A nonlocal analytical approach for torsion of cylindrical nanostructures and the existence of higher-order stress and geometric boundaries

Li, Cheng

doi:10.1016/j.compstruct.2014.08.008

Cited by 76 publications

(35 citation statements)

References 40 publications

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“…It is implied that the deflection decreases with an increase in the ratio of internal to external length scales since a larger external length scale (or a smaller ratio) leads to a higher midpoint deflection under given parameters. This is consistent with the conclusion in previous studies [9,11,13]. Hence, the validity of the present model is confirmed once again.…”

Section: Numerical Examplessupporting

confidence: 94%

“…During the development of nonlocal theory, there were two kinds of nonlocal models in nonlocal differential constitution and both were studied extensively. When increasing the nonlocal scale parameter or when the nonlocal effect gets stronger, the increasing and decreasing trends of deformation result in different kinds of nonlocal differential models, namely, the nonlocal stiffness-weakening model (e.g., [3][4][5]) and the stiffness-strengthening model (e.g., [9,11,13]). The strengthening model declares that nanostructural stiffness is enhanced with stronger nonlocal effects, while the weakening model asserts an opposite conclusion.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solutions for Bending of Nanoscaled Bars Based on Eringen’s Nonlocal Differential Law

Zhang

et al. 2019

Journal of Nanomaterials

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The one-dimensional nanoscaled bar is commonly seen in current nanodevices, and it plays a significant role in nanoelectromechanical system (NEMS) and related nanotechnology. Motivated by this, the paper is concerned with the bending and stability of a nanoscaled bar especially a flexible bar subjected to vertical concentrated, vertical linearly distributed, and horizontal concentrated forces simultaneously. The theoretical model is developed by employing Eringen’s nonlocal differential law. Hence, the nonlocal differential constitutions in terms of stress and bending moment at a nanoscale are applied to the classical equilibrium formulation in order to construct the nonlocal constitutive model and then determine the analytical solutions for bending of such a nanoscale bar. Subsequently, the effect of a nonlocal scale on the midpoint deflections and internal forces is shown numerically, and the internal and external characteristic length scales are also examined. It is revealed that the capacity of resisting compression decreases with increasing the nonlocal effect since the internal characteristic scale cannot be neglected by comparing with the external characteristic scale. There exists a threshold value for bending stiffness. Both the midpoint deflection and bending moment vary monotonously when the material bending stiffness exceeds the threshold value, while the mechanical quantities fluctuate when the bending stiffness is less than its threshold value, namely, for a flexible nanoscaled bar. Accordingly, two different kinds of nonlocal predictions and the related disputes are resolved in the context of Eringen’s nonlocal differential law. The work is expected to be useful for the design, application, and optimization of nanoscaled bars sustaining bending with linear vertical and horizontal forces.

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Section: Numerical Examplessupporting

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Analytical Solutions for Bending of Nanoscaled Bars Based on Eringen’s Nonlocal Differential Law

Zhang

et al. 2019

Journal of Nanomaterials

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“…However, there are strong evidences that the small length scale effect i.e., nonlocal effect has a significant influence on the mechanical behavior of nanostructures. Therefore, classical structural theories have to be modified to use for the small length scale effect (Akgöz, B., & Civalek, O., 2011;Li, 2014;Shen et al, 2012;Li, X. F., & Wang, B. L., 2009;Huang et al, 2013;Shen, J. P., & Li, C., 2017;Mercan, K., & Civalek, O., 2016).…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

Ragb¹,

Mohamed²,

Matbuly³

2019

MAS

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Magneto-Electro-Thermo nanobeam resting on a nonlinear elastic foundation is presented. This beam is subjected to the external electric voltage and magnetic potential, mechanical potential and temperature change. Also, we added the new material PTZ-5H-COFe2O4. The governing equations and boundary conditions are derived using Hamilton principle. These equations are discretized by using three differential quadrature methods and iterative quadrature technique to determine the natural frequencies and mode shapes. Numerical analysis is introduced to explain the influence of computational characteristics of the proposed schemes on convergence, accuracy and efficiency of the obtained results. The obtained results agreed with the previous analytical and numerical ones. A detailed parametric study is conducted to investigate the influences of different boundary conditions, various composite materials, nonlinear elastic foundation, nonlocal parameter, the length-to-thickness ratio, external electric and magnetic potentials, axial forces, temperature and their effects on the vibration characteristics of Magneto-Electro-Thermo-Elastic nanobeam.

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“…Analysis and assessment of size-effects in nano-structures is currently a topic of major interest in the scientific community [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Torsional deformations can frequently occur in structural elements of NEMS, and therefore, various size-dependent elasticity theories have been exploited in literature [21][22][23][24][25][26][27][28][29][30][31][32], as comprehensively discussed in review contributions [33,34].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

et al. 2019

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Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems.In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation.The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest.Both elastostatic torsional responses and torsional free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviours of structures involved in modern Nano-Electro-Mechanical-Systems (NEMS). KeywordsTorsion; nano-beams; nonlocal strain gradient model; strain gradient elasticity; integral elasticity; size effects; analytical modelling; NEMS. d J J dx J J dx J

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A nonlocal analytical approach for torsion of cylindrical nanostructures and the existence of higher-order stress and geometric boundaries

Cited by 76 publications

References 40 publications

Analytical Solutions for Bending of Nanoscaled Bars Based on Eringen’s Nonlocal Differential Law

Analytical Solutions for Bending of Nanoscaled Bars Based on Eringen’s Nonlocal Differential Law

Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

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