Graded Carbon Nanotube-reinforced Composites Research Articles

Buckling and post-buckling of anisogrid lattice-core sandwich plates with nanocomposite skins

This research offers an in-depth examination of the buckling and post-buckling responses observed in sandwich plates distinguished by the presence of an anisogrid lattice core and face layers composed of functionally graded carbon nanotube-reinforced composites (FG-CNTRC). To model this structure, a global continuous model for the lattice core is employed, while the displacement field is approximated using the First-Order Shear Deformation Theory (FSDT). Geometrically nonlinear strain relations based on the von-Kármán assumptions are incorporated to accurately capture the structural response. The homogenization of the FG-CNTRC skins is achieved through the modified rule of mixture, enabling estimations of effective material properties. To separate pre-buckling and post-buckling phases, we implement the adjacent-equilibrium criterion. Solving the linear (pertaining to buckling) and nonlinear (related to post-buckling) equations is based on the Generalized Differential Quadrature (GDQ) technique alongside an iterative method grounded in the displacement control strategy. Our analysis explores the influence of core and skin characteristics on the stability of these sandwich plates. By examining critical buckling thresholds, post-buckling equilibrium paths, and the underlying mechanisms driving these responses, we contribute insights into the structural stability and performance of such composite structures. This study not only enhances our understanding of buckling behavior in anisogrid lattice core sandwich plates but also holds promise for diverse engineering applications where structural stability is paramount.

A NURBS-based IGA using zig-zag plate theory for nonlinear passive/semi-active damping analysis of laminated FG-CNTRC plates

This study introduces an efficient and versatile numerical approach for simulating passive/semi-active damping treatments on laminated structures composed of functionally graded carbon nanotube-reinforced composites (FG-CNTRC) plates. This novel approach integrates an isogeometric finite element formulation that leverages basic functions generated from Non-Uniform Rational Basis Spline (NURBS) with the Murakami zig-zag theory, Von Kármán’s nonlinear strain–displacement model, and the electro-mechanical coupling properties of the constraining layers. The proposed isogeometric formulation can be transformed into the Laplace domain using the Golla–Hughes–McTavish model to successfully simulate the time-dependent passive/semi-active damping mechanism of viscoelastic materials. Subsequently, results obtained in the Laplace domain are reconverted into the time domain using inverse techniques. The validation of the proposed model through two numerical examples showcases its high reliability and demonstrates the feasibility of simulating and controlling FG-CNTRC plates with various geometries within a Computer-Aided Design-Computer-Aided Engineering (CAD-CAE) analysis framework.

Using Laurent’s series in the theoretical solution to estimate the stress resultants of FG-CNTRC plates weakened by a central cutout at different temperatures

Conventional ordinary materials have many weaknesses when exposed to extreme loadings. Hence, scientists develop novel engineered materials to address these weaknesses. Functionally Graded Carbon Nanotube Reinforced Composites (FG-CNTRCs) are a modern group of materials that have recently flourished thanks to their excellent and unique mechanical properties. One common loading condition is subjecting FG-CNTRC plates containing cutouts to in-plane loadings. The presence of an opening disturbs the stress field, especially in the proximity of the cutout, and creates stress concentration. This study estimates the stress and moment resultants on the edge of elliptical cutouts in asymmetric FG-CNTRC plates under various loading conditions using a new analysis based on Lekhnitskii’s complex variables method, mapping function, and Laurent series. Unlike previous studies on perforated asymmetric plates, which were based on numerical methods or the Schwartz formulations, this study presents a new solution using Laurent’s series to represent the holomorphic function. In calculating the stress and moment components around the opening, the effect of determining variables is studied. This approach can be generalized to solve different anisotropic body problems (FG_CNTRC, FGM, Laminate composites). Thus, stress and moment components in perforated anisotropic plates can be determined simply and systematically using this method.

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.

Buckling analysis of carbon nanotube reinforced FG shells using an efficient solid-shell element based on a modified FSDT

This study investigates buckling behaviors of functionally graded carbon nanotube-reinforced composites (FG-CNTRC) shells using a modified first-order enhanced solid-shell element formulation. On that account, a parabolic shear strain distribution through the shell thickness in the compatible strain part is proposed. In fact, the shear correction factors are no longer needed. Five kinds of single-walled carbon nanotubes (SWCNTs) distribution through the thickness of layers are considered, namely, uniform (UD) and functionally graded (FG) symmetric and asymmetric. The buckling behavior of FG-CNTRC plate under uniaxial compressive pressure and FG-CNTRC cylindrical shell under external pressure and axial compression are considered. Comparisons of our numerical results with those reported by other investigators are presented in order to compare different formulations and to illustrate the performance of the developed solid-shell element. The result of the buckling behavior of CNTRC structure makes the present formulation appropriate for a wide range of structure plates and shells. Then, the effects of some geometrical and material parameters on the critical buckling load of shell structures are investigated. • Buckling analysis of carbon nanotube-reinforced FG shells is studied. • Modified first-order enhanced solid-shell element is developed. • Parabolic shear strain distribution through the shell thickness is imposed. • The shear correction factors are no longer needed.

Big data in nanocomposites: ONN approach and mesh-free method for functionally graded carbon nanotube-reinforced composites

Abstract In this paper, the concept of big data in composite materials for design purpose with focus on functionally graded carbon nanotube reinforced composites (FG-CNTRC) has been addressed through mesh-free method and an optimized neural network (ONN) approach. With this regard, mesh-free method as a robust technique was used to analyze the FG-CNTRC for vibrational frequency. The applied nanocomposite is made of aggregated single-walled carbon nanotubes (CNTs) that are embedded in an isotropic polymer as matrix. The material properties are estimated based on the Eshelby–Mori–Tanaka approach. Then a new multi-step approach was used to find optimized neural network for accurate modeling of the nanocomposite which can be used for later goals of optimization and design. Computational time and accuracy of various algorithms were investigated and compared for big data modeling of nanocomposite to come up with the optimal model. Comparative study of the results was carried out to examine and compare the accuracy of the developed ONN model relative to mesh-free method. Furthermore, a comprehensive parametric study was also performed to investigate the effect of geometrical dimensions, CNT distribution and volume fraction on vibrational frequency of the nanocomposite. Highlights Big data in nanocomposites. Analysis of nanocomposite through mesh-free method. Optimized neural network (ONN) for big data mining. Multi-step approach for finding an optimized model. Efficiency of ONN to handle big data.

Imperfection and tangential edge constraint sensitivities of thermomechanical nonlinear response of pressure-loaded carbon nanotube-reinforced composite cylindrical panels

Initial geometrical imperfection and elasticity of tangential edge constraints are inherent in real structures in general and composite cylindrical panels in particular. This paper investigates the nonlinear response of functionally graded nanocomposite cylindrical panels reinforced by single-walled carbon nanotubes (SWCNTs), exposed to thermal environments and subjected to uniform external pressure. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRC) are assumed to be temperature dependent, graded in the thickness direction, and are estimated by the extended rule of mixture through a micromechanical model. The governing equations are based on classical shell theory taking von Karman–Donnell nonlinearity, initial geometrical imperfection and tangential constraints of boundary edges into consideration. Approximate solutions of deflection and stress functions are assumed to satisfy simply supported boundary conditions, and the Galerkin method is applied to obtain closed-form expressions of load–deflection relations. An analysis of separate and simultaneous influences of carbon nanotube volume fraction and distribution types, geometrical parameters, varying degree of tangential edge constraints, thermal environments, geometrical imperfection and temperature dependence of material properties on the buckling behavior and load-carrying capacity of FG-CNTRC cylindrical panels results in interesting remarks and novelty of the present study.

In-plane and shear buckling analysis of FG-CNTRC annular sector plates based on the third-order shear deformation theory using a numerical approach

The buckling analysis of thick composite annular sector plates reinforced with functionally graded carbon-nanotubes (CNTs) is presented under in-plane and shear loadings based on the higher-order shear deformation theory. It is considered that the plate is resting on the Pasternak-type elastic foundation. The overall material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are estimated through the micromechanical model. The governing equations are derived on the basis of the higher-order shear deformation plate theory, and the quadratic form of the energy functional of the system is presented. An efficient numerical method is presented in the context of variational formulation to obtain the discretized version of stability equations. The validation of the present study is demonstrated through comparisons with the results available in the literature and then comprehensive numerical results are given to investigate the impacts of model parameters on the stability of CNT-reinforced composite annular sector plates.

Postbuckling of pressure-loaded nanotube-reinforced composite doubly curved panels resting on elastic foundations in thermal environments

This paper presents an investigation on the postbuckling behavior of doubly curved nanocomposite panels reinforced by carbon nanotubes (CNTs) subjected to lateral pressure. The functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to have CNTs linearly graded in the thickness direction. The overall mechanical properties of the FG-CNTRCs, which include the thermal effect of CNTs and the matrix, are estimated through a micromechanical model. The panels may rest on elastic foundations. The governing differential equations for the doubly curved panels are based on a higher order shear deformation shell theory with von Kármán strain–displacement relationships and the panel–foundation interaction. The initial deflections caused by lateral pressure and thermal bending stresses are both taken into account. The governing equations are further deduced to a boundary layer type problem that includes nonlinear prebuckling deformations and initial geometric imperfections of the panels which are subsequently solved using a two-step perturbation approach. The influences of CNT volume fraction, temperature variation, panel geometric parameters, as well as foundation stiffness on the postbuckling behavior of FG-CNTRC doubly curved panels are investigated.

Large amplitude free vibration of nanotube-reinforced composite doubly curved panels resting on elastic foundations in thermal environments

A large amplitude vibration analysis is presented for nanocomposite doubly curved panels resting on elastic foundations in thermal environments. The doubly curved nanocomposite panels are studied with the consideration of different types of distributions of uniaxial aligned single-walled carbon nanotubes (SWCNTs). The material properties of the functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction according to linear distributions of the volume fraction of CNTs and are estimated through a micromechanical model. The motion equations are based on a higher order shear deformation theory and von Kármán strain-displacement relationships. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The motion equations are solved by a two-step perturbation approach to determine the nonlinear frequencies of the CNTRC doubly curved panel. The numerical illustrations cover small- and large-amplitude vibration characteristics of CNTRC doubly curved panels resting on Pasternak elastic foundations. The present solutions also highlight the effects of CNT volume fraction, temperature variation, foundation stiffness, panel curvature ratio as well as in-plane boundary conditions on the nonlinear free vibration behaviors of CNTRC doubly curved panels.

Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory

This paper presents a simple and effective formulation based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) to investigate the static and dynamic behavior of functionally graded carbon nano-reinforced composite plates. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded through the thickness direction according to several linear distributions of the volume fraction of carbon nanotubes. The governing equation is approximated according to the HSDT model using isogeometric elements based on Non-Uniform Rational B-Spline (NURBS) basis functions. This achieves naturally any desired degree of continuity through the choice of the interpolation order, so that the method easily fulfils the C1-continuity requirement of the HSDT model. The accuracy and reliability of the proposed method is verified by comparing its numerical predictions with those of other available numerical approaches.

Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method

A first known free vibration characteristics of functionally graded nanocomposite triangular plates reinforced by single-walled carbon nanotubes (SWCNTs) is presented. The first-order shear deformation theory (FSDT) is employed to account for the effect of transverse shear deformation of the plates and the element-free IMLS-Ritz method is used for numerical computation. The triangular nanocomposite plates are studied with the consideration of different types of distributions of uniaxial aligned SWCNTs. Material properties of the functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded through the thickness direction according to linear distributions of the volume fraction of carbon nanotubes. Since no existing results are available for such FG-CNTRC triangular plates, comparisons can only be made with isotropic triangular plates of different angles and thickness-to-width ratios. Stability and accuracy of the present method are demonstrated by convergence studies. New sets of vibration frequency parameters and mode shapes for various FG-CNTRC triangular plates are presented. We have also examined the influence of carbon nanotube volume fraction, plate thickness-to-width ratio, plate aspect ratio, and boundary condition on the plate’s vibration behavior. These new results may serve as benchmarks for future studies.

Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells

The influences of centrifugal and Coriolis forces on the free vibration behavior of rotating carbon nanotube reinforced composite (CNTRC) truncated conical shells are examined. 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. The governing equations are derived based on the first-order shear deformation theory (FSDT) of shells using Hamilton’s principle. The initial mechanical stresses are obtained by solving the dynamic equilibrium equations. The differential quadrature method (DQM) is adopted to discretize the equations of motion and the related boundary conditions. After demonstrating the convergence and accuracy of the presented approach, the effects of angular velocity, Coriolis acceleration, geometrical parameters, type of distribution and volume fractions of carbon nanotubes on the frequency parameters of the CNTRC truncated conical shells are studied. The results reveal that the influences of the type of carbon nanotube distribution and its volume fraction on the frequency parameters depend on the semi vertex angle and angular velocity of the shells and the frequency parameters of the shell with FG asymmetric carbon nanotube distribution can become greater than those of the case with FG symmetric distribution ones.

Thermal analysis of randomly oriented carbon nanotube reinforced functionally graded timoshenko beam

The unique thermal properties of carbon nanotubes (CNT) are utilized to increase the use of functionally graded material (FGM) at higher temperatures which resulted in introduction of a new type of material called as functionally graded carbon nanotube-reinforced composites (FG-CNTRCs). To use the FG-CNTRCs at elevated temperatures, their thermal analysis is very important. In this context, this article presents the thermal analysis of a CNT based FG Timoshenko beam. Material properties distribution is assumed to vary along the thickness direction according to power law distribution and linear distributions. Finite difference method is implemented to find out the temperature distribution. Using first order shear deformation theory (FSDT), expressions for strains and stresses are obtained. The results are compared with temperature distribution according to power law. The effect of CNT distribution on strains and stresses is also observed. Based on these results important conclusions have been drawn.

Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment

In this paper, a free vibration analysis of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs), using the element-free kp-Ritz method, is presented. Different types of distributions of uniaxially aligned SWCNTs are considered. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded through the thickness direction according to several linear distributions of the volume fraction of carbon nanotubes. The governing equations are based on the first-order shear deformation plate theory and the two-dimensional displacement fields are approximated by mesh-free kernel particle functions. Convergence and comparison studies have been carried out to verify the stability and accuracy of the present method for analysis of free vibration of various types of CNTRC plates. In computational simulation, several examples are presented to analyze the effects of carbon nanotue volume fraction, plate width-to-thickness ratio, plate aspect ratio and temperature change on natural frequencies and mode shapes of various types of FG-CNTRC plates, and results for uniformly distributed (UD) CNTRC plates are also provided for comparison. The effect of boundary conditions is also examined.

Large deformation analysis for functionally graded carbon nanotube-reinforced composite plates using an efficient and simple refined theory

In this paper, the nonlinear cylindrical bending behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) is studied using an efficient and simple refined theory. This theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. 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-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The fundamental equations for functionally graded nanocomposite plates are obtained using the Von-Karman theory for large deflections and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as comparators.

Dynamic Stability of Functionally Graded Carbon Nanotube-Reinforced Composite Beams

This article presents a dynamic stability analysis of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to vary in the thickness direction and are estimated through the rule of mixture. The differential quadrature method is employed to convert the governing differential equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and elastic buckling are also discussed as subset problems. A parametric study is conducted to investigate the influences of nanotube volume fraction, slenderness ratio, and end supports on the dynamic stability characteristics of FG-CNTRC beams. Numerical results for composite beams reinforced by uniformly distributed carbon nanotube are also provided for comparison.

Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates

In this paper, the nonlinear cylindrical bending of simply supported, functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs), is studied. The plates are subjected to uniform pressure loading in thermal environments and their geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. 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-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations are reduced to linear differential equation with nonlinear boundary conditions yielding a simple solution procedure. Numerical results are presented to show the effect of the material distribution on the deflections and 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.

Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams

This paper investigates the nonlinear free vibration of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory and von Karman geometric nonlinearity. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction and estimated though the rule of mixture. The Ritz method is employed to derive the governing eigenvalue equation which is then solved by a direct iterative method to obtain the nonlinear vibration frequencies of FG-CNTRC beams with different end supports. A detailed parametric study is conducted to study the influences of nanotube volume fraction, vibration amplitude, slenderness ratio and end supports on the nonlinear free vibration characteristics of FG-CNTRC beams. The results for uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) beams are also provided for comparison. Numerical results are presented in both tabular and graphical forms to investigate the effects of nanotube volume fraction, vibration amplitude, slenderness ratio, end supports and CNT distribution on the nonlinear free vibration characteristics of FG-CNTRC beams.