Carbon Nanotube-reinforced Composite Plates Research Articles

Free flexural vibration of cracked carbon nanotube-reinforced composite plates resting on elastic foundations using XFEM

This paper presents detailed investigations on the free flexural vibration of carbon nanotube-reinforced composite plates with cracks resting on elastic foundations. The higher-order shear deformation theory is implemented in an extended finite element framework to derive the vibration equations of cracked plates. Uniform and graded distribution of carbon nanotubes (CNTs) in the thickness direction of plates are considered. The effective material properties are computed using the Halpin Tsai model and the rule of mixture. The crack in the plate is detected using the level set method. The enrichment of the primary variable is done using enrichment functions to address the crack discontinuity issue. Detailed parametric studies have been performed to explore the effect of cracks, CNT’s volume fraction, gradation pattern of CNTs, thickness ratio of the plate, and the elastic foundations on the frequencies. Comparative results are presented by solving a few numerical examples using in-house MATLAB code to validate and ensure the accuracy and robustness of the proposed model.

Dynamic analysis of carbon nanotube-reinforced composite plates using reduced order isogeometric model

In this work, a reduced order isogeometric model is proposed to analyze the dynamic behavior of carbon nanotube-reinforced composite plates. In which, the mechanical properties of the material are functionallygraded through the plate thickness employing four distributions of carbon nanotubes. A third shear deformation theory is employed to represent the displacement along with the plate thickness, whilst a non-uniform rational B-splines surface is utilized to approximate the displacement in the plate plane. The dynamic responses at important degrees of freedom are resolved by the Newmark method instead of dealing with all degrees of freedom as those of the full model. Accordingly, a reduced order model based on the second-order Neumann series expansion is utilized to build the isogeometric analysis. Several examples are tested to illustrate the ability of the suggested paradigm. Obtained outcomes are compared with those of other works and full model to prove the reliability of the reduced Isogeometric analysis.

Nonlinear buckling and postbuckling of FG-CNTRC sandwich plates with multi-layer corrugated FG-CNTRC core

This paper proposes an analytical solution for the nonlinear buckling behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) sandwich plates under axial compressive and external pressure loads is analytically examined in this paper. The considered plates are designed with the multi-layer corrugated FG-CNTRC core and face sheets. The CNT distribution laws of the multi-layer corrugated core are proposed to ensure the material continuity between FG-CNTRC face sheets and multi-layer corrugated core. Classical plate theory (CPT) with geometrical nonlinearities is utilized to formulate the fundamental expressions. In addition, the Ritz energy method is used to achieve the expressions of compression and pressure postbuckling curves, and axial critical buckling loads. The investigations numerically display the influences of multi-layer corrugated core, material, and geometrical properties on the nonlinear buckling and postbuckling behavior of plates.

Forced vibration assessment of moderately thick carbon nanotube-reinforced composite plates

Carbon nanotubes, distributed in composite sheets with various arrangements, can lead to the development of materials with functionally graded properties. In the present study, the method of spectral components was used to investigate the free vibration frequencies and dynamic responses of single-layer sheets reinforced with carbon nanotubes. The spectral component method offers significant advantages for high-frequency dynamic problems, as it requires fewer fine elements to solve boundary conditions. Based on the first-order shear theory, the governing equations of sheet vibration are derived. The discrete Fourier transform is applied to convert the differential equations from the time domain to the frequency domain. Using dynamic shape functions obtained from the exact solutions, the stiffness matrix of the spectral element is constructed. Dynamic frequency responses are then derived, and time-domain responses are obtained using the inverse Fourier transform. The study extracted the exact natural frequencies of functionally graded sheets and verified them with results from the literature, showing high accuracy with a minimal number of elements. The spectral finite element method of fundamental natural frequencies for different ratios of modulus of elasticity and width-to-thickness ratios obtained were investigated and compared with the results of research. The forced vibration was addressed, demonstrating that the method efficiently captures dynamic responses under different carbon nanotube distributions, with spectral displacements verified through numerical comparison. These findings demonstrate the capability and efficiency of the spectral finite element method for analyzing carbon nanotube-reinforced composite plates.

Thermal Buckling and Postbuckling Analysis of Cracked FG-GPL RC Plates Using a Phase-Field Crack Model

A phase-field crack model is developed for numerical analysis of thermal buckling and postbuckling behavior of a functionally graded (FG) graphene platelet-reinforced composite (FG-GPLRC) plate with a central crack. The inclined central crack is represented according to a stable, effective phase-field formulation (PFF) by introducing a virtual crack rotation. The problem is formulated using first-order shear deformation theory (SDT) incorporated with von Kármán geometric nonlinearity. And it is approximated by combining regular Laplace interpolation functions and crack-tip singular functions in the framework of the 2D extended natural element method (XNEM). Troublesome shear locking is suppressed by applying the concept of the MITC (mixed-interpolated tensorial components)3+ shell element to the present numerical method. The results demonstrate the effectiveness of this method in accurately predicting the critical buckling temperature rise (CBTR) and the thermal postbuckling path. In addition, the parametric results reveal that the CBTR and postbuckling path of the FG-GPLRC plate are distinct from those of the FG carbon nanotube-reinforced composite (FG-CNTRC) plate and remarkably affected by the parameters associated with the crack and graphene platelet (GPL).

Comprehensive Analysis of Static, Buckling, and Free Vibration Behavior of Carbon Nanotube Reinforced Composite Plates on Pasternak’s Elastic Foundation

Comprehensive Analysis of Static, Buckling, and Free Vibration Behavior of Carbon Nanotube Reinforced Composite Plates on Pasternak’s Elastic Foundation

Free vibration analysis of functionally graded composite plates reinforced with linearly and nonlinearly distributed carbon nanotubes in hygrothermal environments

This article presents a novel investigation of the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under hygrothermal environments. It explores both uniform and non-uniform (functionally graded) distributions of CNTs across the plate thickness for the first time. The effective material properties of the CNTRC, considering temperature and moisture dependence, are determined using the extended rule of mixture. First-order shear deformation theory (FSDT) is employed to derive the governing equations incorporating hygro-elastic and thermo-elastic relations. These equations are solved using the finite element method. A validation study verifies the accuracy of the employed approaches. Subsequently, a comprehensive parametric study investigates the influence of plate geometry (length-to-width and width-to-thickness ratios), CNTs volume fraction, boundary conditions, linear and non-linear CNTs distributions, and hygrothermal environments on the free vibration behavior of polymeric nanocomposite plates reinforced with CNTs fillers is conducted. The results reveal that the increase in temperature and moisture leads to a decrease in the effective stiffness of the FG-CNTRC plates.

Dynamic response of laminated functionally graded carbon nanotube-reinforced composite viscoelastic plates

The dynamic response of viscoelastic plates reinforced with functionally graded carbon nanotube-reinforced composite material (FG-CNTRC) under dynamic loads was examined in this work. This research investigates the dynamic analysis of CNTRC plates by single-walled CNTs (SWCNTs). SWCNTs were considered to be straight and aligned, with a homogeneous pattern. Carbon nanotube (CNT) configurations were investigated, inclusive of uniform, and three varieties of FG distributions of CNTs across the thickness. The equation of motion of composite plates was obtained using Hamilton’s principle. The time-dependent equations were derived by applying the Navier solution method to the equation of motion. These equations were converted into the Laplace domain. The Modified Durbin procedure was used to convert the resultant computations from the Laplace field to the time field. The resulting findings were compared to other methods. It was demonstrated that the findings are consistent with those of other methods. Then, sensitivity analysis revealed that CNT volume fractions, damping ratios, and FG distributions had a substantial influence on the quasi-static and dynamic behavior of viscoelastic FG-CNTRC plates. Results show that with the help of the Laplace technique no need to use free vibration frequencies or modes, it is possible to solve the problem quite precisely, effectively, and easily.

Thermoelastic nonlinear vibration and dynamical response of geometrically imperfect carbon nanotube-reinforced composite plates on elastic foundations including tangential edge constraints

The combined influences of initial geometrical imperfection, elasticity of in-plane constraints of edges, elastic foundations and elevated temperature on the nonlinear vibration and dynamical response of carbon nanotube-reinforced composite rectangular plates are investigated in this paper. Carbon nanotubes (CNTs) are reinforced into matrix according to functionally graded distributions. The properties of CNTs and matrix are assumed to be temperature dependent and effective properties of nanocomposite are determined using an extended rule of mixture. Governing equations in terms of deflection and stress function are established within the framework of thin plate theory including von Kármán nonlinearity, geometric imperfection and interactive pressure from elastic foundation. Analytical solutions are assumed for simply supported plates and Galerkin method is applied to result in nonlinear time differential equation. This nonlinear equation is solved using fourth-order Runge–Kutta scheme. Parametric studies are executed to examine numerous influences on the natural frequency, nonlinear to linear frequency ratio and nonlinear dynamical response of CNT-reinforced composite plates. The results reveal that increase in imperfection size results in increase and decrease in natural frequencies and the amplitude of forced vibration, respectively. In contrast, it is found that the elevated temperature reduces the natural frequencies and enhances the amplitude of forced vibration.

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

Thermal Buckling and Vibrational Analysis of Carbon Nanotube Reinforced Rectangular Composite Plates Based on Third-Order Shear Deformation Theory

In this paper, thermal buckling and free vibration of a rectangular plate reinforced with carbon nanotubes (CNT) are investigated within the framework of third-order shear deformation theory (TSDT). CNT distribution along the thickness direction of the plate is uniformly or functionally graded. The equivalent properties of the reinforced composite plate are calculated based on the extended rule of mixture. Governing equations of motion are derived using the Hamilton principle. Obtained governing differential equations are analyzed by utilizing Fourier series expansion along the longitudinal and latitudinal direction for simply supported edges boundary conditions whereas for other edges boundary conditions we used the differential quadrature method (DQM) to solve numerically. Validation of the present formulation is assessed by comparing the results with those reported in the open literature. The effect of CNT volume fraction, the different patterns of CNT distribution, temperature difference, aspect ratio, and thickness-to-length ratio on buckling and vibration behavior of carbon nanotube-reinforced composite (CNTRC) plate is studied. The numerical illustration reveals that in the FG-X pattern of CNT distribution natural frequency and thermal buckling load is more significant compared with the other patterns of CNT distribution.

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

Optimization Design of Laminated Functionally Carbon Nanotube-Reinforced Composite Plates Using Deep Neural Networks and Differential Evolution

This study presents a new approach as an integration of deep neural networks (DNN) into differential evolution (DE) to give the so-called DNN-DE for frequency optimization of laminated functionally graded carbon nanotube (FG-CNT)-reinforced composite quadrilateral plates under free vibration. In the presented approach, the DNN is applied to predict the objective and constraints during the optimization process instead of using the time-consuming finite element analysis (FEA) procedures while the DE is used as an optimizer for solving the optimization problem. Several numerical examples are performed to illustrate the performance of the proposed method. Optimal results obtained by the DNN-DE are compared with those achieved by other methods in order to show the reliability and effectiveness of the proposed methodology. Additionally, the influence of various parameters such as the boundary condition, the carbon nanotube (CNT) volume fraction, the CNT distribution on the optimal results is also investigated. The obtained results indicate that the proposed DNN-DE is an effective and promising method in solving optimization problems of engineering structures.

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.

Nonlinear buckling analysis of higher-order shear deformable FG-CNTRC plates stiffened by oblique FG-CNTRC stiffeners

The nonlinear buckling analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates subjected to axial compression load is analytically examined in this paper. Assuming that the FG-CNTRC plates are stiffened by an oblique FG-CNTRC stiffener system. Reddy’s higher-order shear deformation plate theory (HSDPT) with the geometrical nonlinearities of von Kármán is applied to establish the basic formulations. Moreover, the smeared stiffener technique is successfully improved for the higher-order shear deformable anisotropic oblique stiffener system by using a homogeneous model of the anisotropic beam. Galerkin’s method is used to achieve the expressions of critical buckling loads and postbuckling load-deflection curves in explicit form. The numerical values display the influences of FG-CNTRC stiffeners, material, and geometrical properties on the nonlinear buckling response of plates.

Natural frequency and stability analysis of axially moving functionally graded carbon nanotube-reinforced composite thin plates

Natural frequency and stability analysis of axially moving functionally graded carbon nanotube-reinforced composite thin plates

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.

Nonlinear bending analysis of carbon nanotube-reinforced composite plates in combined thermal and mechanical loading

Nonlinear bending analysis of carbon nanotube-reinforced composite plates in combined thermal and mechanical loading

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

In this research, the stability, and vibrational characteristics of functionally graded single-walled carbon nanotube-reinforced composite (FG-SWCNTRC) plates resting on a Visco-Hetenyi medium are perused based on a 12 unknown higher-order shear deformation theory (HSDT). The system is subjected to hygro-thermal environments and both compressive and tensile in-plane loads in both x- and y-direction. In addition to both linear and nonlinear thermal conditions, a two-dimensional (2D) magnetic field’s effects on the stability of the system are studied. The governing equations of motion are solved numerically by means of the generalized differential quadrature method (GDQM) due to its capability to consider the various geometric boundary conditions (BCs). In order to validate the current work, a comparative study is accomplished between the present outcomes and reported ones in the open literature. The impact of the carbon nanotube (CNT) volume fraction, patterns of CNT distribution, environmental attacks, magnetic field strength and direction, structure aspect ratios, BCs, and foundation types on the vibrational behavior of the considered structure are scrutinized. Obtained results represent that considering the impacts of in-plane tensile forces and the magnetic field in modeling improves the system's vibrational behavior. While imposing the hygro-thermal effects similar to the axial compressive loads have destabilizing influences on the system and make the structure more vulnerable to static instability. Moreover, uncertain conditions are assessed for sensitive parameters which have effects on the performance of the system. Finally, using a supervised neural network (NN) learning approach, the accuracy of the model is proved.