• Steel and Composite Structures
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• v.44 no.5
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• pp.707-720
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• 2022

In the present work, bending and free vibration analyses of multilayered functionally graded (FG) graphene platelet (GPL) and fiber-reinforced hybrid composite beams are carried out using the parabolic function based shear deformation theory. Parabolic variation of transverse shear stress across the thickness of beam and transverse shear stress-free conditions at top and bottom surfaces of the beam are considered, and the proposed formulation incorporates a transverse displacement field. The present theory works only with four unknowns and is computationally efficient. Hamilton's principle has been employed for deriving the governing equations. Analytical solutions are obtained for both the bending and free vibration problems in the present work considering different variations of GPLs and fibers distribution, namely, FG-X, FG-U, FG-Λ, and FG-O for beams having simply-supported boundary condition. First, the matrix is assumed to be strengthened using GPLs, and then the fibers are embedded. Multiscale modeling for material properties of functionally graded graphene platelet/fiber hybrid composites (FG-GPL/FHRC) is performed using Halpin-Tsai micromechanical model. The study reveals that the distributions of GPLs and fibers have significant impacts on the stresses, deflections, and natural frequencies of the beam. The number of layers and shape factors widely affect the behavior of FG-GPL-FHRC beams. The multilayered FG-GPL-FHRC beams turn out to be a good approximation to the FG beams without exhibiting the stress-channeling effects.

• Steel and Composite Structures
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• v.38 no.1
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• pp.47-66
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• 2021

This work addresses the free vibration analysis of Functionally Graded Porous (FGP) nanocomposite truncated conical shells with Graphene PLatelet (GPL) reinforcement. In this study, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the direction of the shell thickness. The Halpin-Tsai equations are used to find the effective material properties of the graphene platelet reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders's theory. The Fourier Differential Quadrature (FDQ) technique is implemented to solve the governing equations of the problem and to obtain the natural frequencies of the truncated conical shell. The combination of FDQ with higher-order shear deformation theory allows a very accurate prediction of the natural frequencies. The precision and reliability of the proposed method are verified by the results of literature. Moreover, a wide parametric study concerning the effect of some influential parameters, such as the geometrical parameters, porosity distribution, circumferential wave numbers, GPLs dispersion as well as boundary restraint conditions on free vibration response of FGP-GPL truncated conical shell is also carried out and investigated in detail.

• Advances in Computational Design
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• v.5 no.2
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• pp.177-193
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• 2020

In the present research, dynamic analysis of functionally graded (FG) graphene-reinforced beams under thermal loading has been carried out based on finite element approach. The presented formulation is based on a higher order refined beam element accounting for shear deformations. The graphene-reinforced beam is exposed to transverse periodic mechanical loading. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. Convergences and validation studies of derived results from finite element approach are also presented. This research shows that the resonance behavior of a nanocomposite beam can be controlled by the GPL content and dispersions. Therefore, it is showed that the dynamical deflections are notably influenced by GPL weight fractions, types of GPL distributions, temperature changes, elastic foundation and harmonic load excitation frequency.

• Steel and Composite Structures
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• v.46 no.5
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• pp.659-667
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• 2023

Nonlinear forced vibration behaviors of sandwich plates having graphene platelets (GPL) based face sheets have been researched in this article. Possessing low weight together with low stiffness, square honeycomb cores are mostly constructed by aluminum. Herein, the square shaped core has been fortified by two skins of GPL-based type in such a way that the skins have uniform and linearly graded GPL dispersions. The square shaped core has the effective material specification according to the relative density concept. The whole formulation has been represented based upon classical plate theory (CPT) while harmonic balance approach is applied for solving the problem and plotting the amplitude-frequency curves. The forced vibration behaviors of such plates are influenced by square-shaped core and the relative density, skin's height and GPL fortification.

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.357-370
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• 2024

Due to the fact that the mechanism of the effects of temperature and initial geometric imperfection on low-velocity impact problem of axially moving plates is not yet clear, the present paper is to fill the gap. In the present paper, the nonlinear dynamic behavior of axially moving imperfect graphene platelet reinforced metal foams (GPLRMF) plates subjected to lowvelocity impact in thermal environment is analyzed. The equivalent physical parameters of GPLRMF plates are estimated based on the Halpin-Tsai equation and the mixing rule. Combining Kirchhoff plate theory and the modified nonlinear Hertz contact theory, the nonlinear governing equations of GPLRMF plates are derived. Under the condition of simply supported boundary, the nonlinear control equation is discretized with the help of Gallekin method. The correctness of the proposed model is verified by comparison with the existing results. Finally, the time history curves of contact force and transverse center displacement are obtained by using the fourth order Runge-Kutta method. Through detailed parameter research, the effects of graphene platelet (GPL) distribution mode, foam distribution mode, GPL weight fraction, foam coefficient, axial moving speed, prestressing force, temperature changes, damping coefficient, initial geometric defect, radius and initial velocity of the impactor on the nonlinear impact problem are explored. The results indicate that temperature changes and initial geometric imperfections have significant impacts.

• Steel and Composite Structures
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• v.43 no.6
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• pp.725-734
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• 2022

In this paper, buckling analyses of nanocomposite plate reinforced by Graphen platelet (GPL) is studied. The Halphin-Tsai model is used for obtaining the effective material properties of nanocomposite plate. The nanocomposite plate is modeled by Third order shear deformation theory (TSDT). The elastic medium is simulated by Winkler model. Employing relations of strains-displacements and stress-strain, the energy equations of the plate are obtained and using Hamilton's principle, the governing equations are derived. The governing equations are solved based on analytical solution. The effect of GPL volume percent, geometrical parameters of plate and elastic foundation on the buckling load are investigated. Results show that with increasing GPLs volume percent, the buckling load increases. In addition, elastic medium can enhance the values of buckling load significantly.

• Structural Engineering and Mechanics
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• v.71 no.1
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• pp.99-107
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• 2019

Wave propagation analysis of a porous graphene platelet reinforced (GPLR) nanocomposite shell is investigated for the first time. The homogenization of the utilized material is procured by extending the Halpin-Tsai relations for the porous nanocomposite. Both symmetric and asymmetric porosity distributions are regarded in this analysis. The equations of the shell's motion are derived according to Hamilton's principle coupled with the kinematic relations of the first-order shear deformation theory of the shells. The obtained governing equations are considered to be solved via an analytical solution which includes two longitudinal and circumferential wave numbers. The accuracy of the presented formulations is examined by comparing the results of this method with those reported by former authors. The simulations reveal a stiffness decrease in the cases which porosity influences are regarded. Also, one must pay attention to the effects of longitudinal wave number on the wave dispersion curves of the nanocomposite structure.

• Advances in nano research
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• v.15 no.4
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• pp.367-384
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• 2023

Natural frequency behavior of graphene platelets reinforced composite (GPL-RC) joined truncated conical-cylindrical- conical shells resting on Winkler-type elastic foundation is presented in this paper for the first time. The rule of mixture and the modified Halpin-Tsai approach are applied to achieve the mechanical properties of the structure. Four different graphene platelets patterns are considered along the thickness of the structure such as GPLA, GPLO, GPLX, GPLUD. Finite element procedure according to Rayleigh-Ritz formulation has been used to solve 2D-axisymmetric elasticity equations. Application of 2D axisymmetric elasticity theory allows thickness stretching unlike simple shell theories, and this gives more accurate results, especially for thick shells. An efficient parametric investigation is also presented to show the effects of various geometric variables, three different boundary conditions, stiffness of elastic foundation, dispersion pattern and weight fraction of GPLs nanofillers on the natural frequencies of the joined shell. Results show that GPLO and BC3 provide the most rigidity that cause the most natural frequencies among different BCs and GPL patterns. Also, by increasing the weigh fraction of nanofillers, the natural frequencies will increase up to 200%.

• Advances in nano research
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• v.16 no.1
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• pp.11-26
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• 2024

In this study, free vibration analysis of FG porous spherical cap reinforced by graphene platelets resting on Winkler-type elastic foundation has been surveyed for the first time. Three different types of porosity patterns are considered for the spherical cap whose two types of porosity patterns in the metal matrix are symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in the metal matrix. Tsai-Halpin and extended rule of the mixture are used to determine the Young modulus and mass density of the shell, respectively. Employing 3D FEM elasticity in conjunction with Hamilton's Principle, the governing motion equations of the structure are obtained and solved. The impact of various parameters including porosity coefficient, various porosity distributions in conjunction with different GPL patterns, the weight fraction of graphene Nano fillers, polar angles and stiffness coefficient of elastic foundation on natural frequencies of FG porous spherical cap reinforced by GPLs have been reported for the first time.

• Geomechanics and Engineering
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• v.28 no.5
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• pp.477-491
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• 2022

In the present study, the effects of thermal loading on the buckling and resonance frequency of graphene platelets (GPL) reinforced nano-composites are examined. Functionally graded (FG) material properties are considered in thickness direction for the thermal responses of the composite. The equivalent material properties are obtained using Halphin-Tsai nano-mechanical model for composite layers. Moreover, the effects of nano-scale sizes are taken into account, employing functionally modified couple stress (FMCS) parameter. In this regard, for the first time, it is demonstrated that at certain values of GPL weight fraction, thermal buckling occurs. In obtaining results of vibrational behavior, both analytical solution and deep neural network (DNN) methods are used. The DNN method needs low computational costs to predict the resonance behavior. A comprehensive parametric study is conducted to indicate the effects of several geometrical, material, and loading conditions on the vibrational and buckling behavior of cylindrical shell structures made of GPL-nanocomposites. It is shown that the effect of temperature change on the occurrence of buckling is vital while it has a negligible impact on the resonance frequency of the structure. Moreover, the size-dependency of the results is demonstrated, and it cannot be neglected in nano-scales.