Graphene Platelets Reinforcement Research Articles

Meta-model based stochastic isogeometric analysis of composite plates

A stochastic isogeometric analysis approach (SIGA) is presented for functionally graded porous plates with graphene platelets reinforcement (FGP-GPLs). Different kinds of random fields and variables are applied to describe the uncertain system inputs which are including material properties of the FGP matrix and graphene platelets, magnitudes and directions of applied loads. A Nyström based Karhunen-Loève expansion is presented for random field discretization within the IGA scheme. The arbitrary polynomial chaos-Kriging (aPCK) method is presented for uncertainty quantification. To sustain the robustness of the aPCK approach for engineering problems involving high-dimension of uncertainty, a new Dagum kernel function is introduced in Kriging. The mean, standard deviation, probability density function (PDF) and cumulative distribution function (CDF) of structural outputs can be effectively estimated. Three illustrative examples are investigated to assess the performance of the proposed method for mathematical and engineering applications.

Stochastic isogeometric analysis for the linear stability assessment of plate structures using a Kriging enhanced Neural Network

The stability of functionally graded porous plates with graphene platelets reinforcement (FGP-GPLs) is investigated in this paper. Combining with a new metamodeling approach, namely the Kriging enhanced Neural Network, a stochastic isogeometric analysis (SIGA) framework is proposed for assessing the structural stability. The uncertainties of material properties of both FGP matrix and graphene platelets are considered in the form of random fields and variables. Karhunen-Loève expansion based Nyström method is applied to random field discretization. The Dagum function is adopted as a new kernel function to further improve the performance of the proposed approach. Statistical information including but not limited to statistical moments, probability density function (PDF), and cumulative distribution function (CDF) of the critical buckling load of the plate structure can be effectively estimated through a non-intrusive fashion. In order to illustrate the effectiveness and applicability of the proposed stochastic computational analysis, both theoretical and real-life engineering examples have been investigated in this study.

Thermal Buckling of Graphene Platelets Toughening Sandwich Functionally Graded Porous Plate with Temperature-Dependent Properties

Thermal buckling of graphene platelets (GPLs) reinforced sandwich functionally graded porous (SWFGP) plate with temperature-dependent (TD) properties is investigated. The studied plate is composed of two homogeneous face layers and one functionally graded porous core. Two types of porosity distribution with uniformly distributed GPL reinforcement are included. Based on the first-order shear deformation plate theory, Hamilton principle and Galerkin procedure are employed to build the analytical framework. Uniform, linear, and nonlinear thermal loads along the thickness direction are considered. Subsequently, an iterative procedure is introduced to find out the critical buckling temperature of the plate with the temperature dependence considered. Verifications are conducted to demonstrate the accuracy of the proposed method. Several parametric analyses are investigated in detail where the effects of porosity, GPL weight fraction, geometric configuration, and the boundary condition on the thermal buckling of the plates are discussed.

Magneto-mechanical vibration analysis of single-/three-layered micro-Timoshenko porous beam and graphene platelet as reinforcement based on modified strain gradient theory and differential quadrature method

This article discusses about vibration analysis of single-/three-layered microsandwich Timoshenko beams with porous core and graphene platelet–reinforced composite face sheets under magnetic field and elastic foundation based on the modified strain gradient theory. It is assumed that the material properties of matrix and reinforcement vary in thickness directions. Hamilton’s principle based on the energy approach is used to obtain the governing equations of motions. The equations of motions are solved using a numerical differential quadrature method for various boundary conditions. The obtained results of this study are compared with other previous research studies, and there is a good agreement between them. Moreover, the effects of different parameters such as length-to-thickness ratio, magnetic field, various distributions of graphene platelets and porous beams, and volume fractions of graphene platelets are studied on the dimensionless natural frequencies. In fact, the main idea of this work is combination of structure reinforcement with magnetic field and graphene platelets on the sandwich porous beams at microscale, and the effects of these parameters are developed on the dimensionless natural frequencies of the microbeam. The results of the present study demonstrate that applying magnetic field and increasing its intensity lead to enhance the natural frequency. Also, it is showed that graphene platelet reinforcement with one percent of weight fraction has an effective effect on the increasing dimensionless natural frequencies of the microporous beam. Thus, it can be predicted that graphene platelets can be used instead of nanotubes because they do not have the problem of nanotube accumulation and they are more economical than nanotubes.

Nonlinear supersonic flutter study of porous 2D curved panels including graphene platelets reinforcement effect using trigonometric shear deformable finite element

The nonlinear panel flutter behaviour of two-dimensional porous curved panel reinforced by graphene platelets exposed to a supersonic flow is investigated. A curved beam element developed based on the trigonometric shear deformation theory is employed. The formulation integrates the geometric nonlinearity with von Karman’s approximation. The effort to model the fluid–structure interaction is reduced by implementing the first-order form of piston theory aerodynamics to describe the flow and accounting for the influence of static aerodynamic load due to the inherent geometric curvature of the panel. The nonlinear governing equations are formulated adopting the Lagrangian formulation. The panel deflection under the static aerodynamic load is evaluated using the Newton–Raphson iteration method. The flutter behaviour is analysed with reference to the large deflection equilibrium state through an eigenvalue analysis and by tracing the complex eigenvalues and identifying the first coalescence of any two vibratory modes. The flutter dynamic pressure is also predicted iteratively using the eigenvalue approach for the selected range of limit cycle amplitudes. The influence of static aerodynamic load and vibration amplitude on the flutter characteristics is brought out for both isotropic and graphene reinforced composite panels with different boundary conditions. The pre-flutter static deflection shape of the panel is also examined. The material parameters such as porosity level in the metal foam and the graphene platelet content are assessed on the nonlinear flutter features of 2D panels.

Isogeometric Analysis of Functionally-Graded Graphene Platelets Reinforced Porous Nanocomposite Plates Using a Refined Plate Theory

In this study, we propose a novel and effective computational approach for free and forced vibration analyses of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement under various loads. To this end, the outstanding features of isogeometric analysis (IGA) are first combined with the four-variable refined plate theory (RPT). The non-uniform rational B-splines (NURBS) are adopted to obtain the [Formula: see text]-continuity essential to the RPT model. The various distributions of internal pores as well as GPLs with uniform or non-uniform properties along the plate’s thickness are investigated. The effective elastic properties of the material models are obtained by the Halpin–Tsai micromechanics model for Young’s modulus, the rule of mixture for Poisson’s ratio and mass density. The Newmark’s time integration scheme is implemented to obtain the solutions of the forced vibration problems. Numerical examples are carried out to investigate the effects of various key parameters such as porosity coefficient, GPL weight fraction, porosity distribution, as well as GPL dispersion pattern, on the behaviors of the plate structure.

A novel computational approach to functionally graded porous plates with graphene platelets reinforcement

Abstract In this study, we numerically investigate static and free vibration responses of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using an efficient polygonal finite element method (PFEM). While the bending strain field is approximated through quadratic serendipity shape functions, the shear strain field is calculated by employing Wachspress basis functions. In order to eliminate the shear locking phenomenon, Timoshenko's beam theory is utilized to determine assumed strain fields on each side of polygonal domain. The present formulation possesses various outstanding features: (a) is valid for triangular, quadrilateral and polygonal elements; (b) can conveniently implement various different plate theories via choosing appropriate transverse shear function; (c) eliminates the shear locking phenomenon; (d) does not increase degrees of freedom (DOFs) per polygonal element despite employing the quadratic serendipity shape functions and (e) obtains more accurate and stable results than those of other PFEMs. Various dispersions of internal pores as well as GPLs into metal matrix through the thickness of plate are examined. The effective material properties varying across the plate's thickness can be estimated by Halpin-Tsai model for Young's modulus and the rule of a mixture for Poisson's ratio and mass density. The effect of several important parameters such as porosity coefficient, weight fraction and dimensions of GPLs, distribution of porosity and GPLs into metal matrix are thoroughly investigated via various numerical examples.

A comprehensive review on modeling of nanocomposite materials and structures

This work presents a historical review of the researches procured by various scientists and engineers dealing with the nanocomposite materials and continuous systems manufactured from such materials. Nanocomposites are advanced type of well-known composite materials which have been reinforced with nanosize reinforcing fibers and/or particles. Such materials can be better suit for the industrial applications of which remarkable improved material properties are needed. In other words, the material properties of nanocomposites are superior to those of macroscale composites due to the enhanced features of materials in the nanoscale. These materials are being more and more employed by designers in the aerospace, mechanics and automotive applications as constituent elements instead of the conventional composite materials. Henceforward, it is of great significance to be aware of the researches conducted in this are by researchers to be able to predict the behaviors of structures consisted of such materials in real working conditions. In what follows, the mechanical analyses performed on different types of nanocomposite structures including carbon nanotube reinforced (CNTR), graphene reinforced (GR), graphene platelet reinforced (GPLR), graphene oxide reinforced (GOR) and multi-scale hybrid (MSH) nanocomposite ones will be reviewed and the most crucial highlights of the proposed scientific activities will be discussed.

Effect of Porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures

This article investigates the influence of porosity on free and forced vibration characteristics of a nanoshell reinforced by graphene platelets (GPL). The material properties of piece-wise graphene-reinforced composites (GPLRCs) are assumed to be graded in the thickness direction of a cylindrical nanoshell and estimated using a nanomechanical model. In addition, because of imperfection of the current structure, three kinds of porosity distributions are considered. The nanostructure is modeled using modified strain gradient theory (MSGT) which is a size-dependent theory with three length scale parameters. The novelty of the current study is to consider the effects of porosity, GPLRC and MSGT on dynamic and static behaviors of the nanostructure. Considering three length scale parameters ( l0=5h, l1=3h, l2=5h ) in MSGT leads to a better agreement with MD simulation in comparison by other theories. Finally, effects of different factors on static and dynamic behaviors of the porous nanostructure are examined in detail.

Wave dispersion characteristics of porous graphene platelet-reinforced composite shells

Wave propagation analysis of a porous graphene platelet reinforced (GPLR) nanocomposite shell is investigated for the first time. The homogenization of the utilized material is procured by extending the Halpin-Tsai relations for the porous nanocomposite. Both symmetric and asymmetric porosity distributions are regarded in this analysis. The equations of the shell\'s motion are derived according to Hamilton\'s principle coupled with the kinematic relations of the first-order shear deformation theory of the shells. The obtained governing equations are considered to be solved via an analytical solution which includes two longitudinal and circumferential wave numbers. The accuracy of the presented formulations is examined by comparing the results of this method with those reported by former authors. The simulations reveal a stiffness decrease in the cases which porosity influences are regarded. Also, one must pay attention to the effects of longitudinal wave number on the wave dispersion curves of the nanocomposite structure.

Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler–Pasternak elastic foundation

The nonlinear vibration and the dynamic buckling of a graphene platelet reinforced sandwich functionally graded porous (GPL-SFGP) plate are thoroughly investigated in this paper. The investigated GPL-SFGP plate consists of two metal face layers and a functionally graded porous core with graphene platelet reinforcement. The effects of the Winkler–Pasternak elastic foundation, thermal environment and damping are incorporated. The open-cell metal foam model is implemented to model the mechanical properties of the porous core. Axial compressive stress is applied on the GPL-SFGP plate by exerting various compressive loading speeds at one edge of the plate. Grounded on the classical plate theory, both motion and geometric compatibility equations of the plate are deduced by introducing the Von Kármán strain-displacement relationship and stress function. Both the Galerkin and the fourth-order Runge–Kutta methods are implemented to solve the governing equation of the dynamic system. Meticulously designed numerical experiments are conducted to identify the critical influential factors of the dynamic stability of the GPL-SFGP plate. The influences of loading speed, damping ratio, temperature variation, initial imperfection, elastic foundation parameters, porosity, GPL weight fraction and the dimensions of the GPL on the overall dynamic stability of the GPL-SFGP plate are evidently demonstrated.

Parametric instability of thermo-mechanically loaded functionally graded graphene reinforced nanocomposite plates

This paper investigates the parametric instability of functionally graded graphene reinforced nanocomposite plates that undergo a periodic uniaxial in-plane force and a uniform temperature rise. The plate is composed of multiple graphene platelet reinforced composite (GPLRC) layers in which graphene platelets (GPLs) are uniformly distributed in each individual layer with GPL concentration varying layer-wise across the plate thickness. The modified Halpin–Tsai model that takes into account the GPL geometry effect is employed to calculate the Young's modulus of the GPLRC. Based on the first-order shear deformation theory, the governing equations are deduced and then are solved by using the differential quadrature approach integrated with the Bolotin's method. A parametric study is undertaken to show the influences of GPL distribution pattern, concentration and geometry, temperature change, static in-plane force, plate geometry and boundary condition on the parametric instability of functionally graded multilayer GPLRC plates. It is found that the addition of a small amount of GPL reinforcements considerably increases the critical buckling load and natural frequencies but reduces the size of unstable region. The reinforcing effect is the best when the surface layers of the plate are GPL-rich.

Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection

In this paper, post-buckling behavior of geometrically imperfect porous beams reinforced with graphene platelets (GPLs) and resting on nonlinear hardening foundation is investigated. GPLs are uniformly and non-uniformly distributed thorough the thickness direction. Different porosity distributions called uniform, symmetric and asymmetric are considered. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The present refined beam model satisfies the shear deformation effect needless of any shear correction factor. The post-buckling load-deflection relation is obtained by solving the governing equations having cubic nonlinearity applying Galerkin’s method needless of any iteration process. New results show the importance of porosity coefficient, porosity distribution, GPL distribution, GPL weight fraction, geometrical imperfection and foundation parameters on nonlinear buckling behavior of porous beams. Specially, porosities and GPL reinforcement have a great impact on post-buckling configuration of both ideal and imperfect nanocomposite beams.