Carbon Nanotube-reinforced Composites Research Articles

Nonlinear forced vibration of sandwich cylindrical panel with negative Poisson’s ratio auxetic honeycombs core and CNTRC face sheets

Recently, auxetic cellular solids in the forms of honeycombs and carbon nanotube reinforced composite (CNTRC) have great potential in a diverse range of applications. This paper studies the nonlinear free and forced vibration of sandwich cylindrical panel on visco-Pasternak foundations in thermal environment subjected to blast load The sandwich cylindrical panel consists of auxetic honeycombs core layer and two CNTRC face sheets. The Poisson’ ratio of the auxetic core is negative and the material properties of CNTRC face sheets are assumed to continuously vary in the thickness direction according to four different types of linear functions. The blast load is determined from the distance of the center of blast to center of the structure and the mass of explosive materials. The fundamental equations are established based on Reddy’s higher order shear deformation shell theory taking into account the effect of initial imperfection and visco-Pasternak foundations. The Galerkin and Runge–Kutta methods are used to obtain the nonlinear dynamic response and the natural frequency of the sandwich cylindrical panel. The numerical results show the effect of geometrical parameters, visco foundations, initial imperfection, temperature increment, nanotube volume fraction and blast load on the nonlinear vibration characteristics of the sandwich cylindrical panel. The accuracy of present approach and theoretical results is verified by some comparisons with the known data in the literature.

Finite element model for carbon nanotube-reinforced and graphene nanoplatelet-reinforced composite beams

This paper investigates bending, vibration and buckling analysis of carbon nanotube-reinforced composite (CNTRC) and graphene nanoplatelet-reinforced composite (GPLRC) beams. Both normal and shear effects are included in the formulation of the governing equations of motion of the beams. Finite element model is employed to determine displacements, critical buckling loads and natural frequencies of the beams with different boundary conditions. Several important factors in parametric studies including distribution pattern, volume fraction of CNTs, GPL weight fraction, slenderness ratio, boundary condition, etc. are investigated. Some new results are given as benchmark for further validation.

A novel nonlocal higher-order strain gradient shell theory for static analysis of CNTRC doubly-curved nanoshells subjected to thermo-mechanical loading

Up to now, no researches have been yet presented to investigate the static analysis of the carbon nanotube reinforced composite (CNTRC) doubly-curved nanoshells with considering the effect of thickness stretching in thermal environment. In this paper, deflection analysis of the CNTRC doubly-curved nanoshells subjected to thermo-mechanical loading based on nonlocal strain gradient theory is investigated. The temperature variation vary through the thickness linearly. Five different types of distributions of CNTRC including UD, FGX, FGV, FGO and FGA are considered to investigate their effects on the mechanical behavior of the doubly-curved nanoshells. All of the mechanical properties of the nanoshell are considered as temperature dependent. Hamilton’s principle is applied to derive the governing equations of motion, where Navier method is used to obtain the deflection of the nanoshells with simply-supported boundary conditions. The obtained results demonstrate that the effect of thickness stretching has vital role on the deflection of the CNTRC doubly-curved nanoshells.

Assessment of negative Poisson’s ratio effect on the postbuckling of pressure-loaded FG-CNTRC laminated cylindrical shells

This paper examines the postbuckling behaviors of pressure-loaded laminated cylindrical shells made of carbon nanotube reinforced composite (CNTRC) under thermal environmental conditions. The shell has negative in-plane or out-of-plane effective Poisson’s ratio (EPR). The thermo-mechanical properties of CNTRCs are temperature dependent. The CNT volume fraction of the shell is in a piece-wise functionally graded (FG) distribution across the shell thickness. The extended rule of mixture (EROM) model is applied to determine the thermo-mechanical properties of CNTRCs. Based on the framework of the Reddy's third order shear deformation shell theory and the von Kármán-type of kinematic assumptions, the governing partial differential equations for pressure-loaded CNTRC laminated cylindrical shells are formulated. The thermal environmental condition effect is also included. The postbuckling solution for pressure-loaded FG-CNTRC laminated cylindrical shell is obtained in the asymptotic sense by means of a singular perturbation technique in associate with a two-step perturbation approach. Numerical investigations are carried out for the (10/60/10)S shell including in-plane NPR effect, and (20/-20/20)S and (70/-70/70)S shells including out-of-plane NPR effect. Assessment is presented through numerical comparisons.

Vibration analysis of carbon nanotube‐reinforced composite microbeams

In the present article, free vibration behavior of carbon nanotube‐reinforced composite (CNTRC) microbeams is investigated. Carbon nanotubes (CNTs) are distributed in a polymeric matrix with four different patterns of the reinforcement. The material properties of the CNTRC microbeams are predicted by using the rule of mixture. The microstructure‐dependent governing differential equations are derived by applying Hamilton's principle on the basis of couple stress theory and several beam theories. The obtained vibration equation is solved by using Navier's solution method. The effects of length scale parameter, length/thickness ratio, volume fraction and the reinforcement pattern of CNTs on frequencies are examined. It is observed that the biggest frequencies occur in X‐Beam while O‐Beam has the lowest ones. It is also found that the size effect is more prominent when the thickness of the beam is close to the length scale parameter and this effect nearly disappears as the thickness of the beam increases.

Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam

This work focused on the novel numerical tool for the bending responses of carbon nanotube reinforced composites (CNTRC) beams. The higher order shear deformation beam theory (HSDT) is used to determine strain-displacement relationships. A new exponential function was introduced into the carbon nanotube (CNT) volume fraction equation to show the effect of the CNT distribution on the CNTRC beams through displacements and stresses. To determine the mechanical properties of CNTRCs, the rule of the mixture was employed by assuming that the single-walled carbon nanotubes (SWCNTs)are aligned and distributed in the matrix. The governing equations were derived by Hamilton's principle, and the mathematical models presented in this work are numerically provided to verify the accuracy of the present theory. The effects of aspect ratio (l/d), CNT volume fraction (Vcnt), and the order of exponent (n) on the displacement and stresses are presented and discussed in detail. Based on the analytical results. It turns out that the increase of the exponent degree (n) makes the X-beam stiffer and the exponential CNTs distribution plays an indispensable role to improve the mechanical properties of the CNTRC beams.

On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations

This paper introduces a comprehensive buckling response of cross-ply orientation of carbon nanotube reinforced composite (CNTRC) multilayered nanobeams with different boundary conditions. The nonlocal strain gradient (NLSG) stress-strain governing relations are utilized to include the size-dependence and microstructure effects. Novel hyperbolic higher shear deformation beam theory including thickness stretching effect is used to fulfill both parabolic shear distribution through the thickness and the zero-shear at free boundaries. Parametric studies are performed to inspect the influences of arrangement of reinforcement material distributions functions, different functionally graded (FG) functions, and uniform distribution (UD). The balance equilibrium equations are derived, and Fourier functions are utilized to obtain the critical buckling loads of nanobeam under mechanical loadings. Mechanical properties are assumed to be temperature-dependent by using Touloukian principal. An exact solution is performed satisfying the edge boundary conditions. A detailed numerical analysis is illustrated to examine the impact of CNTs patterns, lamination, side-to-thickness, aspect ratios, microstructure and size scale parameters on critical buckling loads of CNTRC laminated nanobeams.

Free vibration analysis of rotating pre-twisted ceramic matrix carbon nanotubes reinforced blades

A novel dynamic model for rotating pre-twisted carbon nanotubes reinforced composite (CNTRC) blades with elastic boundary constraints is established based on the first-order shear deformation theory (FSDT). The effects of Coriolis and centrifugal forces are considered in the formulation. Based on the Euler-Lagrange equations, the natural frequencies and vibration modes of a rotating pre-twisted blade are obtained. The model’s accuracy is verified by comparing it with the results in the literature and Ansys. The influence of distributions of CNTs, pre-twist angle, rotation speed, and stagger angle on the vibration of the ceramic matrix CNTRC blade is studied in detail.

A Comparison of Nonlinear Bending and Vibration of Hybrid Metal/CNTRC Laminated Beams with Positive and Negative Poisson’s Ratios

Carbon nanotube reinforced composite (CNTRC) is one of the novel classes of advanced composite materials. This paper investigates the nonlinear bending and nonlinear vibration responses of hybrid laminated beams made of CNTRC layers bonded with metal layers on the top and bottom surfaces. We proposed a hybrid metal/CNTRC laminated beam for which out-of-plane Poisson’s ratio is negative. The effective material properties of CNTRC layers are graded in a piece-wise pattern across the thickness of the beam. The material properties of both CNTRC layer and metal layer are temperature dependent. The beams are rested on an elastic foundation and are located in thermal environments. Reddy’s higher-order beam model is used to establish the motion equations of the hybrid metal/CNTRC laminated beam. The motion equations include the von Kármán geometric nonlinearity, the thermal effects and the beam-foundation interaction. By employing a two-step perturbation approach, the bending and nonlinear vibration solutions are obtained. A comparison of nonlinear responses of hybrid metal/CNTRCl laminated beams with positive and negative Poisson’s ratios (NPRs) under different thermal environmental conditions is carried out and discussed in detail.

Thermal postbuckling analysis of FG-CNTRC doubly curved panels with elastically restrained edges using Reddy's higher order shear deformation theory

For the first time, postbuckling behavior of thick doubly curved panels made of carbon nanotube reinforced composite (CNTRC), under preexisting external pressure and subjected to uniform temperature rise is analyzed in this paper. Carbon nanotubes (CNTs) are reinforced into matrix through functionally graded (FG) distribution patterns, and effective properties of CNTRC are determined according to extended rule of mixture. Formulations are based on a higher order shear deformation theory including Von Karman-Donnell nonlinearity, initial geometrical imperfection and elasticity of tangential constraints of boundary edges. Analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is used to obtain nonlinear load-deflection relation. Taking into account temperature dependence of material properties, postbuckling temperature-deflection paths are traced through an iteration process. The effects of preexisting external pressure, CNT volume fraction, tangential edge constraints, initial geometrical imperfection and curvature ratios on thermal postbuckling behavior of CNTRC doubly curved panels are analyzed through numerical examples. The study reveals that thermally loaded panels experiences a quasi-bifurcation response due to the presence of preexisting external pressure. For the most part, perfect panels are deflected toward convex side at the onset of undergoing thermal load. Particularly, imperfect panels may exhibit a bifurcation type buckling response when imperfection size satisfy a special condition.

The effect of negative Poisson’s ratio on the low-velocity impact response of an auxetic nanocomposite laminate beam

In this paper, an investigation on the low-velocity impact (LVI) response of a shear deformable beam laminated by carbon nanotube reinforced composite (CNTRC) layers is performed. The composite beam is “auxetic” due to the negative out-of-plane Poisson’s ratio (NPR) through special symmetric stacking sequences of layers that are designed based on the Classical Laminate Theory. To study the effect of the out-of-plane NPR on the LVI response of the composite beam, a newly defined Hertz model is developed. The motion equations of Karman type for the CNTRC laminate beam are derived in the framework of the Reddy beam theory and solved by means of a two-step perturbation approach while the dynamic equation of the impactor is built on Newton’s Law. Since temperature-dependent material properties of both carbon nanotube (CNT) and matrix are employed, the thermal influence on the LVI behavior is also investigated. Moreover, a piece-wise method is employed herein to investigate the effect of functionally graded (FG) patterns of the CNT reinforcements on the impact response. Numerical results elucidating the effects of temperature, FG distribution, and CNT volume fraction on the out-of-plane Poisson’s ratio and impact response of the beam are obtained by using a Range–Kutta method and discussed in details.

Non-linear stability analysis of CNT reinforced composite cylindrical shell panel subjected to thermomechanical loading

The present study explores the nonlinear stability characteristics of simply supported carbon nanotubes (CNTs) reinforced composite (CNTRC) cylindrical shell panel subjected to combined axial compressive loading and localized heating using semi-analytical approach. The thermomechanical properties of CNTRC panel are considered to be temperature-dependent and are evaluated using extended rule of mixture method. Higher order shear deformation theory and von Kármán type nonlinearity are employed to model the CNTRC cylindrical panel. Two types of localized heating profiles such as rectangular and circular are considered along with full heating. The pre-buckling stresses generated because of applied localized heating are determined using Airy’s stress function by satisfying the strain compatibility relations. The governing equations for stability problem of CNTRC panel are derived using variational principle incorporating the obtained pre-buckling stresses. The partial differential equations obtained are converted to a set of nonlinear algebraic equations by employing the Galerkin’s technique. The buckling temperature and nonlinear equilibrium paths are determined by solving the abovementioned equations using appropriate methods. The obtained results using present semi-analytical approach demonstrated the influence of various dispersion profiles of CNTs, CNT volume fraction and heating profiles on the buckling and post-buckling characteristics of CNTRC cylindrical shell panel subjected to thermomechanical loadings.

Parametric instability of functionally graded carbon nanotube-reinforced hybrid composite plates in thermal environments

This paper studies the parametric instability of hybrid nanocomposite plates under an arbitrary periodic load in thermal environments. The hybrid nanocomposite plate is a three-layer board. It has metal layers on both surfaces and one core reinforced with functionally graded (FG) carbon nanotubes (CNTs). The Galerkin method with a reduced eigenfunction transformation is applied to establish the governing equations of motion. According to the Bolotin method, a set of Mathieu-type differential equations is formed to determine dynamic instability regions and dynamic instability index (DII). The in-plane periodic stress is taken to be a combination of pulsating axial and bending stresses in the example problems. The effects of the layer thickness ratio, CNTs volume fraction, CNTs distribution type, temperature, bending stress, static and dynamic load on the dynamic instability of hybrid nanocomposite plates are investigated and discussed.

Theoretical solutions for auxetic laminated beam subjected to a sudden load

In the current work, the concept of auxetic structures design is introduced into carbon nanotube-reinforced composite (CNTRC) laminate. Larger values of negative Poisson’s ratio (NPR) of CNTRC laminate are obtained by setting the optimal orientation. Meanwhile, a theoretical model is presented for the nonlinear dynamic response of functionally graded (FG) CNTRC beam with NPR.Using Reddy’s higher order shear deformation plate theory with von Karman's strain–displacement relations, the motion equations are obtained A two-perturbation approach and the fourth-order Runge Kutta method are then used to obtain the time-deflection curve of the auxetic FG-CNTRC beam. The effects of factors such as the CNT distribution, thermal field and foundation stiffness on the dynamic characteristic of the auxetic FG-CNTRC beam are studied in details. Numerical results indicate that the thermal–mechanical behavior of FG-CNTRC beams might be significantly improved by determining a proper distribution of CNTs. Furthermore, the results show that the change of temperature and foundation stiffness have a significant effect on the dynamic characteristic of FG-CNTRC laminated beams with NPR.

Geometric Non-Linear Analysis of Auxetic Hybrid Laminated Beams Containing CNT Reinforced Composite Materials.

In the current work, a novel hybrid laminate with negative Poisson’s ratio (NPR) is developed by considering auxetic laminate which is composed of carbon nanotube-reinforced composite (CNTRC) and fiber-reinforced composite (FRC) materials. The maximum magnitude of out-of-plane NPR is identified in the case of (20 F/20 C/−20 C/20 C) S laminate as well. Meanwhile, a method for the geometric non-linear analysis of hybrid laminated beam with NPR including the non-linear bending, free, and forced vibrations is proposed. The beam deformation is modeled by combining higher-order shear-deformation theory (HSDT) and large deflection theory. Based on a two-step perturbation approach, the asymptotic solutions of the governing equations are obtained to capture the linear and non-linear frequencies and load-deflection curves. Moreover, a two-step perturbation methodology in conjunction with fourth-order Runge–Kutta method is employed to solve the forced-vibration problem. Several key factors, such as CNT distribution, variations in the elastic foundation, and thermal stress, are considered in the exhaustive analysis. Theoretical results for some particular cases are given to examine the geometric non-linearity behavior of hybrid beam with NPR as well as positive Poisson’s ratio (PPR).

Thermal effects on the free vibration of joined FG-CNTRC conical-conical shells

In this paper, the effects of temperature on free vibration of carbon nanotube reinforced composite (CNTRC) joined conical-conical shells are investigated. Carbon nanotubes (CNTs) are embedded across the thickness uniformly or functionally. Material properties of the shell are assumed to be functions of temperature. To study the free vibration of shells settled in thermal environments, it requires solving the static equations. Therefore, in order to derive these equations, first order shear deformation theory (FSDT) accompanied by von Kármán types of geometrical nonlinearity are employed in Hamilton's principle. Then, initial stress resultants due to equilibrium state, are extracted via linear membrane solution. Afterward, equations of motion are derived with regard to initial deformations and stresses. With considering the equations of motion for two cones together with boundary and continuity conditions, a set of governing equations is provided. To discretize the governing equations meridionally, generalized differential quadrature (GDQ) method is proposed. The results are primarily validated via comparing them with those of relevant researches in this field. Thereafter, some studies are carried out to exhibit the significant role of temperature variations, CNT distribution patterns, CNT volume fractions, cones' angles and boundary conditions on the free vibrational behaviors of joined conical shells. For the sake of preventing buckling occurrence during the present vibration analysis, critical buckling temperature Tcr is obtained by the procedure that the natural frequency takes zero value for the lowest temperature.

Combined analytical and numerical approach for auxetic FG-CNTRC plate subjected to a sudden load

In the current work, the dynamic behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate with negative Poisson’s ratio (NPR) is investigated by combining higher-order shear deformation theory and large deflection theory. First, explicit solutions are proposed to predict the effective Poisson’s ratio (EPR) of the laminates. Taking carbon nanotube-reinforced composite (CNTRC) as an example, the maximum NPR is obtained for $$\left( { \pm \theta } \right)_{{3{\text{T}}}}$$ laminate as well. Results show that the EPR ( $$v_{13}^{\text{e}}$$ , $$v_{23}^{\text{e}}$$ ) can range from a positive value of 0.311 to a negative value of 0.63. For the dynamic response problem, the asymptotic solutions with a two-step perturbation approach are derived for FG-CNTRC plates to capture the relationship between the center deflection and time. Several key factors such as functionally graded distribution, variations in the elastic foundation, and thermal stress produced by changing the temperature field are considered in the subsequent analysis. Numerical simulations are carried out to examine the corresponding dynamic behavior of FG-CNTRC plates when these factors are taken into account.

Effect of external pressure on the vibration analysis of higher order shear deformable FG-CNTRC spherical panels

The numerical investigation is performed on the vibration of the higher order shear deformable carbon nanotube reinforced composite (CNTRC) spherical panels subjected to the initial external pressure. The functionally graded nanocomposite is reinforced with the non-uniform distribution of CNTs. The problem is formulated following the higher order shear deformation shell theory (HSDT) within the variational differential quadrature numerical approach. For this purpose, the direct discretization of Hamilton’s principle is carried out with the aid of differential quadrature operators. Derivation of the variational formulation of nanocomposite spherical panels based on the HSDT and studying the effects of external pressure on the vibration behavior are the main novel aspects of this research. Several numerical examples are provided to survey the impacts of geometrical and material factors on the vibration of pressurized functionally graded CNTRC spherical panels. It is shown that the internal pressure has the most influence on the vibrational behavior of the thicker panel.

On static bending of multilayered carbon nanotube-reinforced composite plates

In this paper, the bending behavior of single-walled carbon nanotube-reinforced composite (CNTRC) laminated plates is studied using various shear deformation plate theories. Several types of reinforcement material distributions, a uniform distribution (UD) and three functionally graded distributions (FG), are inspected. A generalized higher-order deformation plate theory is utilized to derive the field equations of the CNTRC laminated plates where an analytical technique based on Navier\'s series is utilized to solve the static problem for simply-supported boundary conditions. A detailed numerical analysis is carried out to examine the influence of carbon nanotube volume fraction, laminated composite structure, side-to-thickness, and aspect ratios on stresses and deflection of the CNTRC laminated plates.

Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets

In this paper, the stresses and buckling behaviors of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets are considered based on the high-order shear deformation theory (HSDT) and the modified couple stress theory (MCST). The governing equations of equilibrium are obtained based on the total potential energy principle. The effects of various parameters such as the aspect ratio, elastic foundation, temperature changes, and volume fraction of the canbon nanotubes (CNTs) on the critical buckling loads, normal stress, shear stress, and deflection of the thick-walled micro cylindrical sandwich panel considering different distributions of CNTs are examined. The results are compared and validated with other studies, and showing an excellent compatibility. CNTs have become very useful and common candidates in sandwich structures, and they have been extensively used in many applications including nanotechnology, aerospace, and micro-structures. This paper also extends further applications of reinforced sandwich panels by providing the modified equations and formulae.