Special Issue "Functionally Graded Material (FGM) and Functionally Graded Carbon Nanotube (FG-CNT) Reinforced Composites"

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 (31 August 2018).

Special Issue Editor

Prof. Dr. Francesco Tornabene
E-Mail Website
Guest Editor

Special Issue Information

Dear Colleagues,

It is well-known that the class of Functionally Graded Materials (FGMs) has been introduced to reduce some issues, such as delamination and stress peaks, which commonly affect laminated composites or heterogeneous structures characterized by strong discontinuities at the interfaces.

By means of a continuous gradual variation of the mechanical properties, which can be defined along a proper path, structures made of FGMs do not show these problems related to the material discontinuities just mentioned. In general, this aim can be reached by mixing two or more constituents, both isotropic and orthotropic, following specified constitutive laws. Consequently, stress peaks, residual stresses, and damage growth can be reduced.

The same concepts of FGM are also used to characterize those nanocomposites in which the reinforcing phase is made by Carbon Nanotubes (CNTs). Since their recent discovery, in fact, these constituents have been seen as the perfect candidates to fulfill this aim, due to their excellent properties (thermal, electric, mechanical). The characterization of the properties of CNTs is still an open topic which could be further investigated.

Structural elements composed by FGMs or reinforced through CNTs placed according to variable distributions are known as Functionally Graded Material (FGM) and Functionally Graded Carbon Nanotube (FG-CNT) Reinforced Composites, respectively. In general, their mechanical response can be affected by several mechanical parameters, such as the volume fraction distributions of the constituents, their density or agglomeration features, porosity, thermal environment, load and boundary conditions.

The Special Issue of Applied Sciences “Functionally Graded Material (FGM) and Functionally Graded Carbon Nanotube (FG-CNT) Reinforced Composites” aims to collect various investigations at different levels (nano-, micro-, and macro-scales), focused on the mechanical analysis of composites reinforced by FGMs and FG-CNTs. Authors are encouraged to present research papers regarding new constitutive models, homogenization methods, advanced applications, as well as numerical, theoretical, and experimental analyses related to this topic, to provide a widespread framework on these innovative materials and facilitate their usage in various engineering fields. Structural problems and analyses are also welcomed.

Prof. Dr. Francesco Tornabene
Guest Editor

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Keywords

  • Functionally Graded Materials

  • Functionally Graded Carbon Nanotubes

  • Composite structures

  • Nanocomposites

  • Homogenization techniques

  • Experimental applications

  • Theoretical and numerical results

  • Structural analyses

  • Constitutive models

  • Mechanical characterization

  • Multiscale analyses

Published Papers (7 papers)

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Research

Open AccessArticle
Stress Concentration and Optimized Analysis of an Arbitrarily Shaped Hole with a Graded Layer under Anti-Plane Shear
Appl. Sci. 2018, 8(12), 2619; https://doi.org/10.3390/app8122619 - 14 Dec 2018
Abstract
This paper provides a general solution to the anti-plane problem of an arbitrarily shaped hole reinforced with a functionally graded (FG) layer in a homogenous plate. By using the piece-wise homogeneous layers method and the conformal mapping technique, the complex potentials in the [...] Read more.
This paper provides a general solution to the anti-plane problem of an arbitrarily shaped hole reinforced with a functionally graded (FG) layer in a homogenous plate. By using the piece-wise homogeneous layers method and the conformal mapping technique, the complex potentials in the form of series in the FG layer are derived based on the theory of complex variable functions. The influence of the FG layer on the shear stress distributions around some typically shaped holes are discussed by numerical examples, and then the optimized analysis of the stress concentration factor (SCF) is performed. The results showed that the SCF of various shaped holes can be noticeably reduced by the optimum design of the material variations in the layer, and the most significant one in this paper is the triangular hole, whose SCF can be decreased by more than 50%. Full article
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Open AccessArticle
Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution
Appl. Sci. 2018, 8(5), 731; https://doi.org/10.3390/app8050731 - 05 May 2018
Cited by 2
Abstract
In this study, a set of Föppl–von Kármán equations for a bimodular functionally graded thin plate subjected to a uniformly distributed load is established, and its general perturbation solution in axisymmetric case is also obtained under different boundary conditions. First, the equation of [...] Read more.
In this study, a set of Föppl–von Kármán equations for a bimodular functionally graded thin plate subjected to a uniformly distributed load is established, and its general perturbation solution in axisymmetric case is also obtained under different boundary conditions. First, the equation of equilibrium of the plate is established on the existence of the neutral layer when considering different properties in tension and compression. During the derivation of the consistency equation, the tensile effect in the thin plate with bimodular effect is fully taken into account. The perturbation method is used to solve the set of governing equations under different edge constraints, in which the central deflection and the load of the plate are taken as a perturbation parameter, respectively. The results indicate that the two selections for perturbation parameters are valid and consistent, and the two solutions are convenient for engineering application. This study also shows that the bimodular effect will modify the relation of load versus central deflection of the plate to some extent, and under the same edge constraint, the capacities resisting deformation in different cases of moduli depend on the relative magnitudes among the tensile modulus, the neutral layer modulus, and the compressive modulus. Full article
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Open AccessFeature PaperArticle
Effects of Order of Expansion for the Exponential Matrix and Number of Mathematical Layers in the Exact 3D Static Analysis of Functionally Graded Plates and Shells
Appl. Sci. 2018, 8(1), 110; https://doi.org/10.3390/app8010110 - 14 Jan 2018
Cited by 4
Abstract
This work deals with the study of the convergence ratio of the exponential matrix method used in the 3D static analysis of functionally graded structures subjected to harmonic loads. The equilibrium equations are written in mixed orthogonal curvilinear coordinates. This feature allows plates, [...] Read more.
This work deals with the study of the convergence ratio of the exponential matrix method used in the 3D static analysis of functionally graded structures subjected to harmonic loads. The equilibrium equations are written in mixed orthogonal curvilinear coordinates. This feature allows plates, cylinders, spherical and cylindrical shells to be studied with the same and unique formulation. After a reduction to first order differential equations, the obtained system is solved through the thickness by means of the exponential matrix method. The coefficients of these equations are not constant because the mechanical properties of the considered functionally graded materials change through the thickness. Moreover, the curvature terms introduce a further dependence of the coefficients from the thickness coordinate. The use of several mathematical layers allows for evaluating both the material properties and the curvature terms at certain points through the thickness direction. The M number of mathematical layers to be introduced is here studied in combination with the N expansion order of the exponential matrix. These values are influenced by several parameters. Therefore, different geometries, thickness ratios, lamination sequences, functionally graded material laws and half-wave numbers are considered. Full article
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Open AccessArticle
Closed Form Solutions for Thermal Buckling of Functionally Graded Rectangular Thin Plates
Appl. Sci. 2017, 7(12), 1256; https://doi.org/10.3390/app7121256 - 03 Dec 2017
Cited by 1
Abstract
This work concerns the critical buckling temperature of functionally graded rectangular thin plates; the properties of functionally graded material vary continuously in accordance with the power law of thickness z. Closed form solutions for the critical thermal parameter are obtained for the [...] Read more.
This work concerns the critical buckling temperature of functionally graded rectangular thin plates; the properties of functionally graded material vary continuously in accordance with the power law of thickness z. Closed form solutions for the critical thermal parameter are obtained for the plate with the following boundary condition combinations: simply supported, clamped and guided edges, under uniform, linear and nonlinear temperature fields via the separation-of-variable method. Furthermore, a new method is proposed to determine the critical buckling temperature from the critical thermal parameter. The present results coincide well with those in the literature, verifying the correctness of the present method. The influences of the length–thickness ratio, length–width ratio, power law index and initial temperature on critical buckling temperature are investigated. Full article
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Open AccessArticle
Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory
Appl. Sci. 2017, 7(12), 1252; https://doi.org/10.3390/app7121252 - 02 Dec 2017
Cited by 18
Abstract
Due to some technical issues that can appear during the manufacturing process of Functionally Graded Materials (FGMs), it can be extremely difficult to produce perfect materials. Indeed, one of the biggest problems is the presence of porosities. For this purpose, the vibrational behavior [...] Read more.
Due to some technical issues that can appear during the manufacturing process of Functionally Graded Materials (FGMs), it can be extremely difficult to produce perfect materials. Indeed, one of the biggest problems is the presence of porosities. For this purpose, the vibrational behavior of doubly-curved shells made of FGM including porosities is investigated in this paper. With respect to previous research, the porosity has been added to the mechanical model that characterizes the through-the-thickness distribution of the graded constituents and applied to doubly-curved shell structures. Few papers have been published on this topic. In fact, it is easier to find works related to one-dimensional structures and beam models that take account the effect of porosities. The First-order Shear Deformation Theory (FSDT) is considered as the theoretical framework. In addition, the mechanical properties of the constituents vary along the thickness direction. For this purpose, two power-law distributions are employed to characterize their volume fraction. Strain components are established in an orthogonal curvilinear coordinate system and the governing equations are derived according to the Hamilton’s principle. Finally, Navier’s solution method is used and the numerical results concerning three different types of shell structures are presented. Full article
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Open AccessFeature PaperArticle
Influence of Winkler-Pasternak Foundation on the Vibrational Behavior of Plates and Shells Reinforced by Agglomerated Carbon Nanotubes
Appl. Sci. 2017, 7(12), 1228; https://doi.org/10.3390/app7121228 - 28 Nov 2017
Cited by 54
Abstract
This paper aims to investigate the effect of the Winkler-Pasternak elastic foundation on the natural frequencies of Carbon Nanotube (CNT)-reinforced laminated composite plates and shells. The micromechanics of reinforcing CNT particles are described by a two-parameter agglomeration model. CNTs are gradually distributed along [...] Read more.
This paper aims to investigate the effect of the Winkler-Pasternak elastic foundation on the natural frequencies of Carbon Nanotube (CNT)-reinforced laminated composite plates and shells. The micromechanics of reinforcing CNT particles are described by a two-parameter agglomeration model. CNTs are gradually distributed along the thickness direction according to various functionally graded laws. Elastic foundations are modeled according to the Winkler-Pasternak theory. The theoretical model considers several Higher-order Shear Deformation Theories (HSDTs) based on the so-called Carrera Unified Formulation (CUF). The theory behind CNTs is explained in detail. The theoretical model presented is solved numerically by means of the Generalized Differential Quadrature (GDQ) method. Several parametric studies are conducted, and their results are discussed. Full article
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Open AccessFeature PaperArticle
Thermal Buckling of Nanocomposite Stiffened Cylindrical Shells Reinforced by Functionally Graded Wavy Carbon Nanotubes with Temperature-Dependent Properties
Appl. Sci. 2017, 7(12), 1223; https://doi.org/10.3390/app7121223 - 27 Nov 2017
Cited by 27
Abstract
We study the thermal buckling behavior of cylindrical shells reinforced with Functionally Graded (FG) wavy Carbon NanoTubes (CNTs), stiffened by stringers and rings, and subjected to a thermal loading. The equilibrium equations of the problem are built according to the Third-order Shear Deformation [...] Read more.
We study the thermal buckling behavior of cylindrical shells reinforced with Functionally Graded (FG) wavy Carbon NanoTubes (CNTs), stiffened by stringers and rings, and subjected to a thermal loading. The equilibrium equations of the problem are built according to the Third-order Shear Deformation Theory (TSDT), whereas the stiffeners are modeled as Euler Bernoulli beams. Different types of FG distributions of wavy CNTs along the radial direction of the cylinder are herein considered, and temperature-dependent material properties are estimated via a micromechanical model, under the assumption of uniform distribution within the shell and through the thickness. A parametric investigation based on the Generalized Differential Quadrature (GDQ) method aims at investigating the effects of the aspect ratio and waviness index of CNTs on the thermal buckling of FG nanocomposite stiffened cylinders, reinforced with wavy single-walled CNTs. Some numerical examples are here provided in order to verify the accuracy of the proposed formulation and to investigate the effects of several parameters—including the volume fraction, the distribution pattern of wavy CNTs, and the cylinder thickness—on the thermal buckling behavior of the stiffened cylinders made of CNT-reinforced composite (CNTRC) material. Full article
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