorporating centrifugal and Coriolis accelerations along with initial hoop tension, the set of the governing equations and boundary conditions are derived using Hamilton's principle and are solved numerically using generalized differential quadrature method. Convergence and accuracy of the presented solution are confirmed, and influences of various parameters on the forward and backward frequencies are investigated including circumferential mode number, boundary conditions, rotational speed, semi-vertex angle and also mass fraction, distribution pattern, width and thickness of the GNPs. It is noteworthy that for the first time, the initial hoop tension is incorporated for a rotating conical shell modeled based on the FSDT.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of graphene nanoplatelet reinforcements on the dynamics of rotating truncated conical shells

Afshari

2020

J Braz. Soc. Mech. Sci. Eng.

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“…in which H is presented for a rectangular cross section as [70], Substituting Eqs. (24), (28) and (30) into Eq. 14leads to the following set of governing equations: and the boundary conditions at x = 0 and x = L can be achieved as, Equation (33) can be rewritten as, which can be written using Eqs.…”

Section: Governing Equationsmentioning

confidence: 99%

“…They modeled the nanotubes based on NSGT, incorporated the effects of relative motion between the nanofluid and nanotube using Karniadakis-Beskok assumptions and studied the effect of geometric imperfection on the motion response. Quasi-3D sinusoidal shear deformation theory was hired by Afshari and Adab [30] along with MCST to study size-dependent mechanical buckling and free vibration analyses of rectangular microplates reinforced with graphene nanoplatelets (GNPs). They presented a parametric study to examine the influences of various parameters on the critical buckling load and natural frequencies including material length scale parameter and also width, thickness, total mass fraction and distribution pattern of GNPs.…”

Section: Introductionmentioning

confidence: 99%

A comprehensive study for mechanical behavior of functionally graded porous nanobeams resting on elastic foundation

Enayat

Hashemian

Toghraie

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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In this paper, a comprehensive study is presented for mechanical analysis of functionally graded porous (FGP) nanobeams resting on an elastic foundation. The nanobeam is modeled according to different beam theories along with nonlocal strain gradient theory and Gurtin-Murdoch surface elasticity theory. Using Hamilton's principle, the set of governing equations are derived, and exact solutions are presented using Navier's method for the static bending, mechanical buckling and free vibration analyses of simply supported FGP nanobeams. The effects of various parameters on static deflection, critical buckling load and fundamental natural frequency of FGP nanobeams are studied. It is shown that for all types of porosity distribution patterns, an increase in porosity parameter leads to an increase in static deflection, and a decrease in critical buckling load and effect of porosity parameter on fundamental natural frequency is dependent on the porosity distribution pattern. Numerical results confirm that tensional residual surface stress decreases static deflection and increases both critical buckling load and fundamental natural frequency, but compressive residual surface stress has opposite effects.

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RETRACTED: Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects

et al. 2020

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In the current paper, size‐dependent mechanical analysis of functionally graded porous (FGP) nanobeams resting on Pasternak foundation in thermal environment is presented based on nonlocal strain gradient theory and Gurtin‐Murdoch surface elasticity theory. The nanobeam is modeled based on Euler‐Bernoulli beam theory, Timoshenko beam theory and Reddy's third‐order shear deformation theory and the set of the governing equations are solved for a clamped‐clamped FGP nanobeam using generalized differential quadrature method. Numerical results show that as porosity parameter increases, static deflection increases and critical buckling load decreases, but its effect on the fundamental frequency strongly depends on the porosity distribution pattern. It was revealed that among all studied porosity distribution patterns, the minimum value of the static deflection and maximum values of critical buckling load and fundamental frequency can be achieved using symmetric distribution pattern of pores. It is concluded that tensional residual stress reduces static deflection and increases both critical buckling load and fundamental frequency and temperature rise has reverse effects.

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Size-dependent buckling and vibration analyses of GNP reinforced microplates based on the quasi-3D sinusoidal shear deformation theory

Cited by 58 publications

References 53 publications

Effect of graphene nanoplatelet reinforcements on the dynamics of rotating truncated conical shells

Effect of graphene nanoplatelet reinforcements on the dynamics of rotating truncated conical shells

A comprehensive study for mechanical behavior of functionally graded porous nanobeams resting on elastic foundation

RETRACTED: Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects

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