Carbon Nanotube-reinforced Composite Plates Research Articles

Vibrations of FG-CNT reinforced composite cylindrical panels with cutout

An investigation is performed in this research to analyze the free vibration characteristics of carbon nanotube reinforced composite (CNTRC) cylindrical panels with cutout. Distribution of CNTs in the matrix of the composite panel may be uniform or functionally graded. The cylindrical panel has a cutout at the center in a rectangular shape. Following the first-order shear deformation shell theory with the Donnell type of kinematic assumptions, the total kinetic and strain energies of the cylindrical panel are obtained. The eigenvalues problem governing the natural frequencies of the panel is established using the generalized Ritz method where the shape functions are constructed by means of the Chebyshev polynomials. Different boundary conditions such as free, simply supported, shear diaphragm, and clamped may be assumed for the edge of the panel, however, the perforation part of the panel is considered to be free all around. The obtained frequencies are first validated with the simple cases such as CNTRC plates with cutout and CNTRC panels without cutout. Afterwards novel numerical results are provided to analyze the effects of volume fraction of CNT, graded pattern of CNT, boundary conditions, panel geometry, and the hole size. Results of this study show that as the volume fraction of CNTs as reinforcement increases, the natural frequencies of the plate with/without cutout enhance. Also through a proper functionally graded distribution of CNTs as reinforcement the natural frequencies of the panel may be decreased/increased.

Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton’s energy principle

This paper investigates the buckling behavior of carbon nanotube-reinforced composite plates supported by Kerr foundation model. In this foundation elastic of Kerr consisting of two spring layers interconnected by a shearing layer. The plates are reinforced by single-walled carbon nanotubes with four types of distributions of uniaxially aligned reinforcement material. The analytical equations are derived and the exact solutions for buckling analyses of such type\'s plates are obtained. The mathematical models provided, and the present solutions are numerically validated by comparison with some available results in the literature. Effect of various reinforced plates parameters such as aspect ratios, volume fraction, types of reinforcement, parameters constant factors of Kerr foundation and plate thickness on the buckling analyses of carbon nanotube-reinforced composite plates are studied and discussed.

Dynamic analysis of carbon nanotube reinforced composite plates by using Bézier extraction based isogeometric finite element combined with higher-order shear deformation theory

This study intends to explore the free vibration and dynamic transient response of carbon nanotube reinforced composite (CNTRC) plates by using the Bézier extraction based isogeometric analysis (IGA). Bézier extraction decomposes non-uniform rational B-spline (NURBS) basis functions into the linear combinations of Bernstein polynomial basis through the Bézier extraction operator, hence providing piecewise C0-continuous Bézier elements. The IGA can thus be implemented in the familiar finite element method (FEM) framework. Higher-order shear deformation theory (HSDT) able to remedy the shear locking problem with no use of the shear correction factor is coupled with the variant IGA. The HSDT adopts a hybrid type shape function, and the governing equilibrium equations for the dynamic behavior are formulated by virtue of the Hamilton's principle. The validity of the Bézier extraction based isogeometric approach coupled with the HSDT in obtaining the solutions for the free vibration and dynamic transient response is first evidenced. Compared with the classical FEM based on the first-order shear deformation theory, the proposed IGA method combined with the HSDT is proved to be more accurate, effective and efficient. Illustrative parametric studies are also carried out to further scrutinize the dynamic behavior of CNTRC plates with various reinforcement schemes. The sinusoidally distributed transverse loads with different time-history patterns and harmonic excitation loading are applied for the dynamic transient analysis, and the damping effect on the temporal response is also examined through the Rayleigh damping model.

Vibration analysis of FG-CNTRC plates with an arbitrarily shaped cutout based on the variational differential quadrature finite element method

The vibration analysis of functionally graded carbon nanotube-reinforced composite plates with the arbitrarily shaped cutout is presented using a novel numerical approach called variational differential quadrature finite element method (VDQFEM). The governing equations are expressed in matrix form based on Mindlin’s plate theory. In the proposed numerical approach, the space domain of the plate is first transformed into a number of sub-domains known as finite elements. Then, the variational differential quadrature (VDQ) discretization method is used within each element to obtain the mass and stiffness matrices. In order to use the VDQ method, the irregular domain of the element is transformed into a regular one employing the mapping technique. Finally, the assemblage procedure is performed to present total mass and stiffness matrices. The introduced numerical approach can be effectively used for structural analysis of arbitrarily shaped plates. A wide range of comparative and convergence studies are outlined to show the performance of the method. It is observed that the numerical results are rapidly converged and the proposed solution strategy can be successfully applied to examine the vibration of FG-CNTRC plates with different cutouts.

Static and Free Vibration Analyses of Functionally Graded Carbon Nanotube Reinforced Composite Plates using CS-DSG3

This study presents an extension of the cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular elements for the static and free vibration analyses of carbon nanotube reinforced composite (CNTRC) plates. The single-walled carbon nanotubes (SWCNTs) are assumed to be uniformly distributed (UD) and functionally graded (FG) distributed along the thickness direction. The material properties of carbon nanotube-reinforced composite plates are estimated according to the rule of mixture. The governing equations are developed based on the first-order shear deformation plate theory (FSDT). In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on the whole triangular element is used to smooth the strains on these three sub-triangles. Effects of several parameters, such as the different distribution of carbon nanotubes (CNTs), nanotube volume fraction, boundary condition and width-to-thickness ratio of plates are investigated. In addition, the effect of various orientation angles of CNTs is also examined in detail. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available results in the literature.

Free Vibration Analysis of Smart Laminated Functionally Graded CNT Reinforced Composite Plates via New Four-Variable Refined Plate Theory

This paper presents a new four-variable refined plate theory for free vibration analysis of laminated piezoelectric functionally graded carbon nanotube-reinforced composite plates (PFG-CNTRC). The present theory includes a parabolic distribution of transverse shear strain through the thickness and satisfies zero traction boundary conditions at both free surfaces of the plates. Thus, no shear correction factor is required. The distribution of carbon nanotubes across the thickness of each FG-CNT layer can be functionally graded or uniformly distributed. Additionally, the electric potential in piezoelectric layers is assumed to be quadratically distributed across the thickness. Equations of motion for PFG-CNTRC rectangular plates are derived using both Maxwell’s equation and Hamilton’s principle. Using the Navier technique, natural frequencies of the simply supported hybrid plate with closed circuit and open circuit of electrical boundary conditions are calculated. New parametric studies regarding the effect of the volume fraction, the CNTs distribution, the number of layers, CNT fiber orientation and thickness of the piezoelectric layer on the free vibration response of hybrid plates are performed.

Vibration analysis of porous magneto-electro-elastically actuated carbon nanotube-reinforced composite sandwich plate based on a refined plate theory

In this article, the free vibration response of sandwich plates with porous electro-magneto-elastic functionally graded (MEE-FG) materials as face sheets and functionally graded carbon nanotube-reinforced composites (FG-CNTRC) as core is investigated. To this end, four-variable shear deformation refined plate theory is exploited. The properties of functionally graded material plate are assumed to vary along the thickness direction of face sheets according to modified power-law expression. Furthermore, properties of FG-CNTRC layer are proposed via a mixture rule. Hamilton’s principle with a four-variable tangential–exponential refined theory is used to obtain the governing equations and boundary conditions of plate. An analytical solution approach is utilized to get the natural frequencies of embedded porous FG plate with FG-CNTRC core subjected to magneto-electrical field. A parametric study is led to fulfill the effects of porosity parameter, external magnetic potential, external electric voltage, types of FG-CNTRC, and different boundary conditions on dimensionless frequencies of porous MEE-FG sandwich plate. It is noteworthy that the numerical consequences can serve as benchmarks for future investigations for this type of structures with porous mediums.

Analytical investigation on nonlinear dynamic behavior and free vibration analysis of laminated nanocomposite plates

This work presents the results of the dynamic behavior and natural frequencies of laminated polymer plates that are reinforced by carbon nanotubes. The laminated nanocomposite plates have two components: carbon nanotubes reinforced in different polymer matrices. The nonlinear equations are obtained by Reddy's third-order laminated plate theory with von Kármán's geometrical nonlinearity and solved by both Runge–Kutta and Galerkin methods. Detailed studies for the influences of carbon nanotubes' different types of reinforcements and weight fractions, geometrical parameters, Winkler and Pasternak foundations on the deflection–time curves, and natural frequencies of laminated functionally graded carbon nanotube-reinforced composite plates are examined.

Isogeometric FE analysis of CNT-reinforced composite plates: free vibration

Free vibration behavior of carbon nanotube-reinforced composite plates is studied here, using isogeometric analysis (IGA) based on a higher-order shear deformation theory (HSDT). Carbon nanotubes are considered dispersed into matrix in four different types of volume fraction distributions varying across the thickness. The formulation developed is approximated according to the HSDT model and is incorporated into a computer program developed in-house. IGA uses the same basis function for exact geometric modeling and for analysis, i.e., non-uniform rational B-spline basis function which can easily model the complex geometries exactly, and it can also achieve any desired degree of continuity through the choice of interpolation order so that this method can easily fulfill the C1 continuity for the HSDT model. The effect of variation of width-to-thickness ratio, plate aspect ratio and other parameters, on natural frequencies, are evaluated from parametric studies after due validation with the given literature which is done in FORTRAN.

Elastic guided waves in fully-clamped functionally graded carbon nanotube-reinforced composite plates

This paper is to study the size-dependent characteristics of elastic guided waves in a Functionally Graded Carbon Nanotube-Reinforced Composite (FG-CNTRC) plate with fully clamped ends. The material properties of FG-CNTRC plate vary along the thickness direction via three different distributions of carbon nanotubes. First-order shear deformation plate theory in the framework of Eringen nonlocal differential model is applied to investigate the FG-CNTRC plate. An analytical solution is used to solve the equations of wave motion. Some numerical examples about dispersion curves are given, and the influences of distributions of carbon nanotubes, geometry conditions, the volume fraction of carbon nanotubes, and nonlocal size-dependency on the dispersion are analyzed. In addition, the size-dependent characteristics of elastic guided waves, which has not been mentioned in the previous studies of the FG-CNRC plate, are found with the dispersion curves.

An Edge-Based Smoothed Discrete Shear Gap Method for Static and Free Vibration Analyses of FG-CNTRC Plates

In this paper, an edge-based smoothed stabilized discrete shear gap method (ES-DSG) is integrated with the C0-type high-order shear deformation plate theory (C0-HSDT) for free vibration and static analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The material properties of FG-CNTRC are assumed to be graded through the thickness direction according to several distributions of the volume fraction of carbon nanotubes (CNTs). The stiffness formulation of the ES-DSG based on C0-HSDT is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements. This hence does not require shear correction factors. The accuracy and reliability of the proposed method are confirmed in several numerical examples.

On the vibration of postbuckled functionally graded carbon nanotube-reinforced composite annular plates

This paper studies the free vibration charachterstics of post-buckled functionally graded nanocomposite annular plates reinforced by single-walled carbon nanotubes (SWCNTs). The analysis is performed by employing a generalized differenitail quadrature (GDQ)-type numerical technique and psedue arc-length continuation scheme. The SWCNT reinforcement is considered to be either uniformly distributed (UD) or functionally graded (FG) in the thickness direction. The material properties of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates are estimated using an equivalent continuum model based on the modified rule of mixture. The vibration problem is formulated on the basis of the first-order shear deformation theory for moderately thick laminated plates and von Karman geometric nonlinearity. By employing Hamilton’s principle and a variational approach, the governing equations and the associated boundary conditions (BCs) are derived which are then discretized via the GDQ method. The postbuckling characteristics of FG-CNTRC annular plates are investigated by plotting the equilibrium postbuckling path as the load-deflection curves. Thereafter, the free vibration behavior of FG-CNTRC annular plates in pre- and post-buckled states is examined. Effects of different parameters including type of BCs, CNT volume fraction, outer radius-to-thickness ratio and inner-to-outer radius ratio are investigated in detail.

Static and Dynamic Behavior of Nanotubes-Reinforced Sandwich Plates Using (FSDT)

Based on the first order shear deformation plate theory (FSDT) in the present studie, static and dynamic behavior of carbon nanotube-reinforced composite sandwich plates has been analysed. Two types of sandwich plates, namely, the sandwich with face sheet reinforced and homogeneous core and the sandwich with homogeneous face sheet and reinforced core are considered. The face sheet or core plates are reinforced by single-walled carbon nanotubes with two types of distributions of uniaxially aligned reinforcement material which uniformly (UD-CNT) and functionally graded (FG-CNT). The analytical equations are derived and the exact solutions for bending and vibration analyses of such type’s plates are obtained. The mathematical models provided and the present solutions are numerically validated by comparison with some available results in the literature. Influence of Various parameters of reinforced sandwich plates such as aspect ratios, volume fraction, types of reinforcement and plate thickness on the bending and vibration analyses of carbon nanotube-reinforced composite sandwich plates are studied and discussed. The findings suggest that the (FG-CNT) face sheet reinforced sandwich plate has a high resistance against deflections compared to other types of reinforcement. It is also revealed that the reduction in the dimensionless natural frequency is most pronounced in core reinforced sandwich plate.

A comprehensive study on the free vibration of arbitrary shaped thick functionally graded CNT-reinforced composite plates

The main objective of this paper is to analyze the free vibration of arbitrary shaped thick functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates based on the higher-order shear deformation theory (HSDT) using a variational differential quadrature approach. By means of the generalized differential quadrature (GDQ) numerical operators and Hamilton’s principle, the discretized equations of motion are obtained. In order to use the GDQ differential and integral operators appropriately, the coordinate transformation is considered through the conventional finite element approach for transforming the irregular domain of the plate into the regular computational one. Employing a unified numerical approach to analyze different shapes of thick FG-CNTRC plates based on HSDT is the main novel aspect of the present study. To imply the accuracy of the present model, a wide range of comparison studies are presented. The results indicate the efficiency of the developed numerical methodology to study the vibration of arbitrary shaped thick FG-CNTRC plates. Several results are also given to investigate the impacts of geometrical parameters and material properties on the vibrational behavior of FG-CNTRC plates.

Thermal buckling analysis of temperature-dependent FG-CNTRC quadrilateral plates

The main objective of the present study is to analyze the thermal buckling of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) quadrilateral plates. Functionally graded patterns are introduced for the distribution of the carbon nanotubes (CNTs) through the thickness direction of the plate. The effective material properties of nanocomposite plate reinforced by CNTs are considered to be temperature-dependent (TD) and estimated using the micromechanical model. By the use of minimum total potential energy principle and based on the first-order shear deformation theory of plates, the stability equations are obtained. In order to use the generalized differential quadrature (GDQ) method and solve the stability equations, the irregular domain of quadrilateral plate is transformed into regular computational domain employing the mapping technique. The efficiency and accuracy of the proposed approach are first validated. Then, a comprehensive parametric study is presented to examine the effects of model parameters on the thermal buckling of FG-CNTRC quadrilateral plates. The results indicate that considering temperature dependency of the material properties plays an important role in the stability of the FG-CNTRC quadrilateral plates subjected to thermal loading.

Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation

This work examines vibration and bending response of carbon nanotube-reinforced composite plates resting on the Pasternak elastic foundation. Four types of distributions of uni-axially aligned single-walled carbon nanotubes are considered to reinforce the plates. Analytical solutions determined from mathematical formulation based on hyperbolic shear deformation plate theory are presented in this study. An accuracy of the proposed theory is validated numerically by comparing the obtained results with some available ones in the literature. Various considerable parameters of carbon nanotube volume fraction, spring constant factors, plate thickness and aspect ratios, etc. are considered in the present investigation. According to the numerical examples, it is revealed that the vertical displacement of the plates is found to diminish as the increase of foundation parameters; while, the natural frequency increase as the increment of the parameters for every type of plate.

A comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates

This paper presents a model which is effective and simple based upon Second Order Shear Deformation Theory (SSDT) to comprehensive study of Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) plates including size effects for the first time. Also it is the first time that the size-dependent static, stability and dynamic response of FG-CNTRC plates considering Winkler–Pasternak elastic foundation effects are investigated. It is assumed that the material properties of FG-CNTRC are varied through the thickness direction using four different distributions of carbon nanotubes (CNTs). In order to include the size effects in our modeling, the nonlocal elasticity theory presented by Eringen is utilized. The influences of different parameters such as volume fraction of carbon nanotubes, nonlocality and elastic foundation effects on the response of FG-CNTRC plates are studied. Numerical results prove high accuracy and reliability of the present method in comparison with other available numerical or analytical methods.

Vibration of FG-CNTRC annular sector plates resting on the Winkler-Pasternak elastic foundation under a periodic radial compressive load

The vibration and stability of functionally graded carbon nanotube-reinforced (FG-CNTRC) composite annular sector plates resting on Winkler-Pasternak elastic foundation subjected to a periodic radial compressive load are investigated for various boundary conditions. To this end, a shear deformable plate model is established according to a parabolic theory which can interpret the shear deformation and rotary inertia effects without using any shear correction factor. The modified micromechanical technique is employed to compute the effective material properties of the FG-CNTRCs. The discretized form of higher-order governing equations is directly accessed by employing Hamilton’s principle and the variational differential quadrature (VDQ) method. In addition, by considering the applied radial compressive force as a periodic function, the discretized equations are expressed as the Mathieu–Hill equations, and then the instability regions are determined via the Bolotin’s scheme. In numerical results, the effects of the CNT distribution pattern and volume fraction, geometry parameters, sector angle, elastic foundation and static load factor on the stability of FG-CNTRC annular sector plates subject to arbitrary edge conditions are thoroughly discussed.

Effect of Perforation on the Bending Behavior of Temperature-Dependent Carbon Nanotube Reinforced Composite Plate

In the present article, the bending behaviour of carbon nanotube reinforced composite plate subjected to thermomechanical loading is examined with and without perforations. For the computational purpose, fully clamped support condition is considered. The carbon nanotube reinforced composite plate is comprised of single-walled carbon nanotube reinforced composite as fibre and PmPV as matrix material. The extended rule-of-mixture is employed to evaluate the temperature-dependent material properties of carbon nanotube reinforced composite panel. The bending responses are obtained through finite element tool ANSYS APDL via eight-nodded shell element (SHELL281) with forty eight degrees-of-freedom per element. The kinematic model of the present carbon nanotube reinforced composite plate is based on the first-order shear deformation theory. To exhibit the efficacy of the present model, the present responses are compared with those of the previously published literature. The effect of different parameters such as temperature, thickness ratio, volume fraction and perforation on the bending behaviour of carbon nanotube reinforced composite plate is illustrated through numerous numerical examples.

The effect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates

The purpose of the present study is to examine the impact of initial geometric imperfection on the nonlinear dynamical characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular plates under a harmonic excitation transverse load. The considered plate is assumed to be made of matrix and single-walled carbon nanotubes (SWCNTs). The rule of mixture is employed to calculate the effective material properties of the plate. Within the framework of the parabolic shear deformation plate theory with taking the influence of transverse shear deformation and rotary inertia into account, Hamilton's principle is utilized to derive the geometrically nonlinear mathematical formulation including the governing equations and corresponding boundary conditions of initially imperfect FG-CNTRC plates. Afterwards, with the aid of an efficient multistep numerical solution methodology, the frequency-amplitude and forcing-amplitude curves of initially imperfect FG-CNTRC rectangular plates with various edge conditions are provided, demonstrating the influence of initial imperfection, geometrical parameters, and edge conditions. It is displayed that an increase in the initial geometric imperfection intensifies the softening-type behavior of system, while no softening behavior can be found in the frequency-amplitude curve of a perfect plate.