• Advances in nano research
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• v.15 no.2
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• pp.141-153
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• 2023

The main objective of this paper is to develop the finite element study on the nonlinear free vibration of functionally graded nanocomposite spherical shells reinforced with graphene platelets under the first-order shear deformation shell theory and von Kármán nonlinear kinematic relations. The governing equations are presented by introducing the full asymmetric nonlinear strain-displacement relations followed by the constitutive relations and energy functional. The extended Halpin-Tsai model is utilized to specify the overall Young's modulus of the nanocomposite. Then, the finite element formulation is derived and the quadrilateral 8-node shell element is implemented for finite element discretization. The nonlinear sets of dynamic equations are solved by the use of the harmonic balance technique and iterative method to find the nonlinear frequency response. Several numerical examples are represented to highlight the impact of involved factors on the large-amplitude vibration responses of nanocomposite spherical shells. One of the main findings is that for some geometrical and material parameters, the fundamental vibrational mode shape is asymmetric and the axisymmetric formulation cannot be appropriately employed to model the nonlinear dynamic behavior of nanocomposite spherical shells.

• Advances in environmental research
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• v.4 no.2
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• pp.69-81
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• 2015

A new magnetite-silica core/shell nanocomposite ($Fe_3O4@nSiO_2@mSiO_2$) was synthesized and functionalized with trimethylchlorosilane (TMCS). The prepared nanocomposite was used for the removal of diesel oil from aqueous media. The characterization of magnetite-silica nanocomposite was studied by X-ray diffraction (XRD), Fourier transform infrared (FTIR), transmission electron microscopy (TEM), surface area measurement, and vibrating sample magnetization (VSM). Results have shown that the desired structure was obtained and surface modification was successfully carried out. FTIR analysis has confirmed the presence of TMCS on the surface of magnetite silica nanocomposites. The low- angle XRD pattern of nanocomposites indicated the mesoscopic structure of silica shell. Furthermore, TEM results have shown the core/shell structure with porous silica shell. Adsorption kinetic studies indicated that the nanocomposite was able to remove 80% of the oil contaminant during 2 h and fit well with the pseudo-second order model. Equilibrium studies at room temperature showed that the experimental data fitted well with Freundlich isotherm. The magnetic property of nanocomposite facilitated the separation of solid phase from aqueous solution.

• Steel and Composite Structures
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• v.36 no.6
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• pp.711-727
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• 2020

In the present research, the free vibration analysis of functionally graded (FG) nanocomposite deep spherical shells reinforced by graphene platelets (GPLs) on elastic foundation is performed. The elastic foundation is assumed to be Winkler-Past ernak-type. It is also assumed that graphaene platelets are randomly oriented and uniformly dispersed in each layer of the nanocomposite shell. Volume fraction of the graphene platelets as nanofillers may be different in the layers. The modified HalpinTsai model is used to approximate the effective mechanical properties of the multilayer nanocomposite. With the aid of the first order shear deformation shell theory and implementing Hamilton's principle, motion equations are derived. Afterwards, the generalized differential quadrature method (GDQM) is utilized to study the free vibration characteristics of FG-GPLRC spherical shell. To assess the validity and accuracy of the presented method, the results are compared with the available researches. Finally, the natural frequencies and corresponding mode shapes are provided for different boundary conditions, GPLs volume fraction, types of functionally graded, elastic foundation coefficients, opening angles of shell, and thickness-to-radius ratio.

• Structural Engineering and Mechanics
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• v.74 no.5
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• pp.679-698
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• 2020

In this paper, the meshless local Petrov-Galerkin (MLPG) method is developed for dynamic analysis of non-symmetric nanocomposite cylindrical shell equations of elastic wave motion with nonlinear grading patterns under shock loading. The mechanical properties of the nanocomposite cylinder are obtained based on a micro-mechanical model. In this study, four kinds of grading patterns are assumed for carbon nanotube mechanical properties. The displacements can be approximated using shape function so, the multiquadrics (MQ) Radial Basis Functions (RBF) are used as the shape function. In order to discretize the derived equations in time domains, the Newmark time approximation scheme with suitable time step is used. To demonstrate the accuracy of the present method for dynamic analysis, at the first a problem verifies with analytical solution and then the present method compares with the finite element method (FEM), finally, the present method verifies by using the element free Galerkin (EFG) method. The comparison shows the high capacity and accuracy of the present method in the dynamic analysis of cylindrical shells. The capability of the present method to dynamic analysis of non-symmetric nanocomposite cylindrical shell is demonstrated by dynamic analysis of the cylinder with different kinds of grading patterns and angle of nanocomposite reinforcements. The present method shows high accuracy, efficiency and capability to dynamic analysis of non-symmetric nanocomposite cylindrical shell, which it furnishes a ground for a more flexible design.

• 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.

• Journal of Sensor Science and Technology
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• v.28 no.4
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• pp.225-230
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• 2019

$Au@TiO_2$ core-shell decorated rGO nanocomposite (NC) was prepared using a simple solvothermal method followed by heat treatment for gas sensor application. The crystal structure and morphology of the composites were characterized by X-ray powder diffraction and transmission electron microscopy, respectively. The $NO_2$ sensing response of the $Au@TiO_2/rGO$ NC was tested at operating temperatures from $250^{\circ}C$ to $500^{\circ}C$, and was compared with those of the bare rGO and $Au@TiO_2$ core-shell NPs. The $Au@TiO_2/rGO$ NC-based sensor showed a far higher response than the rGO or $Au@TiO_2$ core-shell based sensors, with the maximum response detected when the operating temperature was $400^{\circ}C$. This improved response was due to the high rGO gas absorption capability for $NO_2$ gas and the catalytic effect of $Au@TiO_2$ core-shell NPs in oxidizing $NO_2$ to $NO_3$.

• Steel and Composite Structures
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• v.46 no.5
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• pp.611-619
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• 2023

In the present work, the flutter characteristics of porous nanocomposite cylindrical shells, reinforced with graphene platelets (GPLs) in supersonic airflow, have been investigated. Different distributions for GPLs and porosities have been considered which are named uniform and non-uniform distributions thorough the shell's thickness. The effective material properties have been determined via Halpin-Tsai micromechanical model. The cylindrical shell formulation considering supersonic airflow has been developed in the context of first-order shell and first-order piston theories. The governing equations have been solved using Galerkin's method to find the frequency-pressure plots. It will be seen that the flutter points of the shell are dependent on the both amount and distribution of porosities and GPLs and also shell geometrical parameters.

• Structural Engineering and Mechanics
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• v.86 no.2
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• pp.157-165
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• 2023

In the present work, the vibration characteristics of sandwich nanocomposite shells, fortified with graphene platelets (GPLs) have been researched. The shell has been considered as the stadium roof shape with double curvatures under vibration due to earthquake. The nanocomposite has the matrix of concrete which is fortified with uniform or linear dispersions of GPLs. Also, the core possesses cellular type square architecture for which the effective elastic modulus has been defined in the context of relative density based relations. Based upon the classic shell strains containing two identical curvatures, the governing equations have been established and solved through differential quadrature approach. It will be seen that the vibrational frequencies rely on the core relative density, height of layers, the amount and dispersions of GPLs and even shell geometric parameters.

• Steel and Composite Structures
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• v.35 no.2
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• pp.249-260
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• 2020

The main purpose of this research work is to investigate the free vibration of conical shell structures reinforced by graphene platelets (GPLs) and the elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. To this end, a shell model is developed based on Donnell's theory. To solve the problem, the analytical Galerkin method is employed together with beam mode shapes as weighting functions. Due to importance of boundary conditions upon mechanical behavior of nanostructures, the analysis is carried out for different boundary conditions. The effects of boundary conditions, semi vertex angle, porosity distribution and graphene platelets on the response of conical shell structures are explored. The correctness of the obtained results is checked via comparing with existing data in the literature and good agreement is eventuated. The effectiveness and the accuracy of the present approach have been demonstrated and it is shown that the Donnell's shell theory is efficient, robust and accurate in terms of nanocomposite problems.

• Structural Engineering and Mechanics
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• v.91 no.3
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• pp.325-334
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• 2024

This paper deals with the dynamic buckling behavior of truncated conical shells composed of carbon nanotube composites, an important area of study in view of their very wide engineering applications in aerospace industries. In this regard, the effective material properties of the nanocomposite have been computed using the Mori-Tanaka model, which has already been established for such analyses. The motion equations ruling the structure's behavior are derived using first order shear deformation theory, Hamilton's principle, and energy method. This will provide adequate background information on its dynamic response. In an effort to probe the dynamic instability region of the structure, differential quadrature method combined with Bolotin's method will be adopted to tackle the resulting motion equations, which enables efficient and accurate analysis. This work considers the effect of various parameters in the geometrical parameters and the volume fraction of CNTs on the structure's DIR. Specifically, it became clear that increasing the volume fraction of CNTs shifted the frequency range of the DIR to higher values, indicating the significant role of nanocomposite composition regarding structure stability.