Three-dimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadrature-based approach

Ansari, R.; Shojaei, M. Faghih; Shahabodini, A.; Bazdid-Vahdati, M.

doi:10.1016/j.compstruct.2015.06.027

Cited by 76 publications

(20 citation statements)

References 48 publications

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“…In Table 2 are compared with the work of Ansari et al [33] that used a numerical solution called "variational differential quadrature (VDQ)" based on the 3D theory of elasticity. Secondly, the closed-form solutions of the first-order shear deformable plate theory from Jung and Han [28] are compared with the present analytical results for the sigmoid law model as listed in Table 3.…”

Section: Reliabilitymentioning

confidence: 99%

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Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity

Panyatong

Chinnaboon

Chucheepsakul

2016

Composite Structures

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Section: Reliabilitymentioning

confidence: 99%

“…Salehipour et al [32] developed the modified nonlocal elasticity for examination of the natural frequency of FG micro/nanoplates. Ansari et al [33] analyzed the bending and vibration of FG nanoplates with three-dimension plate theory in conjunction with Eringen's nonlocal theory.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity

Panyatong

Chinnaboon

Chucheepsakul

2016

Composite Structures

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“…After this, the MCST and the strain gradient elasticity theories have been widely applied to static, buckling and dynamic analysis of nano/micro plates . In these studies, Ansari et al [37] studied three-dimensional bending and vibration analysis of functionally graded nanoplates, Ghadir et al [38] investigated thermomechanical vibration of orthotropic cantilever nanoplate, Kananipour [39] investigated static analysis of nonlocal nanoplates based Kirchhoff and Mindlin plate theories, Arani and Jafari [40] examined nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium and Pradhan and Kumar [41] investigated vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory differential quadrature method.…”

Section: Introductionmentioning

confidence: 96%

Static Analysis of a Nano Plate by Using Generalized Differential Quadrature Method

Akbaş¹

2016

International Journal of Engineering &Amp; Applied Sciences

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In this paper, static analysis of a nano rectangular plate subjected to uniform distributed load is studied based on modified couple stress theory (MSCT) by using Generalized Differential Quadrature (GDQ) Method. The inclusion of an additional material parameter enables the new plate model to capture the size effect. The new non-classical plate model reduces to the classical plate model when the length scale parameter is set to zero. In deriving of the governing equations, the minimum total potential energy principle is used. In the solution of the governing equations, the DQM method is used for simply-supported nano plate within the Kirchhoff-Love plate theory. In the numerical results, the influences the material length scale parameter and the dimension parameters of the plate on the static deflection of the nano plate is presented. Also, the difference between the classical theory (CT) and MSCT is investigated for static responses of nano plate.

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“…Thus, this theory is a suitable candidate for modeling of nanoscale structures [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. This theory is also extensively applied to investigate mechanical behaviors of FG nanoplates [35][36][37][38][39][40][41][42][43][44][45][46][47]. Note that these published papers on FG nanoplate have reported their linear vibration behavior.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions

Barati

Shahverdi

2018

J Braz. Soc. Mech. Sci. Eng.

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This paper deals with the semi-analytical nonlinear thermal vibration analysis of functionally graded (FG) nanoplates modeled by four-variable refined plate theory. The nanoplate is resting on a nonlinear hardening elastic medium and subjected to uniform and nonlinear temperature rises. Temperature-dependent gradient material properties of the nanoplate are described via simple power-law model. A closed-form expression for nonlinear frequency is presented using a novel Hamiltonian approach as well as He's variational method. To the best of the author's knowledge, the nonlinear governing equations and their solution for a refined four-variable nanoplate are very rare in the literature. It is seen that the nonlinear vibration frequency is affected by the uniform temperature rise, nonlinear temperature rise, scale parameter, maximum amplitude, material gradation, foundation parameters and temperature-dependency. The presented formulation and solution approaches can be used in future investigations on macro to nanoscale plates.

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Three-dimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadrature-based approach

Cited by 76 publications

References 48 publications

Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity

Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity

Static Analysis of a Nano Plate by Using Generalized Differential Quadrature Method

Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions

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