Relevant bibliographies by topics / Eringen's nonlocal elastica

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Academic literature on the topic 'Eringen's nonlocal elastica'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Eringen's nonlocal elastica"

1

Jung, Woo-Young, and Sung-Cheon Han. "Nonlocal Elasticity Theory for Transient Analysis of Higher-Order Shear Deformable Nanoscale Plates." Journal of Nanomaterials 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/208393.

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The small scale effect on the transient analysis of nanoscale plates is studied. The elastic theory of the nano-scale plate is reformulated using Eringen’s nonlocal differential constitutive relations and higher-order shear deformation theory (HSDT). The equations of motion of the nonlocal theories are derived for the nano-scale plates. The Eringen’s nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. T
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2

Ebrahimi, Farzad, and Mohammad Reza Barati. "Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams." Journal of Intelligent Material Systems and Structures 28, no. 15 (2017): 2007–22. http://dx.doi.org/10.1177/1045389x16682850.

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This article investigates vibration behavior of magneto-electro-elastic functionally graded nanobeams embedded in two-parameter elastic foundation using a third-order parabolic shear deformation beam theory. Material properties of magneto-electro-elastic functionally graded nanobeam are supposed to be variable throughout the thickness based on power-law model. Based on Eringen’s nonlocal elasticity theory which captures the small size effects and using Hamilton’s principle, the nonlocal governing equations of motions are derived and then solved analytically. Then, the influences of elastic fou
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3

Mikhasev, G., E. Avdeichik, and D. Prikazchikov. "Free vibrations of nonlocally elastic rods." Mathematics and Mechanics of Solids 24, no. 5 (2018): 1279–93. http://dx.doi.org/10.1177/1081286518785942.

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Several of the Eringen’s nonlocal stress models, including two-phase and purely nonlocal integral models, along with the simplified differential model, are studied in the case of free longitudinal vibrations of a nanorod, for various types of boundary conditions. Assuming the exponential attenuation kernel in the nonlocal integral models, the integro-differential equation corresponding to the two-phase nonlocal model is reduced to a fourth-order differential equation with additional boundary conditions, taking into account nonlocal effects in the neighbourhood of the rod ends. Exact analytical
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4

Feo, Luciano, and Rosa Penna. "On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials." Modelling and Simulation in Engineering 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/6369029.

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Evaluation of size effects in functionally graded elastic nanobeams is carried out by making recourse to the nonlocal continuum mechanics. The Bernoulli-Euler kinematic assumption and the Eringen nonlocal constitutive law are assumed in the formulation of the elastic equilibrium problem. An innovative methodology, characterized by a lowering in the order of governing differential equation, is adopted in the present manuscript in order to solve the boundary value problem of a nanobeam under flexure. Unlike standard treatments, a second-order differential equation of nonlocal equilibrium elastic
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5

Mubasshar, Shahid, and Jaan Lellep. "Natural vibrations of circular nanoarches of piecewise constant thickness." Acta et Commentationes Universitatis Tartuensis de Mathematica 27, no. 2 (2023): 295–318. http://dx.doi.org/10.12697/acutm.2023.27.20.

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The free vibrations of elastic circular arches made of a nano-material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch.
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6

Gaygusuzoglu, Guler, Metin Aydogdu, and Ufuk Gul. "Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 7-8 (2018): 709–19. http://dx.doi.org/10.1515/ijnsns-2017-0225.

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AbstractIn this study, nonlinear wave modulation in nanorods is examined on the basis of nonlocal elasticity theory. Eringen's nonlocal elasticity theory is employed to derive nonlinear equations for the motion of nanorods. The analysis of the modulation of axial waves in nonlocal elastic media is performed, and the reductive perturbation method is used for the solution of the nonlinear equations. The propagation of weakly nonlinear and strongly dispersive waves is investigated, and the nonlinear Schrödinger (NLS) equation is acquired as an evolution equation. For the purpose of a numerical in
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7

Shen, Xiao Long, Yong Xin Luo, Lai Xi Zhang, and Hua Long. "Natural Frequency Computation Method of Nonlocal Elastic Beam." Advanced Materials Research 156-157 (October 2010): 1582–85. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.1582.

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After adopting the constitutive equations of the nonlocal elastic media in the form of Eringen, and making use of the Laplace transformation, the vibration governing equation of nonlocal elastic beam in the Kelvin media are established. Unlike classical elastic models, the stress of a point in a nonlocal model is obtained as a weighted average of the field over the spatial domain, determined by a kernel function based on distance measures. The motion equation of nonlocal elastic beam is an integral differential equation, rather than the differential equation obtained with a classical local mod
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8

Xu, S. P., M. R. Xu, and C. M. Wang. "Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/341232.

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Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, t
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9

Sari, Ma’en S., Mohammad Al-Rbai, and Bashar R. Qawasmeh. "Free vibration characteristics of functionally graded Mindlin nanoplates resting on variable elastic foundations using the nonlocal elasticity theory." Advances in Mechanical Engineering 10, no. 12 (2018): 168781401881345. http://dx.doi.org/10.1177/1687814018813458.

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In this research, free vibration behavior of thick functionally graded nanoplates is carried out using the Chebyshev spectral collocation method. It is assumed that the plates are resting on variable elastic foundations. Eringen’s nonlocal elasticity theory is used to capture the size effect, and Mindlin’s first-order shear deformation plate theory is employed to model the thick nanoplates. Hamilton’s principle along with the differential form of Eringen’s constitutive relations are utilized to obtain the governing partial differential equations of motion for the functionally graded nanoplates
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10

Jung, Woo-Young, and Sung-Cheon Han. "Analysis of Sigmoid Functionally Graded Material (S-FGM) Nanoscale Plates Using the Nonlocal Elasticity Theory." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/476131.

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Based on a nonlocal elasticity theory, a model for sigmoid functionally graded material (S-FGM) nanoscale plate with first-order shear deformation is studied. The material properties of S-FGM nanoscale plate are assumed to vary according to sigmoid function (two power law distribution) of the volume fraction of the constituents. Elastic theory of the sigmoid FGM (S-FGM) nanoscale plate is reformulated using the nonlocal differential constitutive relations of Eringen and first-order shear deformation theory. The equations of motion of the nonlocal theories are derived using Hamilton’s principle
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