Carbon Nanotube-reinforced Composites Research Articles

Nonlinear bending analysis of functionally graded CNT-reinforced composite Mindlin polymeric temperature-dependent plate resting on orthotropic elastomeric medium using GDQM

This research deals with the nonlinear bending analysis of nanocomposite polymeric temperature-dependent plates reinforced by single-walled carbon nanotubes (SWCNTs) subjected to a transverse uniform load. For the carbon nanotube-reinforced composite (CNTRC) plate, uniform distribution and three types of functionally graded (FG) distribution patterns of SWCNT reinforcements are assumed. The material properties of FG-CNTRC plate are graded in the thickness direction and estimated based on the rule of mixture. The CNTRC is located in an orthotropic temperature-dependent elastomeric medium. Based on orthotropic Mindlin plate theory along with von Karman geometric nonlinearity, the governing equations are derived using Hamilton’s principle and discretized by generalized differential quadrature method. The influences of the volume fractions of carbon nanotubes, elastomeric medium, aspect ratio, temperature, boundary conditions and applied force are considered on the nonlinear bending of the plate. Results indicate that CNT distribution close to top and bottom is more efficient than that distributed nearby the mid-plane for increasing the stiffness of plates. Furthermore, considering elastomeric medium decreases deflection of the FG-CNTRC plate. Results show good agreement with the solutions obtained by the finite element method and ANSYS software.

Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method

A first known free vibration characteristics of functionally graded nanocomposite triangular plates reinforced by single-walled carbon nanotubes (SWCNTs) is presented. The first-order shear deformation theory (FSDT) is employed to account for the effect of transverse shear deformation of the plates and the element-free IMLS-Ritz method is used for numerical computation. The triangular nanocomposite plates are studied with the consideration of different types of distributions of uniaxial aligned SWCNTs. Material properties of the functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded through the thickness direction according to linear distributions of the volume fraction of carbon nanotubes. Since no existing results are available for such FG-CNTRC triangular plates, comparisons can only be made with isotropic triangular plates of different angles and thickness-to-width ratios. Stability and accuracy of the present method are demonstrated by convergence studies. New sets of vibration frequency parameters and mode shapes for various FG-CNTRC triangular plates are presented. We have also examined the influence of carbon nanotube volume fraction, plate thickness-to-width ratio, plate aspect ratio, and boundary condition on the plate’s vibration behavior. These new results may serve as benchmarks for future studies.

Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review

Research activities related to functionally graded materials (FGMs) have increased rapidly in recent years. The superlative properties of carbon nanotubes, i.e. high strength, high stiffness, high aspect ratio and low density have made them an excellent reinforcement for composite materials. Inspired by the concept of FGMs, the functionally graded (FG) pattern of reinforcement has been applied for functionally graded carbon nanotube reinforced composite (FG-CNTRC) materials. This paper attempts to identify and highlight topics relevant to FG-CNTRC and reviews the recent research works that have been reported in these topics. The present review includes: (i) a brief introduction of carbon nanotube reinforced composite (CNTRC) material; (ii) a review of mechanical analysis of FG-CNTRC; and (iii) a detailed discussion on the recent advances of FG-CNTRC and its prospect.

Mixed Navier-layerwise differential quadrature three-dimensional static and free vibration analysis of functionally graded carbon nanotube reinforced composite laminated plates

The three-dimensional free vibration and static analysis of the laminated plates with functionally graded (FG) carbon nanotube reinforced composite (CNTRC) layers is presented using a semi-analytical approach. The individual layers are assumed to be made from a mixture of aligned and straight single-walled carbon nanotubes (CNTs) with volume fractions graded in the thickness direction, and an isotropic matrix. The effective material properties of the resulting FG-CNTRC layers are estimated through a micromechanical model. The through-the-thickness variations of the displacement components are accurately modeled using a layerwise-differential quadrature method, and their in-plane variations are approximated using the trigonometric series. After demonstrating the convergence and accuracy of the method, the effects of geometrical parameters, type of CNTs distribution and volume fractions, and also lamination scheme on the natural frequencies, displacement and stress components of the FG-CNTRC layered plates are investigated.

Static and free vibration analyses of carbon nanotube-reinforced composite plate using differential quadrature method

This work presents bending and free vibration behaviour of carbon nanotubes reinforced composite (CNTRC) plates using the three dimensional theory of elasticity. The single-walled carbon nanotubes reinforcement is either uniformly distributed or functionally graded (FG) along the thickness direction indicated with FG-V, FG-O and FG-X. In the present study the effective material properties of CNTRC plates, are estimated according to the rule of mixture along with considering the CNT efficiency parameters. For the plate with simply supported edges we used Fourier series expansion across the in plane coordinates as well as the state space technique across the thickness direction to obtain closed form solution. Since in the case of plate with non-simply supported boundary conditions it is not possible to use Fourier series along the longitudinal and width directions, therefore it should be employed numerical method along the above mentioned coordinates. In this investigation we used semi analytical technique, differential quadrature method along the in-plane coordinates and state-space technique across the thickness direction. Present approach is validated by comparing the numerical results with those published results. Furthermore, effect of types of CNT distributions in the polymer matrix, volume fraction of CNT, edges boundary conditions and width-to-thickness ratio on the bending and free vibration behaviour of FG-CNTRC plate are discussed.

Static stress analysis of carbon nano-tube reinforced composite (CNTRC) cylinder under non-axisymmetric thermo-mechanical loads and uniform electro-magnetic fields

Static stresses analysis of carbon nano-tube reinforced composite (CNTRC) cylinder made of poly-vinylidene fluoride (PVDF) is investigated in this study. Non-axisymmetric thermo-mechanical loads are applied on cylinder in presence of uniform longitudinal magnetic field and radial electric field. The surrounded elastic medium is modeled by Pasternak foundation because of its advantages to the Winkler type. Distribution of radial, circumferential and effective stresses, temperature field and electric displacements in CNTRC cylinder are determined based on Mori–Tanaka theory. The detailed parametric study is conducted, focusing on the remarkable effects of magnetic field intensity, elastic medium, angle orientation and volume fraction of carbon nano-tubes (CNTs) on distribution of effective stress. Results demonstrated that fatigue life of CNTRC cylinder will be significantly dependent on magnetic intensity, angle orientation and volume fraction of CNTs. Results of this research can be used for optimum design of thick-walled cylinders under multi-physical fields.

Investigations on Thermal Conductivity of Carbon Nanotubes Reinforced Composites

Natural rubber, as well as natural reinforced rubber, with different carbon nanotubes concentrations, 10 and 20 mm, thick, have been structurally, chemically, and thermally investigated. Scanning electron microscopy techniques, as well as X-ray energy dispersive analysis, Raman, and thermal conductivity analysis, were used in characterizing materials in order to establish a connection among the CNT concentration, homogeneity of reinforcing elements within the natural rubber, and their thermal conductivity characteristics. The theoretical approach reveals the dependence between the thermal conductivity and reinforcing elements. The final result confirms the increase of the effective thermal conductivity with the concentration of CNT.

Postbuckling of axially compressed nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments

This paper presents a postbuckling analysis of carbon nanotube-reinforced composite (CNTRC) cylindrical panels resting on elastic foundations and subjected to axial compression in thermal environments. The cylindrical panels are reinforced by aligned single-walled carbon nanotubes (SWCNTs) which are assumed to be functionally graded (FG) through the thickness direction with different types of distributions. The material properties of FG-CNTRC panels are estimated through an extended rule of mixture micromechanical model. The governing equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The panel–foundation interaction and thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. A singular perturbation technique along with a two-step perturbation approach is employed to determine the buckling loads and postbuckling equilibrium paths. Numerical results reveal that the CNT volume fraction, temperature rise, foundation stiffness, and the panel geometric parameters have a significant effect on the buckling load and postbuckling behavior of CNTRC cylindrical panels. The results for uniformly distributed (UD) CNTRC cylindrical panels are compared with those of FG-CNTRC cylindrical panels. The results also confirm that for an CNTRC cylindrical panel with immovable unloaded straight edges, the postbuckling path of the panel is no longer the bifurcation type.

Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells

The influences of centrifugal and Coriolis forces on the free vibration behavior of rotating carbon nanotube reinforced composite (CNTRC) truncated conical shells are examined. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction and are estimated through a micromechanical model. The governing equations are derived based on the first-order shear deformation theory (FSDT) of shells using Hamilton’s principle. The initial mechanical stresses are obtained by solving the dynamic equilibrium equations. The differential quadrature method (DQM) is adopted to discretize the equations of motion and the related boundary conditions. After demonstrating the convergence and accuracy of the presented approach, the effects of angular velocity, Coriolis acceleration, geometrical parameters, type of distribution and volume fractions of carbon nanotubes on the frequency parameters of the CNTRC truncated conical shells are studied. The results reveal that the influences of the type of carbon nanotube distribution and its volume fraction on the frequency parameters depend on the semi vertex angle and angular velocity of the shells and the frequency parameters of the shell with FG asymmetric carbon nanotube distribution can become greater than those of the case with FG symmetric distribution ones.

Dynamic analysis of functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube under an impact load

This work mainly reports on the effects of the aspect ratio and waviness index of carbon nanotubes (CNTs) on the free vibration and stress wave propagation of functionally graded (FG) nanocomposite cylinders that are reinforced by wavy single-walled carbon nanotubes based on a mesh-free method. In this simulation, an axisymmetric model is used, three linear types of FG distributions of wavy CNTs along the radial direction of the cylinder are considered and their results are compared with the results of a uniform distribution. The material properties are estimated by a micromechanical model. In the mesh-free analysis, moving least squares shape functions are used for approximation of the displacement field in the weak form of motion equation and the transformation method was used for the imposition of essential boundary conditions. Also, the effects of volume fraction and distribution pattern of wavy CNTs and cylinder thickness are investigated on the natural frequency and stress wave propagation of carbon nanotube reinforced composite (CNTRC) cylinders subjected to an impact load. It is observed that waviness has a significant effect on the dynamic behavior of the CNTRC cylinders.

Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers

The free vibration behavior of quadrilateral laminated thin-to-moderately thick plates with carbon nanotube reinforced composite (CNTRC) layers is studied. The governing equations are based on the first-order shear deformation theory (FSDT). The solution procedure is based on transforming the governing differential equations from an arbitrary straight-sided physical domain to a regular computational one, and discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. Four different profiles of single walled carbon nanotubes (SWCNTs) distribution through the thickness of layers are considered, which are uniformly distributed (UD) and three others are functionally graded (FG) distributions. The fast rate of convergence of the presented approach is numerically demonstrated and to show its high accuracy, wherever possible comparison studies with the available results in the open literature are performed. Then, the effects of volume fraction of carbon nanotubes (CNTs), geometrical shape parameters, thickness-to-length and aspect ratios, different kinds of CNTs distribution along the layers thickness and different boundary conditions on the natural frequencies of laminated plates are studied.

Modelling of stress transfer in double-walled carbon nanotube-reinforced composites

Carbon nanotubes with excellent mechanical properties can be utilised as nanoscale reinforcement to carry loads in composite structures. External loads are transferred to carbon nanotubes via the surrounding matrix, through the interfacial shear stress. In this work, the interaction and stress transfer in double-walled carbon nanotube- reinforced composites are investigated. A cylindrical representative element volume containing the double-walled carbon nanotubes and matrix is employed to determine the interfacial shear stress and longitudinal axial stress in the double-walled carbon nanotube. The theoretical predictions of the interfacial shear stress and longitudinal axial stress are verified with the finite element results. The effects of the aspect ratio and volume fraction on the stress transfer are investigated through a parametric study. Numerical results show that stresses transferred to double-walled carbon nanotubes are increasing with the increases of the volume fraction and aspect ratio. It demonstrates that a better load transfer efficiency can be achieved with larger volume fraction and aspect ratio.

Thermal analysis of randomly oriented carbon nanotube reinforced functionally graded timoshenko beam

The unique thermal properties of carbon nanotubes (CNT) are utilized to increase the use of functionally graded material (FGM) at higher temperatures which resulted in introduction of a new type of material called as functionally graded carbon nanotube-reinforced composites (FG-CNTRCs). To use the FG-CNTRCs at elevated temperatures, their thermal analysis is very important. In this context, this article presents the thermal analysis of a CNT based FG Timoshenko beam. Material properties distribution is assumed to vary along the thickness direction according to power law distribution and linear distributions. Finite difference method is implemented to find out the temperature distribution. Using first order shear deformation theory (FSDT), expressions for strains and stresses are obtained. The results are compared with temperature distribution according to power law. The effect of CNT distribution on strains and stresses is also observed. Based on these results important conclusions have been drawn.

Three-dimensional free vibration analysis of functionally graded carbon nanotube-reinforced composite plates with various boundary conditions

A unified formulation of finite prism methods (FPMs) based on Reissner's mixed variational theorem is developed for the three-dimensional (3D) free vibration analysis of functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plates and laminated fiber-reinforced composite (FRC) plates, the edge conditions of which are considered such that one pair of opposite edges is simply supported and the other pair may be combinations of free, clamped or simply supported edges. The single-walled carbon nanotubes (CNTs) and polymer are regarded as the reinforcements and matrices, respectively, to produce the CNTRC plate. Four different distributions of CNTs varying in the thickness direction are considered (i.e. the uniformly distributed, and FG V-, rhombus-, and X-type variations), and the through-thickness distributions of effective material properties of the CNTRC plate are determined using the rule of mixtures. In the formulation, the CNTRC/FRC plate is divided into a number of finite prisms in the domain, in which the trigonometric functions and Lagrange polynomials are used to interpolate the y-direction and plane variations for the primary variables of each individual prism, respectively, and the related orders used for expansion of assorted primary variables in the thickness coordinate can be freely chosen. It is shown that the eight- and nine-node quadratic FPM solutions of frequency parameters of simply supported, CNTRC plates and laminated FRC plates are in excellent agreement with the exact 3D solutions available in the literature, and with the ones obtained using the ANSYS software for those plates with various boundary conditions.

Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams

This research deals with the forced vibration behavior of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on the Timoshenko beam theory along with von Kármán geometric nonlinearity. For the carbon-nanotube reinforced composite (CNTRC) beams, uniform distribution (UD) and three types of functionally graded (FG) distribution patterns of SWCNT reinforcements are considered. It is assumed that the material properties of FG-CNTRC beams are graded in the thickness direction and estimated through the rule of mixture. The nonlinear governing equations and corresponding boundary conditions are derived based on the Hamilton principle and discretized by means of the generalized differential quadrature (GDQ) method. After that, a Galerkin-based numerical technique is employed to reduce the set of nonlinear governing equations into a time-varying set of ordinary differential equations of Duffing type. Since the nanobeam responds periodically to harmonic excitations, a set of periodic differential matrix operators is introduced to discretize the Duffing equations on the time domain using the derivatives of a periodic base function. The vectorized form of final nonlinear parameterized equations is then solved through the use of pseudo-arc length continuum technique. Numerical results are presented to examine the effects of different parameters such as nanotube volume fraction, slenderness ratio, dimensionless damping parameter, dimensionless transverse force, CNT distributions and boundary conditions on the natural frequencies and frequency responses of FG-CNTRC beams.

Stability of carbon nanotube-reinforced composite plates with surface-bonded piezoelectric layers and under bi-axial compression

Based on Reissner’s mixed variational theorem (RMVT), we develop a unified formulation of finite layer methods (FLMs) for the three-dimensional (3D) buckling analysis of simply-supported, functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plates with surface-bonded piezoelectric actuator and sensor layers and under bi-axial compressive loads. In this work, a set of membrane stresses is assumed to exist just before instability occurs, and determined using the predefined 3D deformations for the prebuckling state. The carbon nanotubes (CNTs) are considered to be uniformly distributed (UD), and FG rhombus- and X-type variations through the thickness coordinate, and the effective material properties of the FG CNTRC layer are evaluated using the rule of mixtures, and two different surface conditions, open- and closed-circuit, are considered. In the formulation, the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations for the field variables of each individual layer, respectively. The accuracy and convergence of the FLMs with various orders used for the expansion of each field variable in the thickness are assessed by comparing their solutions with the exact 3D ones available in the literature.

Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments

This paper investigates the large amplitude vibration behavior of nanocomposite cylindrical panels resting on elastic foundations in thermal environments. Two kinds of carbon nanotube-reinforced composite (CNTRC) panels, namely, uniformly distributed and functionally graded reinforcements, are considered. The material properties of FG-CNTRC panels are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The panel-foundation interaction and thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion are solved by a two-step perturbation technique to determine the nonlinear frequencies of the CNTRC panels. Numerical results demonstrate that the natural frequencies of the CNTRC panels are reduced but the nonlinear to linear frequency ratios of the CNTRC panels are increased as the temperature rises. In contrast, natural frequencies are increased but the nonlinear to linear frequency ratios are decreased by increasing the foundation stiffness. The results reveal that the natural frequencies are increased by increasing the CNT volume fraction, whereas the CNTRC panels with intermediate CNT volume fraction do not necessarily have intermediate nonlinear to linear frequency ratios.

Hexagonal Representative Volume Element for Modeling and Analysis of Mechanical Properties of Carbon Nanotube Reinforced Composites

Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide the ultimate reinforcing materials for the development of nanocomposites. In this paper, nanostructure is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix having hexagonal representative volume elements (RVEs) and homogeneous cylindrical nanotubes. Formulas to extract the effective material constants from solutions for the RVE under axial as well as lateral loading conditions are derived based on the continuum mechanics approach. Numerical examples using the FEM are presented, which demonstrate that the load carrying capacities of the CNTs in a matrix are significant. For the RVEs having long carbon nanotube, better values of stiffness in axial direction are found as compared to stiffness in the lateral direction. Also, It is found that the square RVEs tend to overestimate the effective Youngs moduli of the CNT-based composites, and the hexagonal RVEs may be the preferred models for obtaining more accurate results.

Local Aggregation Effect of Carbon Nanotubes on the Elastic Property of Carbon Nanotube Reinforced Composites

Local Aggregation Effect of Carbon Nanotubes on the Elastic Property of Carbon Nanotube Reinforced Composites

Dynamic stability analysis of functionally graded nanocomposite non-uniform column reinforced by carbon nanotube

This paper deals with the dynamic behavior of a non-uniform column reinforced by single-walled carbon nanotubes resting on an elastic foundation and subjected to follower force. The method of solution is the differential quadrature method. The carbon nanotube reinforced composite (CNTRC) columns have smooth variation of carbon nanotube (CNT) fraction in the thickness direction and the material properties are estimated by the extended rule of mixture. Detailed parametric studies have been carried out to reveal the influences of the kind of distribution and volume fractions of CNT on natural frequencies and the critical load for the CNTRC column.