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Recent Advances in Non-Local Modelling of Nano-Structures
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Recent Advances in Non-Local Modelling of Nano-Structures

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Nanotechnology and Applied Nanosciences".

Deadline for manuscript submissions: closed (30 April 2019) | Viewed by 20482

Special Issue Editor

Prof. Dr. Raffaele Barretta

E-Mail Website
Guest Editor
Department of Structures for Engineering and Architecture, University of Naples Federico II, 80125 Naples, Italy
Interests: continuum mechanics; nanostructures; nonlocal models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mechanical modeling of nano-materials and nano-structures is a subject of ever-increasing interest in the scientific literature due to the challenging tasks in theoretical formulations and computational methodologies. Carbon nanotubes and graphene sheets are widely investigated for the development of modern nano-devices. The realization of ground-breaking nano-sensors and nano-actuators, as basic structural elements of scanners, mirrors, gyroscopes, springs and many similar other nanoscale systems, is an important target, with countless conceivable applications. Nano-materials are effectively used also as excellent components for reinforcement in composites nano-structures.

Small-scale structural modeling of 1D, 2D and 3D continua is conveniently resorted to in place of atomistic approaches. Several nonlocal models have been proposed in literature and extensively investigated. This approach is still the focus of an active scientific debate concerning consistency of theoretical formulations, fitting of experimental data and predictive capabilities of phenomena in the small-scale range.

This Special Issue is devoted to collect innovative theoretical proposals and numerical   methodologies aimed to improve the current state of the art on the matter.

Both theoretical and experimental contributions are welcome.

Potential topics include but are not limited to the following:

  1. Nano Engineering;
  2. MEMS and NEMS;
  3. Nonlocal constitutive models;
  4. Nano-beams, nano-plates and nano-shells;
  5. Generalized continua;
  6. Functionally graded materials;
  7. Composite structures.

Prof. Raffaele Barretta
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlocal theories
  • functionally graded materials
  • carbon nanotubes
  • size-effects
  • nano-beams
  • nano-plates
  • nano-shells
  • nano-composites
  • homogenization
  • nano-actuators
  • nano-sensors

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Published Papers (6 papers)

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Research

19 pages, 2027 KiB  
Article
Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations
by Mohammad Arefi, Elyas Mohammad-Rezaei Bidgoli, Rossana Dimitri, Francesco Tornabene and J. N. Reddy
Appl. Sci. 2019, 9(8), 1580; https://doi.org/10.3390/app9081580 - 16 Apr 2019
Cited by 78 | Viewed by 3878
Abstract
This paper presents a free vibration analysis of functionally graded (FG) polymer composite curved nanobeams reinforced with graphene nanoplatelets resting on a Pasternak foundation. The size-dependent governing equations of motion are derived by applying the Hamilton’s principle and the differential law consequent (but [...] Read more.
This paper presents a free vibration analysis of functionally graded (FG) polymer composite curved nanobeams reinforced with graphene nanoplatelets resting on a Pasternak foundation. The size-dependent governing equations of motion are derived by applying the Hamilton’s principle and the differential law consequent (but not equivalent) to Eringen’s strain-driven nonlocal integral elasticity model equipped with the special bi-exponential averaging kernel. The displacement field of the problem is here described in polar coordinates, according to the first order shear deformation theory. A large parametric investigation is performed, which includes different FG patterns, different boundary conditions, but also different geometrical parameters, number of layers, weight fractions, and Pasternak parameters. Full article
(This article belongs to the Special Issue Recent Advances in Non-Local Modelling of Nano-Structures)
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15 pages, 1202 KiB  
Article
Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches
by Małgorzata Chwał and Aleksander Muc
Appl. Sci. 2019, 9(7), 1409; https://doi.org/10.3390/app9071409 - 3 Apr 2019
Cited by 15 | Viewed by 2632
Abstract
The buckling and free vibrations of rectangular nanoplates are considered in the present paper. The refined continuum transverse shear deformation theory (third and first order) is introduced to formulate the fundamental equations of the nanoplate. Besides, the analysis involve the nonlocal strain and [...] Read more.
The buckling and free vibrations of rectangular nanoplates are considered in the present paper. The refined continuum transverse shear deformation theory (third and first order) is introduced to formulate the fundamental equations of the nanoplate. Besides, the analysis involve the nonlocal strain and stress theories of elasticity to take into account the small-scale effects encountered in nanostructures/nanocomposites. Hamilton’s principle is used to establish the governing equations of the nanoplate. The Rayleigh-Ritz method is proposed to solve eigenvalue problems dealing with the buckling and free vibration analysis of the nanoplates considered. Some examples are presented to investigate and illustrate the effects of various formulations. Full article
(This article belongs to the Special Issue Recent Advances in Non-Local Modelling of Nano-Structures)
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21 pages, 1397 KiB  
Article
Modified Nonlocal Strain Gradient Elasticity for Nano-Rods and Application to Carbon Nanotubes
by Raffaele Barretta, Marko Čanadija and Francesco Marotti de Sciarra
Appl. Sci. 2019, 9(3), 514; https://doi.org/10.3390/app9030514 - 2 Feb 2019
Cited by 41 | Viewed by 3640
Abstract
Nowadays, the modified nonlocal strain gradient theory provides a mathematically well-posed and technically reliable methodology to assess scale effects in inflected nano-structures. Such an approach is extended in this paper to investigate the extensional behavior of nano-rods. The considered integral elasticity model, involving [...] Read more.
Nowadays, the modified nonlocal strain gradient theory provides a mathematically well-posed and technically reliable methodology to assess scale effects in inflected nano-structures. Such an approach is extended in this paper to investigate the extensional behavior of nano-rods. The considered integral elasticity model, involving axial force and strain fields, is conveniently shown to be equivalent to a nonlocal differential problem equipped with constitutive boundary conditions. Unlike treatments in the literature, no higher-order boundary conditions are required to close the nonlocal problem. Closed-form solutions of elastic nano-rods under selected loadings and kinematic boundary conditions are provided. As an innovative implication, Young’s moduli of Single-Walled Carbon Nanotubes (SWCNT) weare assessed and compared with predictions of Molecular Dynamics (MD). New benchmarks for numerical analyses were also detected. Full article
(This article belongs to the Special Issue Recent Advances in Non-Local Modelling of Nano-Structures)
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12 pages, 364 KiB  
Article
Size-Dependent Free Vibration of Axially Moving Nanobeams Using Eringen’s Two-Phase Integral Model
by Yuanbin Wang, Zhimei Lou, Kai Huang and Xiaowu Zhu
Appl. Sci. 2018, 8(12), 2552; https://doi.org/10.3390/app8122552 - 10 Dec 2018
Cited by 2 | Viewed by 2316
Abstract
In this paper, vibration of axially moving nanobeams is studied using Eringen’s two-phase nonlocal integral model. Geometric nonlinearity is taken into account for the integral model for the first time. Equations of motion for the beam with simply supported and fixed–fixed boundary conditions [...] Read more.
In this paper, vibration of axially moving nanobeams is studied using Eringen’s two-phase nonlocal integral model. Geometric nonlinearity is taken into account for the integral model for the first time. Equations of motion for the beam with simply supported and fixed–fixed boundary conditions are obtained by Hamilton’s Principle, which turns out to be nonlinear integro-differential equations. For the free vibration of the nanobeam, the critical velocity and the natural frequencies are obtained numerically. Furthermore, the effects of parameters on critical velocity and natural frequency are analyzed. We have found that, for the two-phase nonlocal integral model, regardless of the boundary conditions considered, both the critical velocity and the natural frequency increase with the nonlocal parameter and the geometric parameter. Full article
(This article belongs to the Special Issue Recent Advances in Non-Local Modelling of Nano-Structures)
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19 pages, 2519 KiB  
Article
Postbuckling and Free Vibration of Multilayer Imperfect Nanobeams under a Pre-Stress Load
by S. A. Emam, M. A. Eltaher, M. E. Khater and W. S. Abdalla
Appl. Sci. 2018, 8(11), 2238; https://doi.org/10.3390/app8112238 - 13 Nov 2018
Cited by 57 | Viewed by 3820
Abstract
This paper investigates the postbuckling and free vibration response of geometrically imperfect multilayer nanobeams. The beam is assumed to be subjected to a pre-stress compressive load due to the manufacturing and its ends are kept at a fixed distance in space. The small-size [...] Read more.
This paper investigates the postbuckling and free vibration response of geometrically imperfect multilayer nanobeams. The beam is assumed to be subjected to a pre-stress compressive load due to the manufacturing and its ends are kept at a fixed distance in space. The small-size effect is modeled according to the nonlocal elasticity differential model of Eringen within the nonlinear Bernoulli-Euler beam theory. The constitutive equations relating the stress resultants to the cross-section stiffness constants for a nonlocal multilayer beam are developed. The governing nonlinear equation of motion is derived and then manipulated to be given in terms of only the lateral displacement. The static problem is solved for the buckling load and the postbuckling deflection in terms of three parameters: Imperfection amplitude, size, and lamination. A closed-form solution for the buckling load in terms of all of the beam parameters is developed. With the presence of imperfection and size effects, it has been shown that the buckling load can be either less or greater than the Euler buckling load. Moreover, the free vibration in the pre and postbuckling domains are investigated for the first five modes. Numerical results show that the effects of imperfection, the nonlocal parameter, and layup on buckling loads and natural frequencies of the nanobeams are significant. Full article
(This article belongs to the Special Issue Recent Advances in Non-Local Modelling of Nano-Structures)
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12 pages, 1463 KiB  
Article
Effect of Sinusoidal Corrugated Geometries on the Vibrational Response of Viscoelastic Nanoplates
by Mohammad Malikan, Rossana Dimitri and Francesco Tornabene
Appl. Sci. 2018, 8(9), 1432; https://doi.org/10.3390/app8091432 - 22 Aug 2018
Cited by 25 | Viewed by 3169
Abstract
The vibrational behavior of viscoelastic nanoplates with a corrugated geometry is a key topic of practical interest. This problem is addressed here for wrinkled nanoplates with small corrugations related to incorrect manufacturing. To this end, a new One-Variable First-order Shear Deformation plate Theory [...] Read more.
The vibrational behavior of viscoelastic nanoplates with a corrugated geometry is a key topic of practical interest. This problem is addressed here for wrinkled nanoplates with small corrugations related to incorrect manufacturing. To this end, a new One-Variable First-order Shear Deformation plate Theory (OVFSDT) is proposed in a combined form with a non-local strain gradient theory. The Kelvin–Voigt model is employed to describe the viscoelastic behavior of the nanoplate, whereby the frequency equations are solved numerically according to Navier’s approach, for simply-supported nanostructures. A comparative evaluation between the proposed theory and other approaches in the literature is successfully performed. It follows a large parametric study of the vibration response for varying geometry corrugations and non-local parameters. Full article
(This article belongs to the Special Issue Recent Advances in Non-Local Modelling of Nano-Structures)
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