Thermal effect on bending, buckling and free vibration of functionally graded rectangular micro-plates possessing a variable length scale parameter

Aghazadeh, Reza; Dağ, Serkan; Ciğeroğlu, Ender

doi:10.1007/s00542-018-3773-x

Cited by 14 publications

(6 citation statements)

References 71 publications

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“…According to this aspect, FGP can be classified into nano-plates, micro-plates and "normal" plates. Nano-FGP and micro-FGPs have been studied for thermo-mechanical buckling by many researchers, for example [28]. Nano-FGP and micro-FGP are out of the scope of this review article.…”

Section: Fgp's Plate Characteristicsmentioning

confidence: 99%

A Review on Buckling Analysis of Functionally Graded Plates Under Thermo-Mechanical Loads

Hassan

Kurgan

2019

International Journal of Engineering and Applied Sciences

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Functionally graded materials (FGM) are increasingly used in the engineering field. In many applications, FGMs are modelled as plates. Plates made of functionally graded materials (FGPs) are mostly designed to perform under elevated temperatures. In those circumstances, they are often under the combined effect of thermal and mechanical loads. There have been many studies on buckling analysis of FGP under either mechanical or thermal loads; however, only a few studies have addressed the combined effect of both loads acting together. This article focuses on the review of research on buckling analysis of FGP under the combined thermal and mechanical loads.

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Section: Fgp's Plate Characteristicsmentioning

confidence: 99%

A Review on Buckling Analysis of Functionally Graded Plates Under Thermo-Mechanical Loads

Hassan

Kurgan

2019

International Journal of Engineering and Applied Sciences

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“…The isogeometric analysis of FG-GPLRC microplates [51] and FG microplates [52] based on quasi-3D shear deformation theory have been presented for various supports. The effect of variable LSP on buckling, free vibration, and static analysis of FG microbeams [53] and FG microplates [54] has been investigated. Numerical solutions of vibration of microshells of revolution [55] and thin shallow microshells [56] have been studied based on CPT and MCST and using finite element model.…”

Section: Introductionmentioning

confidence: 99%

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

et al. 2023

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Using modified couple stress plate and Mindlin theories, the present study is a parametric study for revealing the effect of length scale parameter on postbuckling of saturated poroelastic rectangular microplates with pore distribution being functionally graded across thickness. The microplate postbuckling is a nonlinear eigenvalue problem with coupled partial differential equations of equilibrium. In order to find the mode shapes, the eigenfunctions have been approximated by some complete polynomial series expansions in accordance with the conventional Ritz approximation technique. After discretizing the governing equations throughout the microplate grid points, the assembled difference equations construct a nonlinear eigenvalue problem with coupled algebraic equations. The nontrivial coefficients of the expansions were calculated such that the eigenfunctions extremize the microplate potential energy for satisfying the equilibrium homogeneous equations. Variation of the potential energy have been derived with respect to the expansions coefficients from the vantage of using Maple software. By gradual reduction in the initial end shortening of the movable supports and solving the assembled difference equations via Newton-Raphson iterations, the critical postbuckling displacement imposed to the movable supports are found along with the nontrivial coefficients regarding eigenfunctions. The results of the parametric study have revealed how geometric parameters, pore distribution, the Skempton coefficient, porosity, and different boundary conditions modify the influence of length scale parameter on the microplate postbuckling.

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“…Li et al [11] utilized SGT to cope with the nonlinear axisymmetric bending behavior of circular plate. By employing the differential quadrature method, Aghazadeh et al [12] studied the static bending, free vibration and buckling of FG rectangular micro-plates. The strain gradient theory including multiple material length parameters can be simplified into other strain gradient theories, such as MCST and CST and so on.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of graded porous circular micro/nanoplates with various boundary conditions based on the nonlocal elasticity theory

Wang

Zhang

2022

Z Angew Math Mech

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In this article, the free vibrations of graded porous circular nanoplates subjected to various boundary conditions have been investigated. It is assumed that the performance of graded porous materials varies continuously in the whole thickness, and two cosine forms of non‐uniform porosity distribution along its thickness are considered. In order to capture the size effect, the Eringen's nonlocal elastic theory is applied. Then, Mindlin plate theory, combined with Hamilton's principle, is utilized to derive the governing equations of motion. Various types of boundary conditions are assumed for the plate with a combination of clamped, simply supported and free edges. Finally, the governing equations of motion are solved numerically using the shooting technique. The effects of various factors such as porosity coefficient, porosity distribution pattern, thickness‐diameter ratio, and the nonlocal scale effect and boundary conditions on the natural frequencies of grade porous circular nanoplates are discussed in detail.

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Thermal effect on bending, buckling and free vibration of functionally graded rectangular micro-plates possessing a variable length scale parameter

Cited by 14 publications

References 71 publications

A Review on Buckling Analysis of Functionally Graded Plates Under Thermo-Mechanical Loads

A Review on Buckling Analysis of Functionally Graded Plates Under Thermo-Mechanical Loads

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

Free vibration analysis of graded porous circular micro/nanoplates with various boundary conditions based on the nonlocal elasticity theory

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