On the static stability of nonlocal nanobeams using higher-order beam theories

Eltaher, Mohamed A.; Khater, Mahmoud; Park, S.; Abdel‐Rahman, Eihab; Yavuz, Mustafa Murat

doi:10.12989/anr.2016.4.1.051

Cited by 12 publications

(5 citation statements)

References 36 publications

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“…The most popular one is the Eringen differential form of the strain-driven nonlocal elasticity model [15,16]. A countless list of structuralmechanics models have been cooperated with this nonlocal differential model [19][20][21][22]. As one of the earliest research works on the application of the Eringen nonlocal differential model, Peddieson et al [19] investigated flexural responses of nanobeams under different support systems and various loading types using the nonlocal Euler-Bernoulli beam model.…”

Section: Introductionmentioning

confidence: 99%

A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect

Sae-Long

Limkatanyu

Prachasaree

et al. 2020

Journal of Nanomaterials

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This paper presents a bar-elastic substrate model to investigate the axial responses of nanowire-elastic substrate systems considering the effects of nonlocality and surface energy. The thermodynamics-based strain gradient model is adopted to capture the nonlocality of the bar-bulk material while the Gurtin-Murdoch surface theory is utilized to consider the surface energy. To characterize the bar-surrounding substrate interaction, the Winkler foundation model is employed. In a direct manner, system compatibility conditions are obtained while within the framework of the virtual displacement principle, the system equilibrium condition and the corresponding natural boundary conditions are consistently obtained. Three numerical simulations are conducted to investigate the characteristics and behaviors of the nanowire-elastic substrate system: the first is conducted to reveal the capability of the proposed model to eliminate the paradoxical behavior inherent to the Eringen nonlocal differential model; the second is employed to characterize responses of the nanowire-elastic substrate system; and the third is aimed at demonstrating the dependence of the system effective Young’s modulus on several system parameters.

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Section: Introductionmentioning

confidence: 99%

A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect

Sae-Long

Limkatanyu

Prachasaree

et al. 2020

Journal of Nanomaterials

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“…Wu and Kitipornchai [6] investigated the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded (FG)-CNTRC face sheets in a Timoshenko beam theoretical framework. Among coupled thermo-mechanical problems, Eltaher et al [7] investigated the influence of a thermal loading and shear force on the nonlocal buckling response of nanobeams via higher-order shear deformation Eringen beam theories. Similarly, Ebrahimi and Farazmandnia [8] investigated the thermo-mechanical vibration of sandwich FG-CNTRC beams within a Timoshenko-based beam approach; Sobhy and Zenkour [9] illustrated the influence of a magnetic field on the thermo-mechanical buckling and vibration response of FG-CNTRC nanobeams with a viscoelastic substrate.…”

Section: Introductionmentioning

confidence: 99%

Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment

et al. 2021

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This paper presents a mathematical continuum model to investigate the static stability buckling of cross-ply single-walled (SW) carbon nanotube reinforced composite (CNTRC) curved sandwich nanobeams in thermal environment, based on a novel quasi-3D higher-order shear deformation theory. The study considers possible nano-scale size effects in agreement with a nonlocal strain gradient theory, including a higher-order nonlocal parameter (material scale) and gradient length scale (size scale), to account for size-dependent properties. Several types of reinforcement material distributions are assumed, namely a uniform distribution (UD) as well as X- and O- functionally graded (FG) distributions. The material properties are also assumed to be temperature-dependent in agreement with the Touloukian principle. The problem is solved in closed form by applying the Galerkin method, where a numerical study is performed systematically to validate the proposed model, and check for the effects of several factors on the buckling response of CNTRC curved sandwich nanobeams, including the reinforcement material distributions, boundary conditions, length scale and nonlocal parameters, together with some geometry properties, such as the opening angle and slenderness ratio. The proposed model is verified to be an effective theoretical tool to treat the thermal buckling response of curved CNTRC sandwich nanobeams, ranging from macroscale to nanoscale, whose examples could be of great interest for the design of many nanostructural components in different engineering applications.

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“…Therefore, it is important to take into account the porosity effect when designing FGM structures subjected to dynamic loadings [14]. Currently, many functionally graded (FG) plate structures which have been employed for engineering fields led to the development of various plate models to study the static, buckling and vibration responses of FG structures [15][16][17][18][19]. The classical plate theory (CPT) is based on the supposition that straight lines which are normal to the neutral surface before deformation remain straight and normal to the neutral surface after deformation.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium

Saidi¹,

Sahla²

2019

Frattura Ed Integrità Strutturale

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In this scientific work, a new shear deformation theory for free vibration analysis of simply supported rectangular functionally graded plate embedded in an elastic medium is presented. Due to technical problems during the fabrication, porosities can be created in side FGM plate which may lead to reduction in strength of materials. In this investigation the FGM plate are assumed to have a new distribution of porosities according to the thickness of the plate. The elastic medium is modeled as Winkler-Pasternak two parameter models to express the interaction between the FGM plate and elastic foundation. The four unknown shear deformation theory is employed to deduce the equations of motion. The Hamilton's principle is used to derive the governing equations of motion. The accuracy of this theory is verified by compared the developed results with those obtained using others plate theory. Some examples are performed to demonstrate the effect of changing gradient material, elastic parameters, porosity index, and length to thickness ratios on the fundamental frequency of functionally graded plate.

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On the static stability of nonlocal nanobeams using higher-order beam theories

Cited by 12 publications

References 36 publications

A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect

A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect

Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment

Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium

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