• Steel and Composite Structures
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• 제44권4호
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• pp.451-471
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• 2022

In the present paper, the static bending and buckling responses of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) beam under various boundary conditions are investigated within the framework of higher shear deformation theory. The significant feature of the proposed theory is that it provides an accurate parabolic distribution of transverse shear stress through the thickness satisfying the traction-free boundary conditions needless of any shear correction factor. Uniform (UD) and four graded distributions of CNTs which are FG-O, FG-X, FG- and FG-V are selected here for the analysis. The effective material properties of FG-CNTRC beams are estimated according to the rule of mixture. To model the FG-CNTRC beam realistically, an efficient Hermite-Lagrangian finite element formulation is successfully developed. The accuracy and efficiency of the present model are demonstrated by comparison with published benchmark results. Moreover, comprehensive numerical results are presented and discussed in detail to investigate the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, and length-to-thickness ratio on the bending and buckling responses of FG-CNTRC beam. Several new referential results are also reported for the first time which will serve as a benchmark for future studies in a similar direction. It is concluded that the FG-X-CNTRC beam is the strongest beam that carries the lowest central deflection and is followed by the UD, V, Λ, and FG-O-CNTRC beam. Besides, the critical buckling load belonging to the FG-X-CNTRC beam is the highest, followed by UD and FG-O.

• Structural Engineering and Mechanics
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• 제82권6호
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• pp.691-699
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• 2022

This paper is devoted to the presentation of a numerical study on vibration behavior of composite panels reinforced by glass fibres and carbon nanotubes (CNTs) subjected to thermal environments. The effect of temperature variation has been included as thermal load acting on in-plane direction of the panel. To model the composite material, a micromechanical model which contains random dispersion of nanotubes and single-direction fibers has been selected. The geometry of the panel has been considered to have a single curveture along its width. Based on the above assumptions, the governing equations have been derived by using thin shell theory capturing the panel curveture and also nonlinear deflections. Finally, the panel dependence on various factors such as the curveture, nanotube amount, fiber volume, fiber direction and temperature variation has been researched.

• Steel and Composite Structures
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• 제22권3호
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• pp.691-712
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• 2016

In this editorial, buckling analytical investigation of the nanocomposite plate with square cut out reinforced by carbon nanotubes (CNTs) surrounded by Pasternak foundation is considered. The plate is presumed has square cut out in center and resting on Pasternak foundation. CNTs are used as amplifier in plate for diverse distribution, such as uniform distribution (UD) and three patterns of functionally graded (FG) distribution types of CNTs (FG-X, FG-A and FG-O). Moreover, the effective mechanical properties of nanocomposite plate are calculated from the rule of mixture. Domain decomposition method and orthogonal polynomials are applied in order to define the shape function of nanocomposite plate with square cut out. Finally, Rayleigh-Ritz energy method is used to obtain critical buckling load of system. A detailed parametric study is conducted to explicit the effects of the dimensions of plate, length of square cut out, different distribution of CNTs, elastic medium and volume fraction of CNTs. It is found from results that increase the dimensions of plate and length of square cut out have negative impact on buckling behavior of system but considering CNTs in plate has positive influence.

• Steel and Composite Structures
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• 제48권4호
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• pp.419-428
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• 2023

In this paper, dynamic and static bending of ball modelled by nanocomposite microbeam by nanoparticles seeing agglomeration is presented. The structural damping is considered by Kelvin-Voigt model. The agglomeration effects are assumed using Mori-Tanaka model. The football ball is modeled by third order shear deformation theory (TSDT). The motion equations are derived by principle of Hamilton's and energy method assuming size effects on the basis of Eringen theory. Using differential quadrature method (DQM) and Newmark method, the static and dynamic deflections of the structure are obtained. The effects of agglomeration and CNTs volume percent, damping of structure, nonlocal parameter, length and thickness of micro-beam are presented on the static and dynamic deflections of the nanocomposite structure. Results show that with increasing CNTs volume percent, the maximum dimensionless dynamic deflection is reduced about 17%. In addition, assuming CNTs agglomeration increases the dimensionless dynamic deflection about 14%. It is also found that with increasing the CNTs volume percent from 0 to 0.15, the static deflection is decreased about 3 times due to the enhance in the stiffness of the structure. In addition, with enhancing the nonlocal parameters, the dynamic deflection is increased about 3.1 times.

• Advances in nano research
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• 제16권5호
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• pp.445-458
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• 2024

The objective of this paper is to present free vibration and static stability analyses of rotating composite beams reinforced with carbon nanotubes (CNTs) under uniform thermal loads. Beam structural equations and CNT-reinforced composite (CNTRC) beam formulations are derived based on Timoshenko beam theory (TBT). The temperature-dependent properties of the beam material, such as the elastic modulus, shear modulus, and material density, are assumed to vary over the thickness according to the rule of mixture. The beam material is modeled as a mixture of single-walled carbon nanotubes (SWCNTs) in an isotropic matrix. The SWCNTs are aligned and distributed in the isotropic matrix with different patterns of reinforcement, namely the UD (uniform), FG-O, FG-V, FG- Λ and FG-X distributions, where FG-V and FG- Λ are asymmetric patterns. Numerical examples are presented to illustrate the effects of several essential parameters, including the rotational speed, hub radius, effective material properties, slenderness ratio, boundary conditions, thermal force, and moments due to temperature variation. To the best of the authors' knowledge, this study represents the first attempt at the finite element modeling of rotating CNTRC Timoshenko beams under a thermal environment. The results are presented in tables and figures for both symmetric and asymmetric distribution patterns, and can be used as benchmarks for further validation.

• 한국안전학회지
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• 제32권6호
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• pp.9-15
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• 2017

Recently many researches were conducted on the interlaminar fracture that is a delamination between laminates by using ASTM standardized methods. However the experiment of the intralaminar a fracture is difficulty. In this study, four types of CFRP/GFRP composites with different layer structures were compared to evaluate an intralaminar fracture toughness under the mode I. Also the CNTs were added to the layer for the examination of the fracture toughness improvement. And the characteristics of the crack propagation behaviour was observed using a microscope. The obtained results can be useful for the evaluation of the intralaminar fracture toughness of the CNT reinforced CFRP/GFRP composites.

• Steel and Composite Structures
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• 제38권3호
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• pp.293-304
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• 2021

The aim of this paper is to analyze the nonlinear bending of functionally graded (FG) curved nanobeams reinforced by carbon nanotubes (CNTs) in thermal environment. Chen-Yao's surface elastic theory and geometric nonlinearity are also considered. The nanobeams are subjected to uniform loadings and placed on three-parameter substrates. The Euler-Lagrange equations are employed to deduce the equations of equilibrium. Then, the asymptotic solutions and boundary value problems are analytically determined by utilizing the two-step perturbation technique. Finally, the effects of the surface parameters, geometric factors, foundation stiffness, volume fraction, thermal effects and layout type of CNTs on the nonlinear bending of the nanobeams are discussed.

• Advances in nano research
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• 제5권2호
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• pp.69-97
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• 2017

In this study, nonlinear response of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate under low-velocity impact based on the Eshelby-Mori-Tanaka approach in thermal conditions is studied. The governing equations are derived based on higher-order shear deformation plate theory (HSDT) under von $K\acute{a}rm\acute{a}n$ geometrical nonlinearity assumptions. The finite element method with 15 DOF at each node and Newmark's numerical integration method is applied to solve the governing equations. Four types of distributions of the uniaxially aligned reinforcement material through the thickness of the plates are considered. Material properties of the CNT and matrix are assumed to be temperature dependent. Contact force between the impactor and the laminated plate is obtained with the aid of the modified nonlinear Hertzian contact law models. In the numerical example, the effect of layup (stacking sequence) and lamination angle as well as the effect of temperature variations, distribution of CNTs, volume fraction of the CNTs, the mass and the velocity of the impactor in a constant energy level and boundary conditions on the impact response of the CNTRC laminated plates are investigated in details.

• Structural Engineering and Mechanics
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• 제70권6호
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• pp.683-702
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• 2019

The present study aims to analyze the magneto-electro-elastic (MEE) vibration of a functionally graded carbon nanotubes reinforced composites (FG-CNTRC) cylindrical shell. Electro-magnetic loads are applied to the structure and it is located on an elastic foundation which is simulated by visco-Pasternak type. The properties of the nano-composite shell are assumed to be varied by temperature changes. The third-order shear deformation shells theory is used to describe the displacement components and Hamilton's principle is employed to derive the motion differential equations. To obtain the results, Navier's method is used as an analytical solution for simply supported boundary condition and the effect of different parameters such as temperature variations, orientation angle, volume fraction of CNTs, different types of elastic foundation and other prominent parameters on the natural frequencies of the structure are considered and discussed in details. Design more functional structures subjected to multi-physical fields is of applications of this study results.

• Advances in nano research
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• 제12권2호
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• pp.117-137
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• 2022

Effect of thickness stretching on free vibration, bending and buckling behavior of carbon nanotubes reinforced composite (CNTRC) laminated nanoplates rested on new variable elastic foundation is investigated in this paper using a developed four-unknown quasi-3D higher-order shear deformation theory (HSDT). The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Two new forms of CNTs reinforcement distribution are proposed and analyzed based on cosine functions. By considering the higher-order nonlocal strain gradient theory, microstructure and length scale influences are included. Variational method is developed to derive the governing equation and Galerkin method is employed to derive an analytical solution of governing equilibrium equations. Two-dimensional variable Winkler elastic foundation is suggested in this study for the first time. A parametric study is executed to determine the impact of the reinforcement patterns, nonlocal parameter, length scale parameter, side-t-thickness ratio and aspect ratio, elastic foundation and various boundary conditions on bending, buckling and free vibration responses of the CNTRC plate.