Graphene Platelets Reinforcement Research Articles

Forced vibration analysis of sandwich beam reinforced with graphene in piezoelectric medium on elastic substrate

In this study, using an analytical and precise solution, the dynamic transverse deflection of a five-layer beam with Prussian core with graphene platelet reinforced composite (GPLRC) under a moving harmonic load on a Pasternak elastic substrate is analyzed. First, the properties of the porous core materials and the piezoelectric layer and surface, which were graphene platelet reinforcements (GPLRs), were defined. The constitutive relations were extended using the Bonilla’s higher-order theory and Hamilton’s principle, relationships were extracted. Finally, using the Laplace method and analytical solution. A parametric analysis is provided to investigate impact of temperature distribution, porosity coefficient, thickness ratio, spring constant, voltage and excitation frequency on the responses.

Free Vibration and Buckling Analyses of Functionally Graded Plates With Graphene Platelets Reinforcement

Abstract While existing research has focused on using graphene platelets (GPLs) as reinforcement for homogeneous matrices, this study proposes a new nanocomposite for plate structures consisting of GPLs incorporated into a conventional functionally graded matrix with the aim of enhancing their overall stiffness. The performance of such plates is evaluated via free vibration and buckling analyses in the present study. Note that the matrix phase is graded continuously with the power law distribution across the plate's thickness, whereas various GPL dispersion patterns along the thickness are studied. The material properties of the typical functionally graded matrix are determined by the rule of mixture, and then those of the composite are estimated by the modified Halpin–Tsai model as well as the rule of mixture. Based on Hamilton's principle and the novel four-unknown refined plate theory (RPT4), the governing equations of the plate are developed. The Navier-type solution scheme is then adopted to get the critical buckling load and natural frequency of the nanocomposite plate. Numerical findings are examined to evaluate the novel nanocomposite plate model, and a parametric study is also conducted. In addition, high-accurate results are provided via the Navier-type solution here as benchmark solutions for further studies on functionally graded material structures reinforced by GPLs.

Nonlinear low-velocity impact analysis of sandwich plates with titanium face sheets and porous aluminum core reinforced by GPLs

This study examines the nonlinear dynamic response of sandwich plates under low-velocity impacts (LVIs), which consist of a porous aluminum foam core with functionally graded (FG) graphene platelets (GPLs) reinforcement and two titanium alloy face sheets. The finite element method is employed to perform the numerical simulations and the Hertz contact theory is used to model the impact behavior. The generic Halpin-Tsai model, which incorporates the porosity effect, is adopted to estimate the mechanical properties of core made of the FG-GPLRC, based on the experimental data of the closed-cell aluminum alloy foam. The simulation results reveal that the FG-X configuration has the highest impact resistance, and that the addition of GPLs improves the impact performance. Moreover, a thicker core can reduce both the first contact time and the vibration period of plates, while a looser boundary condition can prolong the vibration time after the first impact. Additionally, a higher impactor velocity, mass and radius lead to a higher deflection and contact force. The oblique impact decreases the impact energy. This work provides a lighter and stiffer design for structure engineers when components suffer low-velocity impact.

Nonlocal nonlinear higher-order finite element model for static bending of curved nanobeams including graphene platelets reinforcement

The aim of this work is concerned with the nonlocal nonlinear bending characteristics of non-classical isotropic and composite curved beams based on graphene platelets reinforcement, viz., nano size/micro beams. The size-dependant effect prominent in micro/nanobeams is incorporated in the formulation based on the nonlocal theory using size-dependent continuum approach. The proposed structural model includes both moderately large displacement and rotations, respectively. The system governing equations are established in terms of displacement functions using the principle of virtual work statements. A three-noded shear deformable curved beam finite element using a higher-order sinusoidal function based beam theory is employed; the solutions are obtained by adopting direct iterative procedure. The efficacy of the model is tested against the analytical studies available for the nano-size beams. A detailed analysis is made to highlight the influence of various design variables like thickness ratio, curvature of beam, nonlocal parameter, and the support conditions on the nonlinear bending behavior of curved nano/micro-size beams.

Buckling analysis of stiffened functionally graded multilayer graphene platelet reinforced composite plate with circular cutout embedded on elastic support subjected to in-plane normal and shear loads

Buckling analyses of orthogonally stiffened functionally graded graphene platelet reinforced composite plate with circular cutout supporting on Winkler elastic foundation is conducted according to the third order shear deformation plate theory and the finite element method to achieve the desired solutions. Material properties of the composite plate are evaluated using Rule of mixture and Halpin-Tsai approach. Graphene platelet reinforcements and Poly methyl methacrylate matrix are considered as the two components of the composite media. The material of the stiffeners is selected the same as that of the polymer matrix. In one efficient case, adding a set of stiffeners increased the critical buckling load by 41.8 % with only a 10.3 % increase in weight of the structure. Influence of broad range of factors such as GPLs nanofillers distribution pattern and weight fraction, Winkler-type elastic foundation, uniaxial and biaxial normal and shear loads, plate thickness and aspect ratio, width, height and number of longitudinal and transverse stiffeners are reported in several tabular and graphical data in detail.

A design strategy for multi-span pipe conveying fluid away from resonance by graphene platelets reinforcement

The operation of mechanical systems generates vibrations with a certain range of frequencies. Pipes conveying fluid have multiple natural frequencies. It is difficult to avoid one or more natural frequencies of pipes in the operating frequency range of the system, which can lead to resonance and fatigue failure. In this paper, a design strategy to modulate the multi-span pipe's natural frequency by reinforcing pipes with graphene platelets (GPLs) nanofiller is proposed to solve the pipe resonance in engineering. The multi-span functionally graded (FG) pipe is constructed based on an integral pipe model with GPLs uniformly or non-uniformly distributed in the metal matrix. The effective properties of the nanocomposite are determined by using the Halpin-Tsai micromechanics model and rule of mixture. Subsequently, the safety range and resonance range of the multi-span FG pipe are obtained by comparing the first tenth-order natural frequency and preserved frequency band. A comprehensive investigation on the effect of patterns, weight fraction, and geometric parameters of GPL is conducted to identify the most effective way to modulate the pipe's natural frequency. The results indicate that GPL weight fraction is able to modulate the multi-span pipe's natural frequency and safety range over a wide range. In addition, the natural frequency and safety range of the FG pipe reinforced with GPLs increase as the stiffness and number of retaining clip increase. Based on the results, a pipe design strategy with fewer retaining clips is proposed for pipes away from resonance by reinforcing pipes with GPL nanofiller. In the case of an aircraft hydraulic pipe, the natural frequency of the pipe reinforced with GPLs is far away from the preserved frequency band and without resonance in operation. In summary, the design strategy of pipe reinforced with GPLs shed important insights on reducing the vibration level of multimodal structures.

Static, dynamic and buckling responses of random functionally graded beams reinforced by graphene platelets

This work proposes a multiscale numerical method that can be used to study the static, dynamic and buckling behavior of functionally graded (FG) beams reinforced with graphene platelets (GPLs), whose random gradation is achieved through tailoring the internal porosity and GPLs reinforcement, either along the transverse or the longitudinal direction. The multiscale numerical method consists of microscale homogenization and structural analysis: micromechanics homogenization methods are introduced to predict the elastic moduli of nanocomposite layers with finite thickness along the transverse direction; Explicitly-expressed composite finite elements are then developed through the proposed variational principle and Hamilton principle. In the meantime, the corresponding governing equations are derived for FG beams with Timoshenko theory. On this basis, the static bending deflection, fundamental frequency and critical buckling load of the FG beams are obtained through the proposed FG finite elements. The effectiveness and accuracy of the proposed method are verified against the numerical results in the existing literature and experimental results in 3D printing with good agreement. Based on the credence of the present method, the effects of boundary conditions, gradient distributions of GPLs and pores, microscopic parameters of GPLs and structural geometric dimension on the static and dynamic performance of the FG beams are systematically analyzed, where the bi-directional gradient distribution pattern corresponding to the GPLs along the thickness direction and the pore along the axial direction demonstrates the best improvement of both bending and dynamic performance.

Nonlinear low-velocity impact of graphene platelets reinforced metal foams cylindrical shell: Effect of spinning motion and initial geometric imperfections

A nonlinear analysis is presented for low-velocity impact behavior of a graphene platelets-reinforced metal foams (GPLRMF) cylindrical shell with spinning motion in thermal environment, in which the initial geometric imperfection is incorporated. Taking three different graphene platelets (GPLs) distribution patterns into account, the GPLs reinforcement is either uniformly-distributed or functionally-graded along the shell thickness direction. The temperature-dependent micromechanical model is applied to estimate the material properties of GPLs reinforced composites. The nonlinear Donnell thin shell theory is utilized to derive the motion equations, in which von Kármán-type of kinematic nonlinearity is included. The influences of geometrical imperfections, spinning velocity, different boundary conditions, GPLs distribution patterns, foam distribution types, foam coefficient, GPLs weight fraction, temperature changes, the impactor' radius and initial velocity, prestressing force and damping coefficient on the low-velocity impact problems are discussed using the Runge-Kutta method in detail.

Free vibration analysis of piezoelectric functionally graded porous plates with graphene platelets reinforcement by pb-2 Ritz method

Free vibration analysis of piezoelectric functionally graded porous plates with graphene platelets reinforcement by pb-2 Ritz method

Aeroelastic flutter behaviour of beam: effect of graded GPL and porosity

The present study investigates the aeroelastic flutter characteristics of the graphene platelets (GPL) reinforced metal foam beam. Closed-cell metal foam beams having graded distribution of pores and functionally graded reinforcement of GPLs are considered in this study. The closed-cell metal foam model has been used for deriving the mechanical properties of the foam matrix, which makes provision for determining the relation between the co-efficient of porosity and the co-efficient of density. Modified Halpin-Tsai micromechanics is used to obtain the effective Young’s modulus of the GPLs reinforced composite beam, Density and Poisson’s ratio are calculated with the help of the rule of mixture. The Hamilton’s principle together with the Ritz method, employing the first-order piston theory gives the governing equations of motion for aeroelastic flutter characteristics of the beam for different end conditions. Juxtaposition of dimensionless natural frequencies with the results previously published by others is executed for validating the correctness of the approach followed in the present model. A study of various parameters has been executed, and the results in tables and graphs present the influence of porosity as well as GPLs reinforcement, different boundary conditions and thermal loading on aeroelastic flutter characteristics of the FG-GPL reinforced metal foam beam.

Nonlinear dynamic analysis of the functionally graded graphene platelets reinforced porous plate under moving mass

Recent studies demonstrated that porous materials could gain satisfying improvements in some mechanical properties by adding graphene platelet (GPL) reinforcements. Following this result, the present work exhibits a semi-analytical method to investigate the nonlinear dynamic characteristics of the functionally graded GPLs reinforced porous (FG-GPLRP) plate under a moving mass. Two types of boundary conditions, i.e., simply supported (SSSS) and clamped (CCCC) edges, are incorporated in the study. Based on the refined sinusoidal shear deformation theory (RSSDT) and von Kármán nonlinearity, the governing equations are transformed into a group of ordinary differential equations for the deflection of the plate. Then, the dynamic behaviours of the plate can be investigated by operating the fourth-order Runge–Kutta approach. After verification, several numerical examples are displayed to illustrate the effects of porosity coefficient, GPLs content, Winkler–Pasternak foundation, damping, initial imperfection, and compression stress on the moving-load-bearing capability of the plate. The obtained results demonstrate that, without harming its moving load capacity, it is possible to decrease the mass of the FG-GPLRP plate to a satisfying extent by altering the porosity and GPLs content.

Effect of graphene platelets reinforcement on vibration behavior of functionally graded porous arches under thermal environment

Functionally graded porous (FGP) composites reinforced with graphene platelets (GPL) are a new class of advanced nanocomposite that has surfaced recently in the past years in which the microstructure (mainly porosity) of the single-phase material (i.e., metal or polymer) varies continuously in the preferred directions to meet various functional requirements. Key advantages like low density, light-weightiness, high stiffness-to-weight ratios, excellent energy absorption, and thermal management properties make them the most promising candidates for structural and functional engineering applications. The application of these nanocomposites into the basic structural elements like arches, plates, and shells which are widely used in aerospace industries, requires a thorough and accurate analysis of these components which are made of these nanocomposite materials considering various environmental effects like temperature, moisture, etc.Therefore, this paper conducts the free vibration analysis of functionally graded (FG) porous arches reinforced with graphene platelets (GPLs) which are subjected to thermal loading conditions. A C0 finite element model based on higher-order shear deformation theory has been utilized to predict the structural response of the FG-GPL reinforced porous arches. Convergence and validation have also been performed to ascertain the accuracy of the present finite element formulation. Effect of various influencing parameters such as volume content of GPLs, porosity index, and temperature difference on frequency parameter has been shown, and various mode shapes for different curvature angles and boundary conditions have also been plotted. It is shown that graphene platelets (GPLs) as reinforcement can increase the stiffness of FG porous arches significantly under thermal environment and the mode shapes of FG-GPL reinforced arches are mainly the function of the curvature angle and boundary conditions.

Studying nonlinear vibrations of composite conical panels with arbitrary-shaped cutout reinforced with graphene platelets based on higher-order shear deformation theory

In this article, the vibrational behavior of conical panels in the nonlinear regime made of functionally graded graphene platelet–reinforced composite having a hole with various shapes is investigated in the context of higher-order shear deformation theory. To achieve this aim, a numerical approach is used based on the variational differential quadrature and finite element methods. The geometrical nonlinearity is captured using the von Karman hypothesis. Also, the modified Halpin–Tsai model and rule of mixture are applied to calculate the material properties of graphene platelet–reinforced composite for various functionally graded distribution patterns of graphene platelets. The governing equations are derived by a variational approach and represented in matrix-vector form for the computational purposes. Moreover, attributable to using higher-order shear deformation theory, a mixed formulation approach is presented to consider the continuity of first-order derivatives on the common boundaries of elements. In the numerical results, the nonlinear free vibration behaviors of functionally graded graphene platelet–reinforced composite conical panels including square/circular/elliptical hole and with crack are studied. The effects of boundary conditions, graphene platelet reinforcement, and other important parameters on the vibrational response of panels are comprehensively analyzed.

Acoustic fluid–structure study of 2D cavity with composite curved flexible walls using graphene platelets reinforcement by higher-order finite element approach

In the present study, acousto-vibration analysis of 2D fluid-filled cavities/tanks having flat and curved flexible walls is made using a trigonometric function based shear deformable theory andthe Helmholtz wave model for fluid domain. The governing equation formed here is solved through higher-order finite element approach. The walls are modeled by C1 continuous 3-noded beam element and the fluid is idealized using an eight-noded quadrilateral element. Structural and coupled frequencies are evaluated for fluid-filled cavities with rigid/flexible vertical walls along with flat/curved beam on top.The sound pressure level is also predicted in the fluid domain due to a steady-state mechanical harmonic load on the top of the cavity. This investigation is conducted for metallic cavities and then extended to graphene platelets reinforced cavity. The effect of degree of fluid–structure coupling is examined assuming different fluid domains. Considering a wide range of cavity geometry and material parameters such asthickness ratio, curved beamangle, graded porosity and graphene platelets, porosity coefficient, loading of GPL, fluid medium, a comprehensive investigation is depicted to highlight their impacts on vibro-acoustic nature of fluid-filled cavities. It is observed that the dynamic characteristics of rigid and flexible wall cavities are significantly different from each other.

A refined nonlocal isogeometric model for multilayer functionally graded graphene platelet-reinforced composite nanoplates

This article presents an effective and simple approach based on the four-variable refined plate theory (RPT) and isogeometric analysis (IGA) for bending and free vibration analyses of multilayer functionally graded graphene platelet-reinforced composite (FG GPLRC) nanoplates. The Eringen’s nonlocal elasticity theory is employed to take account of the size-dependent effect of nanoplates. Different distribution patterns of graphene platelets (GPLs) including uniform and non-uniform in the polymer matrix are considered. Governing equations of FG GPLRC nanoplates are then deduced from the principle of virtual work and resolved utilizing NURBS basis functions in the IGA framework. Accordingly, the requirement of third-order derivatives of approximate variables in the nonlocal formulation is fulfilled. Obtained outcomes indicate that the GPLs reinforcement can dramatically improve the stiffness of nanoplates, and GPLs rich at the bottom and the top of the nanoplate can be considered as the best reinforcing effect. Several new results are also considered as benchmark solutions for further studies on the FG GPLRC nanoplates.

Comparisons of nonlinear vibrations among pure polymer plate and graphene platelet reinforced composite plates under combined transverse and parametric excitations

The comparative researches of the nonlinear vibrations are obtained among the pure polymer plate and three types of graphene platelet reinforced polymer composite plates under combined the transverse and parametric excitations. All edges of the pure polymer and graphene platelet reinforced polymer composite plates are simply supported. Both the uniform and functionally graded distribution forms of the graphene platelets are considered. The differential governing equations of motion for the pure polymer and graphene platelet reinforced polymer composite plates are derived based on the first-order shear deformation plate theory, von Kármán strain displacement relationship and Hamilton principle. The fourth-order Galerkin truncation is employed to discretize the partial differential governing equations of motion to four-degree-of-freedom nonlinear dynamical system. The natural frequencies of the first four vibration modes are examined for the pure polymer and graphene platelet reinforced polymer composite plates with different geometric characteristics. In order to compare the nonlinear vibrations of the prestressed pure polymer and prestressed graphene platelet reinforced polymer composite plates subjected to the transverse point excitation and in-plane uniaxial/biaxial excitations, the time histories, phase portraits and Poincare maps are presented. Some validated results are conducted to present the accuracy of the present approach. The effects of the distribution forms and weight fractions of the graphene platelets on the nonlinear vibrations for the graphene platelet reinforced polymer composite plates are investigated in detail. The research results demonstrate that the nonlinear vibration behaviors of the prestressed pure polymer plate under the complex excitations can be remarkably stabilized by the reinforcement of the graphene platelets.

A novel quadrilateral element for analysis of functionally graded porous plates/shells reinforced by graphene platelets

This paper firstly presents numerical analyses of functionally graded porous plates/shells with graphene platelets (GPLs) reinforcement using a novel four-node quadrilateral element with five degrees of freedom per node, namely SQ4P, based on the first-order shear deformation theory and Chebyshev polynomials. The novelty of the present element is to use the high-order shape functions which satisfy the interpolation condition at the points based on Chebyshev polynomials to build the new flat four-node element for analysis of plate/shell structures. The Chebyshev polynomials are a sequence of orthogonal polynomials that are described recursively and the values of these polynomials belong to the interval [−1,1] as well as vanish at the Gauss points. Full Gauss quadrature rule is used to establish the stiffness matrix, geometric stiffness matrix, mass matrix and load vector. Various dispersions of GPLs and internal pores into the metal matrix through the thickness of structure are considered with the rule of a mixture and the Halpin–Tsai model for evaluating effective material properties across the thickness. The influence of weight fraction, porosity coefficient and dimensions of GPLs, distribution of GPLs and porosity into metal matrix are fully studied via several numerical examples from static bending to free vibration and buckling response. Numerical results and comparison with other solutions from available references suggest that the present element has enough reliability and validity to use in structural analysis. With regular and irregular meshes, these results are in close agreement with the exact solutions by using the suitable value for the order of the shape functions.

On the static and dynamic responses of smart piezoelectric functionally graded graphene platelet-reinforced microplates

Application of nano/micro structures has become popular in a wide range of advanced engineering systems in recent years. For a better insight, this paper presents an intensive numerical study on the static and dynamic responses of smart functionally graded microplates with graphene platelets (GPLs) reinforcement under concurrently mechanical and electrical loads. To this end, a powerful and effective numerical model based on refined plate theory (RPT), modified couple stress theory (MCST) and NURBS-based isogeometric analysis (IGA) is introduced to predict the complex behaviors of small-scale structures. Wherein, the MCST containing only one material length scale parameter is utilized to capture the size-dependent effects while the four-variable RPT-based IGA approach is exploited to describe the displacement field. The host microplate can be constituted by four different GPLs dispersions and integrated with two symmetric piezoelectric layers. A closed-loop control procedure based on displacement and velocity feedback gains is employed to actively control the static and dynamic responses of smart small-scale structures, which takes into account the structural damping effect. Several numerical examples are performed to examine the influence of some key parameters such as geometry, material length scale parameter, boundary condition, dynamic load, input electrical voltage as well as weight fraction and distribution of GPLs.

Temperature dependent buckling analysis of graded porous plate reinforced with graphene platelets

The main purpose of this research work is to investigate the critical buckling load of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using generalized differential quadrature (GDQ) method at thermal condition. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the plate thickness direction. Generally, the thermal distribution is considered to be nonlinear and the temperature changing continuously through the thickness of the nanocomposite plates according to the power-law distribution. To model closed cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme are used, through which mechanical properties of the structures can be extracted. Based on the third order shear deformation theory (TSDT) and the Hamilton's principle, the equations of motion are established and solved for various boundary conditions (B.Cs). The fast rate of convergence and accuracy of the method are investigated through the different solved examples and validity of the present study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns through the thickness, porosity coefficient and distribution of porosity on critical buckling load. Results reveal that the importance of thermal condition on of the critical load of FGP-GPL reinforced nanocomposite plates.

Geometrically nonlinear dynamic analysis of functionally graded porous partially fluid-filled cylindrical shells subjected to exponential loads

This article investigates the influence of graphene platelet reinforcements and nonlinear elastic foundations on geometrically nonlinear dynamic response of a partially fluid-filled functionally graded porous cylindrical shell under exponential loading. Material properties are assumed to be varied continuously in the thickness in terms of porosity and graphene platelet reinforcement. In this study, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the direction of the shell thickness. The Halpin–Tsai equations are used to find the effective material properties of the graphene platelet–reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders’s theory. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. An incremental–iterative approach is used to solve the nonlinear equations of motion of partially fluid-filled cylindrical shells based on the Newmark direct integration and Newton–Raphson methods. The governing equations of liquid motion are derived using a finite strip formulation of incompressible inviscid potential flow. The effects of various parameters on dynamic responses are investigated. A detailed numerical study is carried out to bring out the effects of some influential parameters, such as fluid depth, porosity distribution, and graphene platelet dispersion parameters on nonlinear dynamic behavior of functionally graded porous nanocomposite partially fluid-filled cylindrical shells reinforced with graphene platelets.