Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method

In this paper, dynamic analysis of nanocomposite cylinders reinforced by single-walled carbon nanotubes (SWCNTs) subjected to an impact load was carried out by a mesh-free method. Free vibration and stress wave propagation analysis of carbon nanotube reinforced composite (CNTRC) cylinders are presented. In this simulation, an axisymmetric model is used. Four types of distributions of the aligned carbon nanotubes (CNTs) are considered; uniform and three kinds of functionally graded (FG) distributions along the radial direction of cylinder. Material properties are estimated by a micro mechanical model. In the mesh-free analysis, moving least squares (MLSs) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method was used for the imposition of essential boundary conditions. Effects of the kind of distribution and volume fractions of carbon nanotubes and cylinder thickness on the natural frequencies and stress wave propagation of CNTRC cylinders are investigated. Results obtained for this analysis were compared with FEM and previous published work and good agreement was seen between them.     

Material tailoring for orthotropic elastic rotating disks

The tailoring of elastic moduli in the radial direction is studied to design a fiber-reinforced orthotropic linear elastic rotating disk with constant radial or hoop stress or constant in-plane shear stress. For fibers arranged in concentric circles the axes of material symmetry coincide with the radial and the circumferential directions. However, when fibers are aligned along helices, the orientation of material principal axes varies with the radial coordinate of a point. For a solid disk made of an orthotropic material with Young’s moduli proportional to each other, we give explicit expressions for the required variations of the elastic moduli with the radius to attain a given state of stress. For a rotating annular disk composed of a fiber-reinforced composite with fibers placed along concentric circles, the required radial variation of the volume fraction of fibers is calculated numerically and exhibited graphically. For fibers of known volume fraction laid along helices, the radial variation of the fiber orientation angle is determined. We have also analyzed the material tailoring problem for a disk of variable thickness. Results presented herein should help structural engineers and material scientists optimally design rotating disks composed of radially inhomogeneous materials.     

Analysis of nonlinear dynamic stability for carbon nanotube-reinforced composite plates resting on elastic foundations

This article studies nonlinear dynamic stability of carbon nanotube-reinforced composite (CNTRC) plates resting on an elastic foundation. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in the form of uniformly distributed (UD) and functionally graded (FG) reinforcements. The governing equations are established based on classic plate theory, which is converted to a Mathieu-type equation by using a two-step perturbation technique, and then solved by adopting an incremental harmonic balanced (IHB) method. In numerical results, the effects of nonlinear geometric factor, distribution and fraction volume of CNTs, and foundation stiffness on principle dynamic unstable regions are discussed.     

A shear lag model of Piezoelectric composite reinforced with carbon nanotubes-coated Piezoelectric fibers

A novel hybrid piezoelectric composite in which the microscopic piezoelectric fiber reinforcements are coated with radially aligned carbon nanotubes (CNTs) is analyzed in this study. A shear-lag model is developed to analyze the load transferred to such coated fibers from the aligned-CNT reinforced matrix in a hybrid composite application in the absence and the presence of the electric field along the length of the fiber. It is found that if the aligned CNTs are radially grown on the surface of the piezoelectric fiber then the axial load transferred to the fiber is reduced in the absence of the electric field while the axial stress in the fiber increases in the presence of the electric filed only. The radial stress in the active piezoelectric fiber significantly increases due to the radial growth of aligned CNTs on the surface of the fibers. This indicates a probable critical window for engineering the surface of the piezoelectric fiber for improving the effective piezoelectric properties. Effects of the variation of the aspect ratio of the piezoelectric fiber and the CNT volume fraction on the load transferred to such CNT-coated piezoelectric fibers are also investigated.     

Material tailoring for functionally graded hollow cylinders and spheres

We present a technique to tailor materials for functionally graded (FG) linear elastic hollow cylinders and spheres to attain through-the-thickness either a constant hoop (or circumferential) stress or a constant in-plane shear stress. The volume fractions of two phases of a FG material (FGM) are assumed to vary only with the radius and the effective material properties are estimated by using either the rule of mixtures or the Mori-Tanaka scheme; the analysis is applicable to other homogenization methods. For a FG cylinder we find the required radial variation of the volume fractions of constituents to make a linear combination of the radial and the hoop stresses uniform throughout the thickness. The through-the-thickness uniformity of the hoop stress automatically eliminates the stress concentration near the inner surface of a very thick cylinder. The through-the-thickness variations of Young’s moduli obtained with and without considering the variation of Poisson’s ratio are very close to each other for a moderately thick hollow cylinder but are quite different in a very thick hollow cylinder. For an FG sphere the required radial variation of the volume fractions of the two phases to get a constant circumferential stress is similar to that in an FG cylinder. The material tailoring results presented here should help structural engineers and material scientists optimally design hollow cylinders and spheres comprised of inhomogeneous materials.     

The analysis of time-dependent creep in FGPM thick walled sphere under electro-magneto-thermo-mechanical loadings

Time-dependent creep response of a smart sphere made of functionally graded piezoelectric material (FGPM) is investigated. The vessel is subjected to an internal pressure, a uniform temperature field, an electric potential and a uniform magnetic field. Under such a loading condition initial elastic stresses are locked in the vessel at zero time. Due to high temperature, creep evolution causes stress redistribution in the sphere which is followed by electric potential redistribution across the thickness of the sphere. History of radial stresses is always reflected by history of electric potential which can be used for condition monitoring of the smart sphere. From the initial elastic stresses it has been found that imposing an electric potential decreases effective stresses. It has also been concluded from history of electric potential that electric potential redistribution is decreasing due to creep evolution and therefore this is followed by increasing effective stresses.     

Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates

Thermal buckling and postbuckling behavior is presented for functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) subjected to in-plane temperature variation. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. 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. Based on the multi-scale approach, numerical illustrations are carried out for perfect and imperfect, geometrically mid-plane symmetric FG-CNTRC plates and uniformly distributed CNTRC plates under different values of the nanotube volume fractions. The results show that the buckling temperature as well as thermal postbuckling strength of the plate can be increased as a result of a functionally graded reinforcement. It is found that in some cases the CNTRC plate with intermediate nanotube volume fraction does not have intermediate buckling temperature and initial thermal postbuckling strength.     

Multiphysical time-dependent creep response of FGMEE hollow cylinder in thermal and humid environment

In this paper, we investigate the history of radial displacement, stresses, electric potential, and magnetic potential of a functionally graded magneto-electro-elastic (FGMEE) hollow cylinder subjected to an axisymmetric hygro-thermo-magneto-electro-mechanical loading for the plane strain condition. The material properties are taken as a power-law function of radius. Using stress-displacement relations, equations of equilibrium, electrostatic and magnetostatic equations, we find a differential equation including creep strains. Initially, eliminating creep strains, we obtain an analytical solution for the primitive stresses and electric and magnetic potential. In the next step, considering creep strains, we find the creep stress rates by applying the Norton law and Prandtl–Reuss equations for steady-state hygrothermal boundary condition. Finally, using an iterative method, we find the time-dependent creep stresses, radial displacement, and magnetic and potential field redistributions at any time. In numerical section, are comprehensively investigate the effects of grading index, hygrothermal environmental conditions, rotating speed, and temperature- and moisture-dependency of elastic constant of FGMEE.

     

Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets

This paper studied the large amplitude vibration and the nonlinear bending of a sandwich plate with carbon nanotube-reinforced composite (CNTRC) face sheets resting on an elastic foundation in thermal environments. The material properties of CNTRC face sheets are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equation of the plate that includes plate-foundation interaction is solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both CNTRC face sheets and homogeneous core layer are assumed to be temperature-dependent. A detailed parametric study is conducted to study the effects of nanotube volume fraction, core-to-face sheet thickness ratio, temperature change, foundation stiffness and in-plane boundary conditions on the nonlinear vibration characteristics and nonlinear bending behaviors of sandwich plates with functionally graded CNTRC face sheets. The results for the same plate with uniformly distributed CNTRC face sheets are also provided for comparison.     

Magneto-thermo-mechanical dynamic buckling analysis of a FG-CNTs-reinforced curved microbeam with different boundary conditions using strain gradient theory

In this article, dynamic buckling analysis of an embedded curved microbeam reinforced by functionally graded carbon nanotubes is carried out. The structure is subjected to thermal, magnetic and harmonic mechanical loads. Timoshenko beam theory is employed to simulate the structure. Furthermore, the temperature-dependent surrounding elastic foundation is modeled by normal springs and a shear layer. Using strain gradient theory, the small scale effects are taken into account. The extended rule of mixture is employed to estimate the equivalent properties of the composite material. The governing equations and different boundary conditions are derived based on the energy method and Hamilton’s principle. Dynamic stability regions of the system are obtained using differential quadrature method. The aim of this paper is to investigate the influence of different parameters such as small scale effect, boundary conditions, elastic foundation, volume fraction and distribution types of carbon nanotubes, magnetic field, temperature and central angle of the curved microbeam on the dynamic stability region of the system. The results indicate that by increasing the volume fraction of CNTs, the frequency of the system increases and thus the dynamic stability region occurs at higher frequencies.     

Three Phase Composite Cylinder Assemblage Model for Analyzing the Elastic Behavior of MWCNT-Reinforced Polymers

Evolution of computational modeling and simulation has given more emphasis on the research activities related to carbon nanotube (CNT) reinforced polymer composites recently. This paper presents the composite cylinder assemblage (CCA) approach based on continuum mechanics for investigating the elastic properties of a polymer resin reinforced by multi-walled carbon nanotubes (MWCNTs). A three-phase cylindrical representative volume element (RVE) model is employed based on CCA technique to elucidate the effects of inter layers, chirality, interspacing, volume fraction of MWCNT, interphase properties and temperature conditions on the elastic modulus of the composite. The interface region between CNT and polymer matrix is modeled as the third phase with varying material properties. The constitutive relations for each material system have been derived based on solid mechanics and proper interfacial traction continuity conditions are imposed. The predicted results from the CCA approach are in well agreement with RVE-based finite element model. The outcomes reveal that temperature softening effect becomes more pronounced at higher volume fractions of CNTs.     

Thermal shock analysis and thermo-elastic stress waves in functionally graded thick hollow cylinders using analytical method

Transient stress field and thermo-elastic stress wave propagation are studied in functionally graded thick hollow cylinder under arbitrary thermo-mechanical shock loading, in this article. Thermo-mechanical properties of functionally graded (FG) cylinder are assumed to be temperature independent and vary continuously and smoothly in the radial direction. The governing dynamic equations are analytically solved in temperature and elastic fields. To solve the problem, Laplace transform is used respect to time in all constitutive equations and boundary conditions. At first, temperature field equation analytically solved using Laplace transform and series method. The dynamic behaviors of thermo-elastic stresses are illustrated and discussed for various grading patterns of thermo-mechanical properties in several points across the thickness of FG cylinder. Time history of temperature field and thermal stresses are obtained using the residual theorem and the fast Laplace inverse transform method (FLIT), respectively. Also, the effects of the cylinder thickness and convection heat transfer coefficient on dynamic response of FG cylinder are revealed and discussed. The presented analytical method provides a ground to study the time histories of radial and hoop stresses in FG cylinders with different thickness and various volume fraction exponents. The advantage of this method is its mathematical ability to support simple and complicated mathematical function for the thermo-mechanical boundary conditions. A reasonable agreement can be seen in comparison of obtained results based on the presented analytical method with published data.     

Formation and mechanical characterisation of SU8 composite films reinforced with horizontally aligned and high volume fraction CNTs

Carbon nanotube (CNT) reinforced composites have been identified as promising structural materials for the mechanical components of microelectromechanical systems (MEMS), potentially leading to advanced performance. High alignment and volume fraction of CNTs in the composites are the prerequisites to achieve such desirable mechanical characteristics. In particular, horizontal CNT alignment in composite films is necessary to enable high longitudinal moduli of the composites which is crucial for the performance of microactuators. A practical process has been developed to transfer CNT arrays from vertical to horizontal alignment which is followed by in situ wetting, realign and pressurized consolidation processes, which lead to a high CNT volume fraction in the range of 46-63%. As a result, SU8 epoxy composite films reinforced with horizontally aligned CNTs and a high volume faction of CNTs have been achieved with outstanding mechanical characteristics. The transverse modulus of the composite films has been characterised through nanoindentation and the longitudinal elastic modulus has been investigated. An experimental transverse modulus of 9.6 GPa and an inferred longitudinal modulus in the range of 460-630 GPa have been achieved, which demonstrate effective CNT reinforcement in the SU8 matrix.     

Elastic wave propagation in a functionally graded nanocomposite reinforced by carbon nanotubes employing meshless local integral equations (LIEs)

The transient dynamic analysis of displacement field and elastic wave propagation in finite length functionally graded nanocomposite reinforced by carbon nanotubes are carried out using local integral equations (LIEs) based on meshless local Petrov–Galerkin (MLPG) method. The distribution of the aligned carbon nanotubes (CNTs) is assumed to vary as three kinds of functionally graded distributions as well as uniform distribution (UD) through radial direction of axisymmetric reinforced cylindrical composites. The mechanical properties are simulated using a micro-mechanical model in volume fraction form. A unit step function is used as a test function in the local weak form, which leads to local integral equations (LIEs). The analyzed domain is divided into small subdomains with a circular shape. The radial basis functions are used for approximation of the spatial variation of field variables. For treatment of time variations, the Laplace-transform technique is utilized. The 2D propagation of elastic waves through 2D domain is illustrated for various kinds of carbon nanotubes distributions. The time histories of displacement fields are studied in detail for various kinds of carbon nanotube distributions in reinforced cylindrical composites.     

无限长导电圆柱体的磁弹性振动

对处于均匀静磁场中表面承受周期性负载的无限长导电圆柱体进行了分析,给出了径向位移的解析表达式。以具体的算例,计算了几种不同负载频率下圆柱体的径向应力     

电场诱导碳纳米管在聚合物中定向有序排列的研究进展

碳纳米管特殊的结构和优异的性能使之成为复合材料增强的首选填料,综述了电场条件下碳纳米管在聚合物中有序排列的研究进展。分析了电场类型、碳纳米管表面官能化、加电时间、碳纳米管尺寸和含量等因素对电场诱导碳纳米管有序排列的影响,讨论了定向有序排列的碳纳米管对复合材料的力学、电学和热学等性能的影响,分析了碳纳米管定向排列机理以及碳纳米管定向程度的表征方法。     

Mechanical and electrical property improvement in CNT/Nylon composites through drawing and stretching

The excellent mechanical properties of carbon nanotubes (CNTs) make them the ideal reinforcements for high performance composites. The misalignment and waviness of CNTs within composites are two major issues that limit the reinforcing efficiency. We report an effective method to increase the strength and stiffness of high volume fraction, aligned CNT composites by reducing CNT waviness using a drawing and stretching approach. Stretching the composites after fabrication improved the ultimate strength by 50%, 150%, and 190% corresponding to stretch ratios of 2%, 4% and 7%, respectively. Improvement of the electrical conductivities exhibited a similar trend. These results demonstrate the importance of straightening and aligning CNTs in improving the composite strength and electrical conductivity.     

Effect of carbon nanotube orientation on the mechanical properties of nanocomposites

Carbon nanotubes (CNTs) have been regarded as ideal reinforcements of high-performance composites with enormous applications. In this paper, nano-structure is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix having hexagonal representative volume elements (RVEs) and homogeneous cylindrical nanotubes with various inclination angles. Effects of inclined carbon nanotubes on mechanical properties are investigated for nano-composites using 3-D hexagonal representative volume element (RVE) with short and straight CNTs. The CNT is modeled as a continuum hollow cylindrical shape elastic material with different angles. The effect of the inclination of the CNT and its parameters is studied. Numerical equations are used to extract the effective material properties for the hexagonal RVE under axial as well as lateral loading conditions. The computational results indicated that elastic modulus of nano-composite is remarkably dependent on the orientation of the dispersed SWNTs. It is observed that the inclination significantly reduces the effective Young’s modulus of elasticity under an axial stretch. When compared with lateral loading case, effective reinforcement is found better in axial loading case. The effective moduli are very sensitive to the inclination and this sensitivity decreases with the increase of the waviness. In the case of short CNTs, increasing trend is observed up to a specific value of waviness index. It is also found from the simulation results that geometry of RVE does not have much significance on stiffness of nano-structures. The results obtained for straight CNTs are consistent with ERM results for hexagonal RVEs, which validate the proposed model results.     

Modulus–density negative correlation for CNT-reinforced polymer nanocomposites: Modeling and experiments

Mechanical and weight properties of polymer nanocomposites (PNCs) are measured and modeled at the interlaminar region, predicting the density and elastic modulus of individual carbon nanotubes (CNTs). A simple model of the CNTs density and elastic modulus within the PNC, accounting for fundamental material properties, geometry, and interactions, is developed, capable of predicting CNT contributions in the PNCs. Furthermore, the model is validated with experimental results that demonstrate enhancement of the elastic modulus, while reducing density in the presence of aligned CNTs. By establishing an inverse relation of density and elastic modulus (negative correlation), it is demonstrated the potential of increasing mechanical properties while reducing weight. Therefore, by introducing controlled nanoporosity through suitable CNT distributions within the interlayer of multi-lamina structures, it is possible to simultaneously control effective weight reduction and enhanced modulus, toward bio-inspired carbon fiber reinforced polymer composites.     

Hygro-Thermo-Electric Properties of Carbon Nanotube Epoxy Nanocomposites with Agglomeration Effects

In the present study, the effective electric, thermal, and moisture properties of carbon nanotube (CNT) epoxy composites are derived by considering the agglomeration effect of CNT concentrations in the epoxy matrix. In this direction, the Voigt and Reuss homogenization method is adopted in the derivations. It is well known from experiments that the CNT thermal and electrical conductivities and the epoxy hygro-thermal expansion coefficients have significant effects on the behavior of CNT nanocomposites. Moreover, it has been experimentally proved that the agglomeration of CNTs in the matrix with high and low concentrations of the CNTs certainly affects the resistivity and, hence, the thermal expansion properties. Therefore, the effective elastic, thermal, electrical, and moisture properties for the randomly distributed CNTs in the matrix has been derived in terms of the agglomeration volume fractions of CNTs. In the effective relations, a single agglomeration parameter is considered to be active for a given potential. The results of variation in the hygro-electro-thermal properties due to change in CNT volume fraction as well as agglomeration parameters have been presented. The results and observation show that CNT agglomeration has a strong influence on the effective hygro-thermo-electric properties of the nanocomposites.