Graded Carbon Nanotube-reinforced Composite Plates Research Articles

Nonlinear dynamic analysis of functionally graded carbon nanotube-reinforced composite plates using MISQ20 element

Nonlinear dynamic analysis of functionally graded carbon nanotube-reinforced composite plates using MISQ20 element

Three-Dimensional Thermal Vibration of CFFF Functionally Graded Carbon Nanotube-Reinforced Composite Plates

Three-Dimensional Thermal Vibration of CFFF Functionally Graded Carbon Nanotube-Reinforced Composite Plates

Piezoelectric Patches for Deflection Control of Functionally Graded Carbon Nanotube-Reinforced Composite Plates

In the present work, a smart structure is being investigated, where a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate is equipped with piezoelectric actuators to provide vibration control. Due to their high mechanical properties coupled with lightweight, FG-CNTRCs are mainly used in the aerospace industry and in advanced engineering applications. The CNTs have a linear and non-linear distribution along the thickness of the plate and are distributed according to five configurations, namely: UD, FG-X, FG-O, FG-A and FG-V. The first order shear deformation (FOSD) theory is considered in the formulation of a 9-node quadratic finite element with 5 degrees-of-freedom per node, and an additional degree of freedom is provided for the piezoelectric layer. The model developed in this study assesses the free vibration behavior and controls the nanocomposite plate deflection through the electromechanical coupling factor piezoelectric. In addition, it investigates: (i) the effect of the plate configuration, (ii) the CNT volume fraction, (iii) the CNT destruction patterns, (iv) the linear and nonlinear distribution of CNTs, (v) the number of CNTRC ply, (vi) the boundary conditions and (vii) the dimensions with different locations of actuators. The results obtained show the first natural frequencies for all configurations, which are considered to be in good agreement with those available in the literature and illustrate that the effective stiffness of the nanocomposite plates can be improved further when the reinforcement is dispersed according to the FG-X pattern. In addition, for the case of the deflection control analysis, results indicate that the distributed piezoelectric layers (actuators) attenuate the deflection of the CNTRC to the desired tolerance. It is noted that patches with partial coverage compared to the case of total coverage of piezoelectric layers require more electrical power to reach the same level of attenuation. The developed numerical model is intended to be used in a variety of potential advanced engineering applications.

Three-dimensional isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates

Three-dimensional isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates

Nonlinear flutter analysis of functionally graded carbon

In this paper, geometrical nonlinear flutter analysis of functionally graded carbon nanotube-reinforced composite plates is presented. The governing equations of the system are obtained using the Mindlin plate theory and von Karman geometric nonlinearity. The linear piston theory is utilized to determine the aerodynamic pressure. Applying the Hamilton principle, equations of motion of a system are derived in the matrix form, and then the finite element method is used to obtain the discretized equations. Application of Newmark’s time integration and Newton–Raphson method are used to solve the nonlinear oscillation equations for determining the nonlinear flutter response and critical flow velocity. To check the validity of the present formulation, numerical results are compared with the previous data in the literature. The effects of stiffeners, type carbon nanotube (CNT) and angle of attack of airflow, thickness (ratio h/a) of the plate on critical airflow velocity and nonlinear dynamic response of the SFG-CNTRC plates are studied.

Static and thermal instability analysis of embedded functionally graded carbon nanotube-reinforced composite plates based on HSDT via GDQM and validated modeling by neural network

Static and thermal instability analysis of embedded functionally graded carbon nanotube-reinforced composite plates based on HSDT via GDQM and validated modeling by neural network

Multi-Objective Optimization of Laminated Functionally Graded Carbon Nanotube-Reinforced Composite Plates Using Deep Feedforward Neural Networks-NSGAII Algorithm

This paper proposes a novel and efficient DNN-NSGAII approach which is an integration of the deep feedforward neural network (DNN) and the nondominated sorting genetic algorithm II (NSGAII) to solve multi-objective optimization (MOO) problems of laminated functionally graded carbon nanotube-reinforced composite (FG-CNTRC) quadrilateral plates. The core idea of the proposed approach is to use the DNN as an analyzer to evaluate the objective and constraint functions instead of using the time-consuming finite element analysis methods (FEAMs) during the optimization process, while the NSGAII is employed to find a set of Pareto-optimal solutions of the MOO problems. Accordingly, the proposed DNN-NSGAII remarkably saves the computational cost, but still provides a high accurate optimal solution. The precision, efficiency, and capability of the proposed method are demonstrated through two different MOO problems of the FG-CNTRC quadrilateral plates. Obtained results of the DNN-NSGAII are compared with those of other methods to investigate the reliability and efficiency of proposed method. Moreover, the effects of various boundary conditions and carbon nanotube (CNT) distributions on the Pareto-optimal solutions of MOO problems are also examined.

A deep feed-forward neural network for damage detection in functionally graded carbon nanotube-reinforced composite plates using modal kinetic energy

A deep feed-forward neural network for damage detection in functionally graded carbon nanotube-reinforced composite plates using modal kinetic energy

Dynamic property of functionally graded carbon nanotube-reinforced composite plates with viscoelastic core

There is no literature on the dynamic property of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates with a viscoelastic core. So this paper exhibits an application of the first-order discrete layer model combined with the Navier solution to the dynamic property analysis of FG-CNTRC sandwich plates. Five stacking sequences of FG-CNTRC sandwich plates are taken into account. The extended mixture rule method is adopted to evaluate the effective properties of the FG-CNTRC. Kinematic relations of the FG-CNTRC sandwich plates are developed based on first-order plate theory. Then the dynamic equations are deduced according to the Hamilton approach and are simplified using displacement continuity conditions at the interfaces. After validating the efficiency and accuracy, detailed parametric studies are carried out to reveal the change rule of vibration frequencies and loss factors of five kinds of FG-CNTRC sandwich plates for obtaining a better dynamic property. The numerical results can provide a reference for engineers to design large stiffness and high damping composite structures.

The Linear and Nonlinear Bending Analyses of Functionally Graded Carbon Nanotube-Reinforced Composite Plates Based on the Novel Four-Node Quadrilateral Element

This paper presents the linear and nonlinear analyses of functionally graded carbon nanotube- reinforced composite (FG-CNTRC) plates using a four-node quadrilateral element based on the C0-type of Shi’s third-order shear deformation theory (C0-STSDT). Shi’s theory is taking the advantages and desirable properties of the third-order shear deformation theory. Besides, material properties of FG-CNTRC plates are changed from the bottom to top surface and based on the rule of mixture. Numerical results and comparison with other reference solutions suggest that the advantages of present element are accuracy and efficiency in analysis of FG-CNTRC plates. Some nonlinear numerical results of FG-CNTRC plates are also given in this paper and this contributes to providing additional data for future research work.

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.

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.

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.

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.

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.

Large amplitude flutter analysis of functionally graded carbon nanotube reinforced composite plates with piezoelectric layers on nonlinear elastic foundation

This paper presents a study of geometrical nonlinear flutter of functionally graded carbon nanotube-reinforced composite plates embedded with piezoelectric layers subjected to supersonic flow on nonlinear elastic foundation. The governing equations of the system are obtained using the classical plate theory and von Karman geometric nonlinearity. The linear piston theory is utilized to evaluate the aerodynamic pressure. Galerkin method is used to reduce the governing equations to an ordinary differential equation with respect to time in the form of Duffing equation. The homotopy perturbation method is employed to study the effect of large amplitude on the nondimensional flutter pressure. It is assumed that carbon nano-tubes are distributed along thickness in two different manners namely uniform distribution and functionally graded. The effects of volume fraction of carbon nanotubes, large amplitude, different distribution types, piezoelectric layers, and applied voltage on flutter pressure are studied.

Nonlinear thermo-elastic bending of functionally graded carbon nanotube-reinforced composite plates resting on elastic foundations by dynamic relaxation method

ABSTRACTIn this study, the nonlinear thermo-elastic bending analysis of a functionally graded carbon nanotube-reinforced composite plate resting on two parameter elastic foundations is investigated. The material properties of the carbon nanotube-reinforced composite plates are assumed to be temperature dependent and graded in the thickness direction. The nonlinear formulations are based on a first-order shear deformation plate theory and large deflection von Karman equations. A dynamic relaxation method is employed to solve the plate nonlinear partial differential equations. The effects of volume fraction of carbon nanotubes, thermal gradient, temperature dependency, elastic foundation, boundary conditions, plate width-to-thickness ratio, aspect ratio, and carbon nanotubes distribution are studied in detail.

A new approach for nonlinear buckling analysis of imperfect functionally graded carbon nanotube-reinforced composite plates

This paper presents an analytical approach to analyze the nonlinear static buckling of imperfect functionally graded carbon nano-reinforced composite (FG-CNTRC) plates subjected to axial compression. The material properties of the FG-CNTRC are assumed to be graded through the thickness direction according to several linear distributions of the volume fraction of carbon nanotubes. The theoretical formulations are based on the classical plate theory (Kirchhoff plate) with von Karman-type of nonlinearity and the initial geometrical imperfection. The approximate solution is developed for simply supported and freely movable boundary conditions. By applying the traditional Galerkin method and the Airy stress function, the results for the critical load are obtained in closed-form solutions, which are convenient to be used in engineering design. Some illustrative examples are also presented in details to investigate the effects of the imperfection, carbon nanotubes, and geometrical parameters on the nonlinear static behavior the plates.

Buckling Analysis of Functionally Graded Carbon Nanotube-reinforced Composite Plates using Incremental Loading and Dynamic Relaxation Methods

Buckling Analysis of Functionally Graded Carbon Nanotube-reinforced Composite Plates using Incremental Loading and Dynamic Relaxation Methods

Forced vibration analysis of functionally graded carbon nanotube-reinforced composite plates using a numerical strategy

In this paper, the nonlinear forced vibration behavior of composite plates reinforced by carbon nanotubes is investigated by a numerical approach. The reinforcement is considered to be functionally graded (FG) in the thickness direction according to a micromechanical model. The first-order shear deformation theory and von Kármán-type kinematic relations are employed. The governing equations and the corresponding boundary conditions are derived with the use of Hamilton's principle. The generalized differential quadrature (GDQ) method is utilized to achieve a discretized set of nonlinear governing equations. A Galerkin-based scheme is then applied to obtain a time-varying set of ordinary differential equations of Duffing-type. Subsequently, a time periodic discretization is done and the frequency response of plates is determined via the pseudo-arc length continuation method. Selected numerical results are given for the effects of different parameters on the nonlinear forced vibration characteristics of uniformly distributed carbon nanotube- and FG carbon nanotube-reinforced composite plates. It is found that with the increase of CNT volume fraction, the flexural stiffness of plate increases; and hence its natural frequency gets larger. Moreover, it is observed that the distribution type of CNTs significantly affects the vibrational behavior of plate. The results also show that when the mid-plane of plate is CNT-rich, the natural frequency takes its minimum value and the hardening-type response of plate is intensified.