Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics

Farajpour, Ali; Shahidi, Alireza; Mohammadi, M.; Mahzoon, Mojtaba

doi:10.1016/j.compstruct.2011.12.032

Cited by 123 publications

(31 citation statements)

References 60 publications

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“…The most comprehensive work was done by Mindlin[14] which contained five additional material parameters and encompassed other non-local theories as special cases Non-local elasticity has been used to study buckling, bending vibration dislocation mechanics, fracture mechanics, surface tension fluids, etc. (Reddy, 2007;Mohammadi et al, 2012;2013;Moosavi et al, 2011;Danesh et al, 2012;Farajpour et al, 2012) Lam et al (2003, introduced a modified strain gradient theory with three material length scale parameters relevant to dilatation gradient, deviatoric gradient, and symmetric rotation gradient tensors. While some simple size dependent models based on modified couple stress theory have been applied to analyze the pull-in instability of MEMS/NEMS (Tadi HRokni, et al, 2013;Noghrehabadi et al, 2013;Zhang and Fu, 2012;Mindlin and Tiersten, 1962;Yin et al, 2011), only rare works have utilized strain gradient theory for analyzing.…”

Section: Using Various Approachesmentioning

confidence: 99%

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Koochi

Sedighi

Abadyan

2014

Lat. Am. j. solids struct.

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It is well recognized that size dependency of materials characteristics, i.e. size-effect, often plays a significant role in the performance of nano-structures. Herein, strain gradient continuum theory is employed to investigate the size dependent pull-in instability of beam-type nano-electromechanical systems (NEMS). Two most common types of NEMS i.e. nano-bridge and nano-cantilever are considered. Effects of electrostatic field and dispersion forces i.e. Casimir and van der Waals (vdW) attractions have been considered in the nonlinear governing equations of the systems. Two different solution methods including numerical and Rayleigh-Ritz have been employed to solve the constitutive differential equations of the system. Effect of dispersion forces, the size dependency and the importance of coupling between them on the instability performance are discussed.

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Section: Using Various Approachesmentioning

confidence: 99%

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Koochi

Sedighi

Abadyan

2014

Lat. Am. j. solids struct.

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“…The scale coefficients are assumed as Duan and Wang (2007) presented the constitutive relations of nonlocal elasticity theory for application in the analysis of circular graphene sheet. Recently, these values for the nonlocal parameter are used by many researchers (Farajpour et al 2011b;Danesh et al 2012;Farajpour et al 2012;Mohammadi et al 2013b). Properties of the orthotropic graphene sheet in this paper are considered same as mentioned in the reference .…”

Section: Validation Of Present Resultsmentioning

confidence: 99%

Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium

Mohammadi

Moradi

Ghayour

et al. 2014

Lat. Am. j. solids struct.

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In this paper, the effect of the temperature change on the vibration frequency of mono-layer graphene sheet embedded in an elastic medium are studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets. Using Levy and Navier solutions, analytical frequency equations for single-layered graphene sheets are obtained. Using Levy solution, the frequency equation and mode shapes of orthotropic rectangular nanoplate are considered for three cases of boundary conditions. The obtained results are subsequently compared with valid result reported in the literature. The effects of the small scale, temperature change, different boundary conditions, Winkler and Pasternak foundations, material properties and aspect ratios on natural frequencies are investigated. It has been shown that the non-dimensional frequency decreases with increasing temperature change. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the nanoplates.

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“…They obtained the most general form of boundary conditions and also governing equations. Buckling analysis of orthotropic micro-plates/nano-plates under linearly varying in-plane load via non-local continuum mechanics was carried out by Farajpour et al [30]. They used non-local theory and determined the governing equations.…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories

Mohammadi

Mahani

2015

Acta Mech

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In this study, a size-dependent Kirchhoff plate model is developed for determining the critical buckling loads of rectangular micro-plates. Modified strain gradient theory with three length scale parameters is used. It should be noted that this theory is reduced to modified couple stress theory by setting two length scale parameters to zero. Using the variational approach and the principle of minimum total potential energy, the nonlinear form of the governing equations and all possible boundary conditions are determined. It is assumed that the micro-plate is simply supported on two opposite edges. The stability equations are solved analytically, and the critical buckling loads are obtained based on the modified strain gradient and modified couple stress theories. Also, the effects of length scale parameters, dimensions and loading states on the buckling loads are investigated in detail.

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Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics

Cited by 123 publications

References 60 publications

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium

An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories

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