Analytical treatment on the nonlocal strain gradient vibrational response of postbuckled functionally graded porous micro-/nanoplates reinforced with GPL

Sahmani, S.; Fattahi, Ashghar Mohammadpour; Ahmed, Noor A.

doi:10.1007/s00366-019-00782-5

Cited by 40 publications

(11 citation statements)

References 83 publications

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“…at is the reason why numerous researchers focus on investigating the dynamic as well as static behaviors of the FGM structures, for example, beams [5][6][7][8][9][10], plates [11][12][13][14][15][16][17][18], shells [19][20][21], and other structures [22,23]. Many plate theories have been established and/or applied to investigate these structures, for example, classical plate theory (CPT), first-order shear deformation (FSDT), higherorder shear deformation theory (HSDT), and quasi-3D shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

Vinh

2021

Mathematical Problems in Engineering

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A new mixed four-node quadrilateral element (MiQ4) is established in this paper to investigate functionally graded material (FGM) plates with variable thickness. The proposed element is developed based on the first-order shear deformation and mixed finite element technique, so the new element does not need any selective or reduced numerical integration. Numerous basic tests have been carried out to demonstrate the accuracy and convergence of the proposed element. Besides, the numerical examples show that the present element is free of shear locking and is insensitive to the mesh distortion, especially for the case of very thin plates. The present element can be applied to analyze plates with arbitrary geometries; it leads to reducing the computation cost. Several parameter studies are performed to show the roles of some parameters such as the power-law index, side-to-thickness ratio, boundary conditions (BCs), and variation of the plate thickness on the static bending behavior of the FGM plates.

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Section: Introductionmentioning

confidence: 99%

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

Vinh

2021

Mathematical Problems in Engineering

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“…e porosity is distributed through the thickness of the plate with four different patterns, namely, patterns A, B, C, and D, and they are described by the following formula [58,71]:…”

Section: Materials Properties Of Fgm Nanoplates With Porositymentioning

confidence: 99%

“…where P 0 ≤ 0.5 is the maximum porosity value [72]. e effective Young's modulus, shear modulus, and mass density can be calculated as the following formula [58,71]:…”

Section: Materials Properties Of Fgm Nanoplates With Porositymentioning

confidence: 99%

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Influence of Variable Nonlocal Parameter and Porosity on the Free Vibration Behavior of Functionally Graded Nanoplates

Vinh

Huy

2021

Shock and Vibration

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This paper studies the influence of the variable nonlocal parameter and porosity on the free vibration behavior of the functionally graded nanoplates with porosity. Four patterns of distribution of the porosity through the thickness direction are considered. The classical nonlocal elasticity theory is modified to take into account the variation of the nonlocal parameter through the thickness of the nanoplates. The governing equations of motion are established using simple first-order shear deformation theory and Hamilton’s principle. The closed-form solution based on Navier’s technique is employed to solve the governing equations of motion of fully simply supported nanoplates. The accuracy of the present algorithm is proved via some comparison studies in some special cases. Then, the effects of the porosity, the variation of the nonlocal parameter, the power-law index, aspect ratio, and the side-to-thickness ratio on the free vibration of nanoscale porous plates are investigated carefully. The numerical results show that the porosity and nonlocal parameter have strong effects on the free vibration behavior of the nanoplates.

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“…Based on the first order shear deformation theory, Reddy et al [ 25 ] investigated the vibrations of GPL reinforced thick multi-layer, moderately thick and thin plates. Sahmani et al [ 26 ] examined the nonlocal vibration behavior of a GPL reinforced microplate with pores. Employing a numerical-based generalized differential quadrature method, Lori et al [ 27 ] analysis the free vibrations of microdisks reinforced with GPLs.…”

Section: Introductionmentioning

confidence: 99%

Wave Propagation in Rotating Functionally Graded Microbeams Reinforced by Graphene Nanoplatelets

Zhao

Zhou

et al. 2021

Molecules

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This paper presents a study on wave propagation in rotating functionally graded (FG) microbeams reinforced by graphene nanoplatelets (GPLs). The graphene nanoplatelets (GPLs) are considered to distribute in the diameter direction of the micro-beam in a gradient pattern, which leads to the functionally graded structure. By using the Halpin-Tsai micromechanics model and the rule of mixture, the effective material properties of the microbeam are determined. According to the Euler-Bernoulli beam theory and nonlocal elasticity theory, the rotating microbeams are modeled. A comprehensive parametric study is conducted to examine the effects of rotating speed, GPL distribution pattern, GPL length-to-thickness ratio, GPL length-to-width ratio, and nonlocal scale on the wavenumber, phase speed and group speed of the microbeam. The research findings can play an important role on the design of rotating graphene nanoplatelet (GPL) reinforced microbeams for better structural performance.

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Analytical treatment on the nonlocal strain gradient vibrational response of postbuckled functionally graded porous micro-/nanoplates reinforced with GPL

Cited by 40 publications

References 83 publications

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

Influence of Variable Nonlocal Parameter and Porosity on the Free Vibration Behavior of Functionally Graded Nanoplates

Wave Propagation in Rotating Functionally Graded Microbeams Reinforced by Graphene Nanoplatelets

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