Graphene-reinforced Composite Research Articles

Nonlinear Forced Vibration of Functionally Graded Graphene-Reinforced Composite (FG-GRC) Laminated Cylindrical Shells under Different Boundary Conditions with Thermal Repercussions

The key aim of this research is to develop an analytical model for the forced vibration of graphene-reinforced composite (GRC) cylindrical shell with viscous damping and thermal environment effects under several boundary conditions. The prescribed mechanical and thermal characteristics of the GRC layer are evaluated utilizing a micromechanical extended Halpin–Tsai technique. Further, the governing equations are determined to be grounded on the shear deformation theory (SDT) with the von Kármán-form in terms of the geometric nonlinearity. The basic nonlinear partial differential governing equation is transformed into a nonlinear ordinary differential equation with the Galerkin-based method. The resulting ordinary governing differential equations are systematically solved based on the multiple scales scheme in order to obtain the nonlinear forced vibration frequency response of the laminated GRC cylindrical shell in the presence of damping impact and subjected to multiple boundary conditions. The validation of the obtained expressions is achieved by comparing them with the available literature data where the comparison revealed a clear consistency between them. Moreover, a parametric investigation is provided to illustrate the impacts of the distribution of graphene layers, elastic foundation coefficients, damping ratios, temperature effects and dimensionless radial excitation amplitude on the forced nonlinear amplitude-frequency ratio responses for a functionally-graded graphene-reinforced composite (FG-GRC)-layered cylindrical shells. The analytical outcomes indicate that the different distribution types of graphene, elastic foundation coefficients, damping ratios, temperature, and radial excitation parameters have a noteworthy impact on the frequency–amplitude behaviors of an FG-GRC-layered cylindrical shell. In addition, the new insights gained from this research might contribute to a deeper understanding of the nonlinear forced vibration responses in subsequent analysis and design techniques for giving appropriate benchmark findings.

Non-linear vibration and parametric optimization of sandwich composite curved shell panels with graphene reinforced skins and auxetic honeycomb core

This study aims to investigate the non-linear free vibration behavior of composite sandwich panels composed of Graphene-reinforced composite (GRC) skins and honeycomb auxetic core. Here, modified Halpin-Tsai micromechanics and bottom-up multi-scale-based schemes are employed to compute the spatial-dependent elastic properties of Graphene nanocomposite and auxetic honeycomb core, respectively. The non-linear kinematic field is based on Kant’s higher-order shear-deformation theory and the Green strain. Using the Hamilton principle, the nonlinear governing equations are affirmed and solved further through Picard’s iteration-based 2D-isoparametric finite element approximations via Lagrangian elements. The mesh convergence and validation tests are executed to confirm the consistency and correctness of the developed model. The established sandwich model is further employed for various parametric conditions by varying the core-to-face sheet thickness, auxetic honeycomb properties, graphene volume fraction, shell configurations, temperature, and support conditions. These numerous results exemplify the non-linear frequencies at small-to-large amplitudes for the sandwich shell structures and are discussed in detail. In addition, parametric optimization is conducted using the response surface method to investigate the optimal values of auxetic honeycomb parameters, resulting in maximum frequency response. Findings confirm that, within the selected ranges of the geometric parameters of auxetic honeycomb core, higher values of the thickness of the cell rib (∼1.9 cm) and the length of the vertical cell rib (∼0.15 cm) and lower value of the core thickness (∼5 cm) yield the maximum frequency.

A Model for Direct Effect of Graphene on Mechanical Property of Al Matrix Composite

Direct effect of graphene on mechanical property of Al matrix composite has been studied by using molecular dynamic (MD) methods. The models of graphene-reinforced composite are achieved by modeling the sintering system consisting of Al particles and graphene nanosheets (GNSs), while pure Al models are obtained by deleting graphene in the composites. Structural analysis on composites indicate the increment of GNSs can promote the densification of metal matrix, increase the porosity in composite, and restrict the metal grain size. Such analysis is also performed on pure Al models, and the similarity in structure between pure Al and composite models is confirmed by the tiny difference in the nanopores, atomic images, and the number of ordered atoms. Tensile processes on the similar structures with or without graphene reveal that the direct effect of graphene shows an obvious anisotropy, low graphene content may weaken the composite in some directions, while high graphene content can strengthen the composite in more directions. However, the highest content of GNSs just brings a slight increase of 2.7% in tensile strength. The atomic images of crack propagation and the atomic stress confirm that graphene is not efficient in load transfer. Therefore, the direct effect of graphene is believed to play a very small role in strengthening mechanisms.

Design and nonlinear dynamics of FG curved sandwich beams with self-adapted auxetic 3D double-V meta-lattice core

The functionally graded (FG) curved sandwich beams with the self-adapted auxetic 3D double-V meta-lattice core and GRC (graphene reinforced composite) facesheets are designed, modeled, and analyzed to reveal their linear vibration and nonlinear dynamic behaviors. The 3D double-V meta-lattices with negative Poisson’s ratio (NPR), developed from the 2D double arrowed honeycombs, are designed that can be self-adapted to meet the spatial requirements of curved sandwich beams. Through micromechanical modeling according to the extended Halpin-Tsai model, the material properties are determined for GRC facesheets, which are further designed to have different distributions of graphene sheets along the structural radial direction, to make the whole sandwich beams possess FG configurations. By linear vibration analysis, the distinct influences of FG configurations on the fundamental natural frequencies are presented. Results from full-scale FE modeling and nonlinear analysis have shown the significant effects of structural curvature radii. The influences of beam lengths, strut radii, thicknesses of the core layer and facesheets, and charge parameters of the blast loadings are followed.

Nonlinear low-velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads

This paper presents an investigation on thermo-electro-mechanical nonlinear low-velocity impact behaviors of the geometrically imperfect functionally graded (FG) graphene-reinforced composite (GRC) beam with surface-bonded piezoelectric layers. Both uniformly distributed and FG patterns of graphene nanoplatelets (GPLs) are considered along the thickness of the GRC host beam. The effective Young’s modulus is calculated by the Halpin–Tsai model. The Poisson ratio and mass density are calculated by the rule of mixture. The modified nonlinear Hertz contact law is employed to predict the impact force between the spherical impactor and the geometrically imperfect GRC piezoelectric beam during impacting. By considering the first-order shear deformation theory and von Kármán nonlinear displacement–strain relationship, the nonlinear governing equations are obtained by Hamilton principle and dispersed by differential quadrature (DQ) method. The Newmark-β method associated with Newton–Raphson iterative process is adopted to parametrically identify the impact force and the dynamic response of the system. The effects of geometric imperfection, weight fraction and distribution pattern of GPLs, temperature variation, thickness of piezoelectric layer and impactor’s initial velocity on nonlinear low-velocity impact behaviors of geometrically imperfect GRC beams are discussed in detail. Our results illustrate that the coupling effect of geometric imperfection and thermo-electro-mechanical load has a significant effect on the nonlinear low-velocity impact behavior of GRC beam, and GPLs distributing into the piezoelectric layers is better for reducing the impact response of geometrically imperfect GRC piezoelectric beam.

Low-velocity impact response of cylindrical sandwich shells with auxetic 3D double-V meta-lattice core and FG GRC facesheets

The cylindrical sandwich shells with auxetic 3D double-V meta-lattice core and functionally graded (FG) GRC (graphene-reinforced composite) facesheets are designed, modeled and analyzed to reveal their nonlinear dynamic response when subjected to low-velocity impact. The 3D double-V meta-lattices, developed from the 2D double arrowed honeycombs, are further self-adapted to meet the requirements of the curved space between facesheets of sandwich shells. By means of micromechanical modeling according to the extended Halpin-Tsai model, the temperature-dependent properties are determined for GRC facesheets, which are further designed to possess FG configurations along the radical direction of the shell structures. Full-scale FE modeling and nonlinear dynamic analysis are then carried out. Numerical results reveal the novelty of FG configurations of GRC facesheets, and include the effects of drop-heights, shell lengths, strut radii, shell radii and thermal environments. Present models, including 3D meta-lattice cores and polymer matrix composite facesheets, are believed to provide new thoughts for the design of lightweight sandwich shells and their applications in the fields of ocean engineering.

Postbuckling of pressure-loaded auxetic sandwich cylindrical shells with FG-GRC facesheets and 3D double-V meta-lattice core

The sandwich cylindrical shells with auxetic 3D double-V meta-lattice core and graphene-reinforced composite (GRC) facesheets are designed, modeled and analyzed to predict their postbuckling behaviors under external pressure. The 3D double-V meta-lattices, developed form the 2D double arrowed honeycombs, are designed that can be self-adapted to meet the requirements of the curvature variation of sandwich cylindrical shells. By means of micromechanical modeling according to the extended Halpin–Tsai model, the material properties are determined for GRC facesheets. Moreover, with the consideration of thermal environments, all the material properties are taken to be temperature-dependent. The GRC facesheets are further designed to have different distributions of graphene sheets along the shell radial direction, to make the sandwich cylindrical shells possess functionally graded (FG) configurations, which has a distinct influence on the buckling and postbuckling behaviors, as demonstrated by numerical results from full-scale FE simulations. The effects of thermal environments, strut radii, shell lengths and curvature radii are also discussed in detail.

A numerical solution for thermal free vibration analysis of rotating pre-twisted FG-GRC cylindrical shell panel

A numerical solution based on finite element method is presented for free vibration analysis of rotating pre-twisted graphene reinforced composite (GRC) cylindrical shell. The piece-wise GRC layers are considered to stack according to functionally graded (FG) scheme across its thickness. The temperature-dependent material properties of the FG-GRCs are estimated using the extended Halpin–Tsai model. The motion equation is formulated through Lagrange's equation of motion considering moderate rotational speeds wherein Coriolis effect is ignored. The effects of type of shell, graphene distribution pattern, pre-twist angle, temperature, rotational speed, and hub radius to blade length ratio on the vibration characteristics are scrutinized.

Buckling and free vibration analysis of shear deformable graphene-reinforced composite laminated plates

Within the framework of the first-order shear deformation theory (FSDT), semi-analytical solutions for buckling and free vibration analysis of graphene-reinforced composite (GRC) laminated plates are presented by the means of the multi-term Kantorovich-Galerkin method. The method begins with expanding the displacements as the products of trial and unknown functions, in which the trigonometric trial functions fulfill all the boundary conditions at two opposite edges. Then, the Galerkin technique is adopted to reduce the governing partial differential equations into the ordinary differential equations, which are solved with the spectral element method (SEM). With the excitation approach, the critical buckling loads and natural frequencies are identified from the response curves and validated with the existing solutions. Then, the effects of graphene distribution pattern, graphene volume fraction, aspect ratio, thickness ratio, and shear correction factor are examined. It is interesting to find that the two uniaxial buckling loads for simply-supported square GRC laminated plates are same, which are twice of the biaxial buckling load. It is also found that the buckling mode under the uniaxial compression along the x direction for the simply-supported GRC laminated plates will change from mode (1,1) to mode (2,1) as the aspect ratio increases from 1 to 1.5.

Mechanical buckling analysis of functionally graded composite laminated plates reinforced with temperature dependent graphene sheets resting on elastic foundation

AbstractPresent study aims to investigate the mechanical buckling including the shear buckling and the in‐plane mechanical buckling of composite laminated plates reinforced with graphene sheets with temperature dependent features resting on Winkler‐Pasternak elastic foundation in a thermal ambient. The governing equations in the framework of the first order shear deformation theory are attacked by the Ritz method. The plate is subjected to uniaxial, biaxial and shear loads. The innovation of the present paper is considering the temperature dependency and anisotropicity of the material properties of a nanocomposite layer that reinforced with graphene sheets for the purpose of the determination of the mechanical buckling treatment of a graphene reinforced composite (GRC) laminated plate with different boundary condition types. Resorting to the extended Halpin–Tsai micromechanical model, the thermo‐mechanical characteristics of a lamina is defined. Numerical outcomes of the present study are confirmed with the presented data in the literature. The effects of the elastic foundation parameter, the temperature, the plate side to its thickness ratio, the layup scheme, the boundary condition type and the distribution pattern of graphene‐reinforced composites on the critical buckling load are investigated. It is found that, the impact of elastic foundation incorporation is less visible on the critical shear buckling load rather than the critical uniaxial and biaxial mechanical loads. Moreover, the largest critical buckling load belongs to layup [0]10 among the all under studied lamination schemes.

Low-velocity impact response of sandwich plates with GRC face sheets and FG auxetic 3D lattice cores

This paper presents multi-scale modeling and nonlinear low-velocity impact analysis of sandwich plates with graphene reinforced composite (GRC) face sheets and functionally graded (FG) auxetic 3D lattice cores. The temperature-dependent material properties of GRC face sheets are determined through a micromechanical model of extended Halpin-Tsai type. The 3D lattice cores are designed to have negative effective Poisson's ratios (EPRs) and possess two FG configurations through the plate thickness direction. Considering the localized deformation and accompanying shape and effective properties changes of 3D lattices, a full-scale FE simulation was then conducted. Numerical results demonstrated that, when compared with their non-auxetic compactors, the auxetic 3D lattice cores can bring about significantly enhanced impact resistance. Moreover, distinct effects of FG configurations are found on both the back face sheet displacements and contact forces of sandwich plates subjected to a rigid spherical impactor. Numerical results show the superiority of FG auxetic lattices. The present model is expected to be instructive for potential engineering applications and beneficial for further research.

Vibration and Snapthrough of Fluid-Conveying Graphene-Reinforced Composite Pipes Under Low-Velocity Impact

There exists complex fluid–structure coupling vibration in the fluid-conveying pipes under the combined actions of internal flow and external loads in the aircraft. The impact dynamic behaviors of the flow-inducing pre- and postbuckled pipes are studied with the surfaces made of functionally graded graphene-reinforced composites and an interlayer made of isotropic viscoelastic materials. It is assumed that the fluid is nonrotating, nonviscous, incompressible; and steady; and the pipe is simply supported at both ends. Under the framework of refined displacement fields, a reduced constitutive relation is developed. On this basis, the nonlinear governing equations are derived through the Hamilton variational principle. The two-step perturbation–Galerkin integral is extended to obtain the equilibrium paths as the initial configurations of the pipes for impact studies. The fourth-order Runge–Kutta method is employed to numerically obtain the contact force and the pipe vibration responses. The effects of flow velocity, impact velocity, structural material, and geometric factors on the dynamic responses are discussed. The numerical results reveal that even the parameters which have little influence on the contact force may have a great effect on the vibration response of the fluid-conveying pipe.

The thermo-elastic vibration of graphene reinforced composite stiffened plate with general boundary conditions

In this numerical study, four different graphene sheets distributions, such as uniformly distributed (UD), functionally graded (FG-X), functionally graded (FG-O), and functionally graded (FG-V), are considered for the free vibration of graphene reinforced composite (GRC) stiffened plate. The graphene is distributed through the thickness of the GRC stiffened plate. The volume fraction of graphene is different in each composite layer except UD cases in which distributions are uniform. The effective material properties of the GRC stiffened plate are obtained based on the Halpin-Tsai approach. An eight-noded isoparametric plate bending element is used to model the present finite element formulation based on first-order shear deformation theory. Three noded isoparametric beam elements with four degrees of freedom per node are used to model the stiffener. In this present investigation, two different X and Y-directional eccentrically at the bottom stiffener is considered. The different parametric studies are also analyzed in this numerical study to determine its consequence on natural frequency. The effect of the number of stiffeners, stiffeners thickness, aspect ratio, thickness ratio, boundary conditions, and temperature on the natural frequency is investigated in detail. The mode shapes of the GRC stiffened plate are also plotted.

Large amplitude vibration of doubly curved FG-GRC laminated panels in thermal environments

Abstract A study on the large amplitude vibration of doubly curved graphene-reinforced composite (GRC) laminated panels is presented in this paper. A doubly curved panel is made of piece-wise GRC layers with functionally graded (FG) arrangement along the thickness direction of the panel. A GRC layer consists of polymer matrix reinforced by aligned graphene sheets. The material properties of the GRC layers are temperature dependent and can be estimated by the extended Halpin-Tsai micromechanical model. The modelling of the large amplitude vibration of the panels is based on the Reddy’s higher order shear deformation theory and the effects of the von Kármán geometric nonlinearity, the panel-foundation interaction and the temperature variation are included in the derivation of the motion equations of the panels. The solutions for the large amplitude vibration of the doubly curved FG-GRC laminated panels are obtained by applying a two-step perturbation approach. A parametric study is carried out to determine the influences of foundation stiffness, temperature variation, FG distribution pattern, in-plane boundary condition and panel curvature ratio on the natural frequencies and the nonlinear to linear frequency ratios of the doubly curved FG-GRC laminated panels.

Nonlinear Dynamics of Temperature-Dependent FG-GRC Laminated Beams Resting on Visco-Pasternak Foundations

This paper studies the nonlinear dynamic responses of graphene-reinforced composite (GRC) beams in a thermal environment. It is assumed that a laminated beam rests on a Pasternak foundation with viscosity and consists of GRC layers with various volume fractions of graphene reinforcement to construct a functionally graded (FG) pattern along the transverse direction of the beam. An extended Halpin–Tsai model which is calibrated against the results from molecular dynamics (MD) simulations is used to evaluate the material properties of GRC layers. The mechanical model of the beam is on the establishment of a third-order shear deformation beam theory and includes the von-Kármán nonlinearity effect. The model also considers the foundation support and the temperature variation. The two-step perturbation technique is first applied to solve the beam motion equations and to derive the nonlinear dynamic load–deflection equation of the beam. Then a Runge–Kutta numerical method is applied and the solutions for this nonlinear equation are obtained. The influence of FG patterns, visco-elastic foundation, ambient temperature and applied load on transient response behaviors of simply supported FG-GRC laminated beams is revealed and examined in detail.

Nonlinear Dynamic Analysis of Functionally Graded Graphene Reinforced Composite Truncated Conical Shells

Functionally graded (FG) graphene reinforced composite (GRC) is a new class of advanced composite materials. In GRC, several layers of graphene platelets (GPLs) are randomly or uniformly dispersed in matrix. These GPLs have uniform arrangement, or are arranged with gradient, in the direction of thickness in accordance with three different graphene distribution rules. In this study, the nonlinear dynamic analysis of FG GRC truncated conical shells, subjected to a combined action of transverse excitation and axial force, is performed using the first shear deformation theory (FSDT). Estimation of equivalent Young’s modulus of the composites is calculated using a modified Halpin–Tsai model. In addition, a partial differential equation model is developed based on the Hamilton principle and nonlinear strain-displacement relationship. The Galerkin method and the fourth-order Runge–Kutta method are used to solve the equation. The dimensionless linear natural frequency of an FG GRC truncated conical shell is calculated by the Rayleigh–Ritz method and compared with available results in the literature to verify the accuracy of the present model. Simultaneously, significant effects of the different parameters, such as the total layer numbers, semi-vertex angles, GPLs weight fractions, distribution patterns and the length-to-thickness ratios, on the nonlinear dynamics including bifurcation and chaos of FG GRC truncated conical shells are investigated.

Nonlinear Vibration of Thermally Postbuckled FG-GRC Laminated Beams Resting on Elastic Foundations

Investigated herein are the small- and large-amplitude vibrations of a thermally postbuckled graphene-reinforced composite (GRC) laminated beam supported by an elastic foundation. The piecewise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the beam. The temperature-dependent material properties of functionally graded graphene-reinforced composites (FG-GRCs) are estimated through the extended Halpin–Tsai micromechanical model. The nonlinear governing differential equations are derived from the higher-order shear deformation beam theory and the von Kármán-type strain–displacement relationships. The thermal effect, the beam–foundation interaction and the initial deflection caused by thermal postbuckling are also included. A two-step perturbation approach is applied to determine the thermal postbuckling equilibrium paths as well as the nonlinear vibration solutions for the FG-GRC laminated beams. Results are presented to demonstrate the nonlinear vibration responses of thermally postbuckled FG-GRC laminated beams under a uniform temperature field. The effects of the FG reinforcement patterns and the foundation stiffness on the nonlinear vibration responses of FG-GRC laminated beams are examined and discussed.

Postbuckling of pressure-loaded FG-GRC laminated cylindrical panels resting on elastic foundations in thermal environments

This paper investigates the postbuckling behavior of graphene-reinforced composite (GRC) laminated cylindrical panels under lateral pressure loading. The panels are placed in a thermal environment and are supported by a Pasternak-type elastic foundation. The GRC layers are arranged in a piece-wise functionally graded (FG) pattern in the panel thickness direction. The anisotropic and temperature dependent material properties of GRC layers are predicted using the extended Halpin-Tsai micromechanical model. The higher order shear deformation theory and the von Karman strain-displacement relationships are employed to obtain the governing differential equations of the panels which also include the effects of temperature variation and panel-foundation interaction. The postbuckling of a cylindrical panel involves the boundary layer effect and the effects of the initial geometric imperfections. The nonlinear prebuckling deformations of the panel are also considered in the solution process. The postbuckling equilibrium path for the perfect and geometrically imperfect GRC laminated cylindrical panels are obtained by applying a singular perturbation technique along with a two-step perturbation approach. It is observed that, in the present examples, the considered FG-GRC laminated cylindrical panels subjected to lateral pressure experience pre-buckling deformation and the postbuckling equilibrium paths of the panels are no longer of the bifurcation type.

A novel technique for nonlinear dynamic instability analysis of FG-GRC laminated plates

This paper presents a novel technique for the nonlinear dynamic instability analysis of graphene-reinforced composite (GRC) laminated plates resting on an elastic foundation and in thermal environments. The GRC layers are arranged in a piece-wise functionally graded (FG) pattern along the plate thickness direction and each layer of the plate contains different volume fractions of graphene reinforcement. The material properties of a GRC layer are assumed to be temperature-dependent and are estimated by the extended Halpin–Tsai micromechanical model. The governing equations are based on a higher-order shear deformation plate theory with the geometric nonlinearity being defined by the von Kármán strain-displacement relationships. The plate-foundation interaction and thermal effects are also included. The novelty of this study is that the motion equation and the postbuckling equilibrium equation are derived by a two-step perturbation technique and are then solved simultaneously to determine the dynamic in-plane load and frequency uniquely for a given plate amplitude. The numerical illustrations reveal the nonlinear dynamic instability responses of FG-GRC laminated plates under different sets of thermal environmental conditions, from which results for uniformly distributed (UD) GRC laminated plates are obtained as comparators.

Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations

This paper investigates the small- and large-amplitude vibrations of thermally postbuckled graphene-reinforced composite (GRC) laminated plates resting on elastic foundations. The piecewise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the plate. The anisotropic and temperature-dependent material properties of the FG-GRC layers are estimated through the extended Halpin–Tsai micromechanical model. Based on the Reddy's higher order shear deformation plate theory and the von Kármán strain–displacement relationships, the motion equations of the plates are derived. The foundation support, the thermal effect, and the initial deflection caused by thermal postbuckling are also included in the derivation. A two-step perturbation approach is applied to determine the thermal postbuckling equilibrium paths as well as the nonlinear vibration solutions for the FG-GRC laminated plates. The numerical illustrations concern small- and large-amplitude vibration characteristics of thermally postbuckled FG-GRC laminated plates under a uniform temperature field. The effects of graphene reinforcement distributions and foundation stiffnesses on the vibration responses of FG-GRC laminated plates are examined in detail.