Carbon Nanotube-reinforced Composite Plates Research Articles

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

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

Probabilistic Progressive Failure of Multiwall Carbon Nanotube-Reinforced Composite Plate Under Transverse Patch Loading

Second-order statistics of progressive failure response of multiwall carbon nanotube-reinforced composite (MWCNTRC) plate subjected to the transverse loading is presented. The mathematical model is based on the higher-order shear deformation theory (HSDT) and von Karman nonlinear kinematics through the mechanics of the material approach. Second-order perturbation technique (SOPT) and polynomial chaos (PC) methods are used for the uncertainty quantification. The properties of the MWCNTRC plate are obtained by using the Halpin–Tsai model. Epoxy-matrix reinforced with multiwall carbon nanotube (MWCNT) is considered as a new matrix and boron fiber is reinforced with this new matrix in an orthotropic way to get MWCNTRC. The distribution of volume fraction of carbon nanotube (CNT) in the epoxy matrix is considered in the functionally graded (FG) manner for thermo-mechanical loading. Stochastic progressive failure analysis (PFA) along with the probability of failure of MWCNTRC plate is performed by using the progressive damage model incorporated in the ply discount method and considering randomness in the material properties, the geometry of plate and loading. The conclusions are based on the effect of the parameters like stacking sequence, fiber volume fraction, temperature, CNT distribution, fiber material and number of CNT on the mean of first and last ply failure loads (FPFL and LPFL) and coefficient of variance (COV) of MWCNTRC plate. Stochastic failure analysis of MWCNTRC plate up to last ply failure by considering patch loading, nonlinearity and FG distribution of CNT is unique in this work.

Investigation of Mechanical Behaviors of Functionally Graded CNT-Reinforced Composite Plates.

In this paper, the mechanical behavior of a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate is numerically investigated. According to the concept of a hierarchical model, the displacement is decomposed into the in-field functions and the assumed thickness-wise monomial. The former is defined on the plate midsurface and is approximated by the 2-D meshfree natural element method (NEM). The FG-CNTRC plate is modeled as a homogenized orthotropic body, and its effective elastic properties are determined by referring to MD simulation and the linear rule of mixtures. Regarding the thickness-wise distribution of CNTs, one uniform and three functionally gradient distributions are taken. Through comparative numerical experiments, the reliability of the numerical method is justified with the maximum relative difference of 6.12%. The effects of the volume fraction and vertical distribution of CNTs, the plate width-thickness and aspect ratios, and the boundary conditions on the bending, free vibration, and buckling behaviors of FG-CNTRC plates are examined. It is found that the mechanical behavior of FG-CNTRC plates is significantly dependent of these major parameters.

Nonlinear bending analysis of FG-CNTRC plate resting on elastic foundation by natural element method

A nonlinear numerical analysis is addressed for a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate on elastic foundation. The large deflection bending problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)* hierarchical model. And, it is numerically solved by 2-D (two-dimensional) natural element method (NEM) which is characterized by a high accuracy even for coarse grid. The derived nonlinear matrix equations are iteratively calculated by combining the load increment scheme and the Newton-Raphson iteration method. The present method was verified through the benchmark test, where the present method shows excellent agreement with the reference solutions. The nonlinear behavior of FG-CNTRC plate on elastic foundation is evaluated in terms of the non-dimensional deflection and bending moment. These non-dimensional quantities are examined with respect to the foundation stiffness, the volume fraction and gradient pattern of CNT, the aspect and width-thickness ratios of plate and the boundary condition. From the parametric experiments, it is found that both non-dimensional quantities are significantly influenced by such parameters.

Active Vibration Control of Functionally Graded Carbon Nanotube Reinforced Composite Plate with Coupled Electromechanical Actuation

Piezoelectric materials possess excellent electromechanical coupling characteristics, which are functional and suitable in structural vibration control. This study investigates the active control of free and forced vibration for piezoelectric-integrated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate using the finite element method (FEM). Based on the first-order shear deformation theory (FSDT), the governing equations of the motion of a piezoelectric-integrated FG-CNTRC plate are derived by Hamilton’s principle. The convergence and accuracy of the numerical method is verified through the results of natural frequencies. The influences of CNT volume fraction, CNT distribution type, piezoelectric layer thickness-to-plate thickness ratio, and boundary condition on the natural frequencies are investigated. A constant gain velocity feedback algorithm is used to achieve the dynamic response control of the piezoelectric-integrated FG-CNTRC plate. In addition, the effects of dynamic load, feedback control gain, and boundary condition on the dynamic response of the plate are studied. Numerical results indicate that active control is promising for practical applications in civil and mechanical engineering.

Hygro-thermo-magnetically induced vibration of FG-CNTRC small-scale plate incorporating nonlocality and strain gradient size dependency

Free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) small-scale rectangular plates resting on Kerr foundation and subjected to complex environments and in-plane axial loads are analyzed. Based on the higher-order shear deformation theory (HSDT) and using nonlocal strain gradient theory, governing equations of plate are extracted. Utilizing the generalized differential quadrature method (GDQM), the governing equations of motion are solved numerically. To validate the present work, a comparative study is accomplished between the present results and the reported ones in the literature. Effect of size-dependent parameter, the CNT volume fraction, pattern of CNT distribution, humid and thermal environments, magnetic fields, structure aspect ratios, boundary conditions, and foundation types, on the natural frequencies of the structure are studied. Acquired outcomes represent that considering the impacts of the strain gradient parameter and the magnetic field in modeling improve the system vibrational behavior. While imposing the nonlocal term and hygro-thermal effects similar to the in-plane loads have destabilizing influences on the system and make the structure more vulnerable to static instability. Meanwhile, it is deduced that when the Scale Factor <1 (Scale Factor >1), the softening (hardening) impact of the nonlocal (strain gradient) parameter is prominent on the FG-CNTRC small-scale plate.

Thermal stress analysis of perforated unsymmetric FG-CNTRC plate using a general analytical solution

In this study, based on the development of the complex variable method, a general solution is presented to calculate thermal stresses in unsymmetric functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates weakened by a hole under uniform heat flux. The extracted equations can also be used for thermal analysis of perforated FGM plates and unsymmetric composites laminates. Due to the fact that size and temperature affect the mechanical properties of carbon nanotubes (CNT), the material properties of the unsymmetric FG-CNTRC plates are approximated based on gradual changes in the direction of thickness and extended rule of the mixture. The present analysis considers the effect of important parameters such as CNT volume fraction, CNT angle, hole aspect ratio, hole orientation, and heat flux angle on the distribution of thermal stresses and moments around elliptical and circular holes. The present comprehensive parametric study shows that the aforementioned variables have a significant effect on the thermal stresses in perforated FG-CNTRC plates. Therefore, by properly selecting their values in the design of such plates, thermal stresses can be significantly reduced.

A closed-form solution for thermoelastic stress analysis of perforated asymmetric functionally graded nanocomposite plates

Issues related to stress concentration in cracks, perforated plates, and the use of new generation materials to strengthen this type of plates are of great importance. When a functionally graded carbon nanotube-reinforced composite plate (FG-CNTRC) has a hole in its center of the plate that is exposed to a combination of mechanical and thermal loads, due to various couplings such as bending-extension, shear-extension, and bend-twist couplings that occur in the stress–strain relationships and due to the presence of nonhomogeneous equations, the analytical solution approach will be accompanied by new challenges. Hence, a general solution for the FG-CNTRC plates weakened by a central hole is presented. To achieve this goal, the Lekhnitskii complex potential approach is developed using the appropriate conformal mapping function. The present solution provides the ability to calculate the stress distribution of perforated plates made of asymmetric composite laminates and functionally graded materials by introducing holomorphic potential functions in the form of Laurent series. In this research, an attempt has been made to depict the effect of important parameters on the stress resultants and moments around the hole. The results clearly show that the studied parameters significantly change the stress resultants and moments due to thermal and mechanical loads applied to perforated FG-CNTRC plates. As a result, it is possible to significantly reduce stress resultants and moments by properly selecting the values of effective parameters in the design of such perforated plates.