Nonlocal buckling of double-nanoplate-systems under biaxial compression

Murmu, T.; Sienz, Johann; Adhikari, Sondipon; Arnold, C.

doi:10.1016/j.compositesb.2012.07.053

Cited by 82 publications

(36 citation statements)

References 64 publications

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“…Recently, Radic et al [9] investigated buckling analysis of DONPs embedded in Pasternak elastic medium using nonlocal elasticity theory. In these works [5][6][7][8][9], the effects of non-local parameter were studied for multilayered nanoplates based on CPT and, because of using classical solutions, e.g., Navier's method as used for simply supported boundary conditions, the above-mentioned researchers were not able to investigate other boundary conditions and shear buckling. In recent years, Sarrami et al [10] studied vibration and buckling of single and multilayered graphene sheets based on non-local elasticity theory using finite strip method.…”

Section: Introductionmentioning

confidence: 99%

“…Shi et al [6] investigated vibration analysis of nanomechanical systems resonators for circular double-layer graphene sheets. Murmu et al [7] analyzed buckling of double-nanoplate systems under biaxial compression. Asemi et al [8] studied the vibration characteristics of double-piezoelectric nanoplate systems.…”

Section: Introductionmentioning

confidence: 99%

“…Asemi et al [8] studied the vibration characteristics of double-piezoelectric nanoplate systems. The shear stiffness effects [5][6][7][8] were not taken into account. Recently, Radic et al [9] investigated buckling analysis of DONPs embedded in Pasternak elastic medium using nonlocal elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

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Buckling analysis of double-orthotropic nanoplates embedded in elastic media based on non-local two-variable refined plate theory using the GDQ method

Shokrani

Karimi

Tehrani

et al. 2015

J Braz. Soc. Mech. Sci. Eng.

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In this article, buckling analysis of doubleorthotropic nanoplates (DONP) embedded in elastic media under biaxial, uniaxial and shear loading is numerically studied. The analysis is based on non-local theory. Both two-variable refined plate theory (TVRPT) and first-order shear deformation plate theory (FSDT) are used to derive the governing equations. Generalized differential quadrature method (GDQM) is utilized to solve the governing equations. In buckling analysis, both in-phase and out-ofphase modes are studied. A graphene sheet is selected as the case study to investigate the numerical results. GDQM results are validated by comparing with the Navier's solutions. After validating the formulation and method of solution, the effect of non-local parameter, geometrical parameters and boundary conditions on the critical buckling load of the double-orthotropic nanoplate are investigated and discussed in detail. It is shown that the effects of non-local parameter for shear buckling are more noticeable than that of biaxial buckling. Moreover, for higher values of non-local parameter, the shear buckling is not dependent on the van der Waals and Winkler moduli.Keywords Two-variable refined plate theory Á Non-local theory Á Buckling analysis Á Generalized differential quadrature method Á Double-orthotropic nanoplate Abbreviations DONP Double-orthotropic nanoplate DQM Differential quadrature method GDQM Generalized differential quadrature method TVRPT Two-variable refined plate theory FSDT First-order shear deformation theory HSDT Higher-order shear deformation theories CPT Classical plate theory NDCBL Non-dimensional critical buckling load

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Buckling analysis of double-orthotropic nanoplates embedded in elastic media based on non-local two-variable refined plate theory using the GDQ method

Shokrani

Karimi

Tehrani

et al. 2015

J Braz. Soc. Mech. Sci. Eng.

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“…Inspired by the previous studies, this paper presents the nonlocal buckling problem of the bilayer composite plates, where two plates are isotropic with different material parameters, and the adhesive layer between the two plates is modeled as the Winkler elastic medium [17] . Effects of the nonlocal parameter, the non-dimensional Winkler parameter, the thickness ratio, the ratio of Young's moduli, and the aspect ratio are considered based on the buckling theory and nonlocal elastic theory.…”

Section: Introductionmentioning

confidence: 99%

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Peng

Guo

Liu

et al. 2015

Appl. Math. Mech.-Engl. Ed.

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Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young's moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young's moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small.

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“…A doublenanostructure-based system is the simplest model of a coupled multiple-nanostructure systems, which can be composed of two nanobeams, nanorods or nanoplates coupled through a medium with elastic or viscoelastic properties. Murmu and Adhikari conducted detailed vibration studies of a double-nanorod, nanobeam, and nanoplate systems [20][21][22][23], where partial differential equations of motion are obtained based on the D' Alembert's principle and nonlocal elasticity theory and solved by using analytical methods. They investigated the influence of small-scale effects and other physical parameters on natural frequencies and critical buckling loads and compared analytical results with results obtained by molecular dynamics simulations.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability of a nonlinear multiple-nanobeam system

2018

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We use the incremental harmonic balance (IHB) method to analyse the dynamic stability problem of a nonlinear multiple-nanobeam system (MNBS) within the framework of Eringen's nonlocal elasticity theory. The nonlinear dynamic system under consideration includes MNBS embedded in a viscoelastic medium as clamped chain system, where every nanobeam in the system is subjected to time-dependent axial loads. By assuming the von Karman type of geometric nonlinearity, a system of m nonlinear partial differential equations of motion is derived based on the Euler-Bernoulli beam theory and D' Alembert's principle. All nanobeams in MNBS are considered with simply supported boundary conditions. Semi-analytical solutions for time response functions of the nonlinear MNBS are obtained by using the single-mode Galerkin discretization and IHB method, which are then validated by using the numerical integration method. Moreover, Floquet theory is employed to determine the sta- method, we obtain an incremental relationship with the frequency and amplitude of time-varying axial load, which defines stability boundaries. Numerical examples show the effects of different physical and material parameters such as the nonlocal parameter, stiffness of viscoelastic medium and number of nanobeams on Floquet multipliers, instability regions and nonlinear amplitude-frequency response curves of MNBS. The presented results can be useful as a first step in the study and design of complex micro/nanoelectromechanical systems.

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Nonlocal buckling of double-nanoplate-systems under biaxial compression

Cited by 82 publications

References 64 publications

Buckling analysis of double-orthotropic nanoplates embedded in elastic media based on non-local two-variable refined plate theory using the GDQ method

Buckling analysis of double-orthotropic nanoplates embedded in elastic media based on non-local two-variable refined plate theory using the GDQ method

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Dynamic stability of a nonlinear multiple-nanobeam system

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