Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method

Babaei, Hashem; Shahidi, Alireza

doi:10.1007/s00419-010-0469-9

Cited by 80 publications

(30 citation statements)

References 32 publications

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“…In the recent decades, on the basis of the nonlocal elasticity theory proposed by Eringen, many vibration, buckling and bending studies of nanobeams [15,16] and nanoplates [17,18] have been reported. For example, Babaei and Shahidi [19] studied the static instability behavior of arbitrary quadrilateral nanoplates by taking into account the small scale effects. Ravari et al [20] incorporated nonlocal elasticity approach equations into the classical Kirchoff-plates theory to establish a nonlocal plate model which takes into account the size effect.…”

Section: Introductionmentioning

confidence: 99%

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

2016

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In this study, nonlocal elasticity theory in conjunction with Gurtin-Murdoch elasticity theory is employed to investigate biaxial buckling and free vibration behavior of nanoplate made of functionally graded material (FGM) and resting on a viscoPasternak standard linear solid-type of the foundation. The material characteristics of simply supported FGM nanoplates are assumed to be varied continuously as a power law function of the plate thickness. Hamilton's principle is implemented to derive the non-classical governing equations of motion and related boundary conditions, which analytically solved to obtain the explicit closed-form expression for complex natural frequencies and buckling loads. Finally, attention is focused on considering the influences of various parameters on variation of damped natural frequency and buckling load ratio such as nonlocal parameter, surface effects, geometric parameters, power law index and properties of visco-Pasternak foundation and it is clearly demonstrated that these factors highly affect on vibration and buckling behavior.

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Section: Introductionmentioning

confidence: 99%

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

2016

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“…Saadatpour and Azhari (1998) used Galerkin technique for static analysis of simply supported plates of arbitrary quadrilateral shape. Furthermore, the small-deflection stability analysis of various quadrilateral nanoplates, such as skew, rhombic, and trapezoidal nanoplates, was carried out on the basis of the Galerkin method (Babaei and Shahidi 2010). Using the general procedure of the method yields the following: …”

Section: Solutions By Galerkin Methodsmentioning

confidence: 99%

A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory

Asemi

Mohammadi

Farajpour

2014

Lat. Am. j. solids struct.

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Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. In the present work, the posbuckling response of orthotropic single-layered graphene sheet (SLGS) is investigated in a closedform analytical manner using the nonlocal theory of Eringen. Two opposite edges of the plate are subjected to normal stresses. The nonlocality and geometric nonlinearity are taken into consideration, which arises from the nanosized effects and mid-plane stretching, respectively. Nonlinear governing differential equations (nonlocal compatibility and equilibrium equations) are derived and presented for the aforementioned study. Galerkin method is used to solve the governing equations for simply supported boundary conditions. It is shown that the nonlocal effect plays a significant role in the nonlinear stability behavior of orthotropic nanoplates. Unlike first and second postbuckling modes, nonlocal effects decrease with the increase of lateral deflection at higher postbuckling modes. It is also observed that the nonlocality and nonlinearity is more pronounced for higher postbuckling modes.

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“…All of these models were based on Kirchhoff plate theory 8,12,[14][15][16][17][18][19][22][23][24][25][26][27] , Mindlin plate theory 9,11,20,[28][29][30] , and Reddy plate theory 10,13,31 . It should be noted that the Kirchhoff plate theory (KPT) is only applicable for thin plates.…”

Section: Introductionmentioning

confidence: 99%

A nonlocal sinusoidal plate model for micro/nanoscale plates

Thai

Nguyen

et al. 2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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A nonlocal sinusoidal plate model for micro/nanoscale plates is developed based on Eringen's nonlocal elasticity theory and sinusoidal shear deformation plate theory. The small scale effect is considered in the former theory while the transverse shear deformation effect is included in the latter theory. The proposed model accounts for sinusoidal variations of transverse shear strains through the thickness of the plate, and satisfies the stress-free boundary conditions on the plate surfaces, thus a shear correction factor is not required. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions for bending, buckling, and vibration of simply supported plates are presented, and the obtained results are compared with the existing solutions. The effects of small scale and shear deformation on the responses of the micro/nanoscale plates are investigated.

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Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method

Cited by 80 publications

References 32 publications

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory

A nonlocal sinusoidal plate model for micro/nanoscale plates

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