Dispersion Of Graphene Platelets Research Articles

Nonlinear thermal buckling analysis of temperature-dependent porous annular and circular microplates reinforced by graphene platelets by using isogeometric analysis method

In this research, by using isogeometric analysis (IGA) method, nonlinear thermal buckling analysis of porous circular and annular microplates reinforced by graphene platelets (GPLs) under uniform temperature rise is performed by taking both the temperature dependence of the material properties and the size effects into account. The closed-cell metal foam scheme combined with the Halpin-Tsai micromechanics model and the rule of mixture is utilized to identify the effective material properties of the porous nanocomposites for three GPL dispersion patterns and three porosity distributions. With the aid of the virtual work principle, the classical and the non-classical motion equilibrium formulation based on the higher-order shear deformation theory in conjunction with the modified strain gradient (MSG) theory for the nonlinear temperature-dependent buckling behaviour are established. The higher-order NURBS basis functions capable of accomplishing easily the smoothness of arbitrary continuity order are successfully utilized to solve the nonlinear governing equations by satisfying the C2-continuity of the displacement field required by the MSG theory. The thermal buckling behaviour is assessed in detail by using various parameters such as the thickness-to-radius ratio, the porosity coefficient, the GPL weight fraction and the material length scale as well as the porosity distribution scheme and the GPL dispersion pattern. The results show the significance of incorporating the temperature dependency of the material properties when analyzing the thermal buckling behaviour and present the combination scheme of porosity and GPL distributions for enhancing the thermal buckling resistance.

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 across the thickness are studied. Based on Hamilton's principle, 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. Eventually, numerical findings are examined to evaluate the novel nanocomposite plate model, and a parametric study is also conducted.

Improving the Mechanical Properties of GPLs-SiAlON Composites by Microfluidization Technique as a New Approach to Dispersion of GPLs

Graphene platelets (GPLs) are frequently preferred as reinforcement material to improve the mechanical properties of many advanced technology ceramics, thanks to their superior properties. However, their reinforcement levels vary depending on whether they are homogeneously distributed in the matrix microstructure. This is generally controlled by the thickness (number of layers) of the GPLs. In general, single- or few-layer GPLs show high performance as reinforcement but are commercially expensive. This limits their large-scale use. This study aims to achieve the performance of the GPLs (GPLRef), which is determined to have a high mechanical reinforcement level but is quite expensive, by economically thinning other GPLs (C0-GPL) with similar platelet size but cheaper and thicker structure. For this purpose, the microfluidization technique, a new approach to the dispersion of GPLs, was applied. C0-GPL is exposed to 1, 2, 4 and 8 cycles of microfluidization process. Microfluidized GPLs were added to the SiAlON matrix at a ratio of 1.5 wt %, and the GPLs-SiAlON composites were sintered using the spark plasma sintering (SPS) technique. The platelet size of C0-GPL decreased as the number of applied microfluidization cycles increased. However, while this reduction in platelet size was not significant up to 2 cycles, it was very pronounced at 4 and 8 cycles. Raman analyses revealed that GPLs could be dispersed effectively for up to 4 cycles. After this point, the GPLs fragmented rather than thin as the number of cycles increased. GPLs slightly thinner than GPLRef could be obtained with 2 cycles of microfluidization (C2-GPL). Therefore, C2-GPL were more homogeneously dispersed in SiAlON matrix microstructure compared to GPLRef. As a result, both the through-plane and in-plane direction fracture toughness values of SiAlON matrix containing C2-GPL, which partially preserved the platelet size, were higher than those of GPLRef-SiAlON. The fracture toughness of SiAlON matrix composites containing 4 and 8 cycles of microfluidized GPLs were lower than that of GPLRef-SiAlON as an adverse effect of decreasing platelet size. It has been determined that the mechanical reinforcement performance of commercially expensive GPLRef can be achieved economically by applying 2 cycles of microfluidization to cost-effective C0-GPL.

Combination of FEM-DQM for nonlinear mechanics of porous GPL-reinforced sandwich nanoplates based on various theories

In this novel work, applying boundary shape function differential quadrature hierarchical finite element method (DQHFEM) will be employed to analyze frequency, damping, bending, and buckling of an embedded sandwich nanoplate using different plate theories such as refined zigzag theory (RZT), sinusoidal shear deformation theory (SSDT), first-order shear deformation theory (FSDT) and classical plate theory (CPT). The face sheets as well as the core layer of the sandwich structure respectively are formed by porous material and nanocomposites reinforced with graphene platelets (GPLs) considering various dispersion. According to the Halpin–Tsai micromechanics model, Young’s modulus, as well as the rule of mixture for density as well as Poisson’s ratio related to the face sheets, can be obtained. Further, for modeling the mentioned sandwich structure much more realistic, Kelvin–Voigt model is applied. In order to gain motion of equations, D’Alembert’s principle is utilized where size influences can be contemplated as well using higher-order strain gradient nonlocal theory. In this comprehensive research, diverse parameters featuring the influences of structural damping, strain gradient parameters, GPL volume percent, dispersion, viscoelastic medium, porosity, boundary edges, and geometric variables upon vibration, buckling, and bending behaviors correlative to this structure. It is ascertained that RZT is the most accurate theory among other mentioned theories in estimating the static and dynamic response of structure which needs no shear correction factors. Moreover, the presence of GPLs can make the entire sandwich structure stiffer and dispersion patterns of pores, as well as GPLs, can affect the vibration, buckling, and bending of the structure.

Vibration smart control analysis of sandwich porous nanoshell with GPL-reinforced smart layers using surface-visco-piezo-elasticity theory

Smart nanostructures have many practical application in nano-electro-mechanical systems (NEMS) as sensor and actuator. Present research deals with the vibration and damping of advanced sandwich smart nanoshells. This nanostructure comprised of porous nanoshell coated by nanocomposite piezoelectric layers as sensor and actuator. The nanocompisite layers are reinforced by graphene platelets (GPLs) with various distributions based on Halpin-Tsai model. In order to presume this sandwich structure much more realistic, Kelvin model will be utilized and it is surrounded by visco-Pasternak foundation. Further, non-local surface piezoelasticity theory is employed for considering the small scale and surface effects. On the basis of zigzag shear-deformation theory and Hamilton principle, the motion equations are derived. Differential cubature method (DCM) is used as numerical method for calculating natural frequency and damping ratio. In order to validate the results, this paper is compared by another simplified cases and ABAQUS commercial software. Finally, the influences of porosity and its distribution, volume percent and distribution of GPLs, surface stresses, small scale parameter, and external voltage are shown on natural frequency and damping. The results show that the damping ratio and frequency of system considering surface effect with symmetric porosity distribution decrease and increases about 17% and 25% compared to the without surface effect case and asymmetric porosity respectively. In addition, the nanostructure in critically damped state can be turned into underdamped state by applying negative voltage. Furthermore, the dispersion of GPLs near the bottom and top surface of nanocomposite layers is the best choice due to high stiffness and frequency.

Static and free vibration analyses of functionally graded porous skew plates reinforced by graphene platelet based on three-dimensional elasticity theory

This paper deals with the static and free vibration analyses of FG porous skew plates reinforced by graphene platelets (GPL). The plate comprises of a layered model with uniform or non-uniform dispersion of graphene platelets in a metallic matrix including open-cell interior pores. The extended rule of mixture in conjunction with the modified Halpin–Tsai approach is used to obtain the equivalent properties of the porous nanocomposite plate. Three various types of porosity distributions are assumed through the plate thickness including uniform and two kinds of symmetric functionally graded distributions. Besides, five various kinds of GPL dispersion patterns are assumed along the plate thickness. By substituting in the expression for functional of element and Rayleigh–Ritz method, the equations of motion are derived and a 3D FEM approach is applied to solve the governing equation of motions. The influences of different parameters including various porosity coefficients, porosity distribution in conjunction with GPL pattern and the weight fraction of GPL as nanofiller, different boundary conditions and various angles of skew plates on static response, and free vibration behavior of the skew nanocomposite plate have been surveyed.

Transient Thermal Stresses in FG Porous Rotating Truncated Cones Reinforced by Graphene Platelets

The present work studies an axisymmetric rotating truncated cone made of functionally graded (FG) porous materials reinforced by graphene platelets (GPLs) under a thermal loading. The problem is tackled theoretically based on a classical linear thermoelasticity approach. The truncated cone consists of a layered material with a uniform or non-uniform dispersion of GPLs in a metal matrix with open-cell internal pores, whose effective properties are determined according to the extended rule of mixture and modified Halpin–Tsai model. A graded finite element method (FEM) based on Rayleigh–Ritz energy formulation and Crank–Nicolson algorithm is here applied to solve the problem both in time and space domain. The thermo-mechanical response is checked for different porosity distributions (uniform and functionally graded), together with different types of GPL patterns across the cone thickness. A parametric study is performed to analyze the effect of porosity coefficients, weight fractions of GPL, semi-vertex angles of cone, and circular velocity, on the thermal, kinematic, and stress response of the structural member.

A unified modeling method for dynamic analysis of GPLs-FGP sandwich shallow shell embedded SMA wires with general boundary conditions under hygrothermal loading

In this research, the dynamic analysis of graphene platelets (GPLs) reinforced functionally graded porous (FGP) sandwich shallow shell embedded shape memory alloy (SMA) wires with general boundary conditions under hygrothermal loading is conducted. Four different porosity distributions of FGP reinforced with four various GPLs dispersion patterns are considered. Based on the Brinson formulation, the constitutive equation of the SMA is established. The energy functional of the sandwich shallow shell is constructed by employing the Hooke’s law and the first-order shear deformation theory (FSDT). Ultimately, the dynamic characteristics of the sandwich shallow shell are obtained by solving the energy functional with the Rayleigh-Ritz method. After the verification of accuracy and reliability, parametric studies on the effects of material properties, geometrical parameters, and boundary conditions are investigated.

Nonlinear dynamic investigation of the perovskite solar cell with GPLR-FGP stiffeners under blast impact

The perovskite solar cell (PSC), as a potential disruptive space market entrant, has fascinated both the scientific community and aerospace industry due to the high specific power, flexibility, and low fabrication cost. With the aim of reducing structure weight while strengthening the blast-carrying capacity of the PSC, the novel graphene platelets (GPL) reinforced functionally graded porous (GPLR-FGP) stiffeners have been incorporated as enhancements against impact. This research explores the nonlinear dynamic characteristics of the PSC with GPLR-FGP stiffeners under blast load. Integrating the von-Kármán geometric nonlinearity and the first-order shear deformation theory, the governing motion equations are derived by utilizing Airy's stress function and the Galerkin method. The fourth-order Runge-Kutta approach is employed to capture the solutions of dynamic equations effectively. Diverse influences of the stiffener material, boundary condition, plate theory, porosity distribution, GPL dispersion, porosity coefficient, GPL weight fraction, GPL geometry, damping, nonlinear elastic foundation, and initial imperfection are investigated in the numerical study. Besides, the optimal parameters of the PSC with GPLR-FGP stiffeners are discovered, facilitating the following paces of space design and practical implementation in extraterrestrial circumstances.

Analytical solution approach for nonlinear vibration of shear deformable imperfect FG-GPLR porous nanocomposite cylindrical shells

This study presents an analytical solution approach to examine the nonlinear vibration of geometrically imperfect functionally graded porous circular cylindrical shells reinforced with graphene platelets (GPL) surrounded on an elastic foundation. First-order shear deformation theory is employed to formulate the considered problem. Four porosity distributions and four GPLs dispersion patterns are considered which vary through the thickness direction. The effective mechanical properties of considered functionally graded graphene platelet-reinforced porous nanocomposites are characterized via a micromechanical model. Governing equations are derived by Hamilton’s principle and then were transformed into a set of ordinary differential equations using the Galerkin method. Afterward, the nonlinear frequency response curves are obtained with the use of the method of multiple scales. Numerical results are provided to explore the effect of parameters such as initial imperfection, geometry, porous distribution, porosity coefficient, and GPLs’ scheme and weight fraction on the nonlinear frequency-response curve.

An ES-MITC3 Finite Element Method Based on Higher-Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique (MITC) for triangular elements, named as ES-MITC3, was recently proposed to enhance the accuracy of the original MITC3 for analysis of plates and shells. In this study, the ES-MITC3 is extended to the static and vibration analysis of functionally graded (FG) porous plates reinforced by graphene platelets (GPLs). In the ES-MITC3, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains created by two adjacent triangular elements sharing an edge. The effective material properties are variable through the thickness of plates including Young’s modulus estimated via the Halpin–Tsai model and Poisson’s ratio and the mass density according to the rule of mixture. Three types of porosity distributions and GPL dispersion pattern into the metal matrix are examined. Numerical examples are given to demonstrate the performance of the present approach in comparison with other existing methods. Furthermore, the effect of several parameters such as GPL weight fraction, porosity coefficient, porosity distribution, and GPL dispersion patterns on the static and free vibration responses of FG porous plates is discussed in detail.

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.

Probabilistic stability analysis of functionally graded graphene reinforced porous beams

This paper presents the first attempt to study the probabilistic stability characteristics of functionally graded (FG) graphene platelets (GPLs) reinforced beams by taking into account the multidimensional probability distributions, such as stochastic porosity and GPL distribution patterns as well as random material properties. For this purpose, a non-inclusive Chebyshev metamodel (CMM), which is implemented on deterministic analysis using discrete singular convolution (DSC) method with excellent computational efficiency and accuracy, is proposed and used to obtain both deterministic and probabilistic results including probability density functions (PDFs), cumulative density functions (CDFs), means and standard deviations of the critical buckling load. The present analysis is rigorously validated through direct comparisons against the results obtained by a direct quasi-Monte Carlo simulation (QMCS) method and those available in open literature. The influences of material properties, porosity distribution, GPL dispersion pattern and boundary condition on probabilistic buckling behaviour of the FG-GPL beam are comprehensively investigated. The global sensitivity analysis is also conducted. The results suggest that the critical buckling load of the FG-GPL beam is most sensitive to porosity distribution, followed by porosity coefficient and GPL weight fraction.

Structural failure performance of the encased functionally graded porous cylinder consolidated by graphene platelet under uniform radial loading

Abstract This paper investigates the structural failure mechanism of the functionally graded porous (FGP) cylinder consolidated by graphene platelet (GPL) encased in the rigid medium. Three porous distributions and three GPL dispersion patterns are discussed. The pressurized FGM-GPL cylinder may deform in the shapes characterized by “single-lobe” or “multi-lobe” due to the constraint of the medium. The nonlinear equilibrium equations are developed by the differential of the total potential energy function of the cylinder. The critical buckling pressure of the confined cylinder is obtained theoretically and increases with a higher value of the lobe number. The verification of the present analytical solution is conducted by establishing a two-dimensional (2D) finite element model (FEM). The pressure-displacement equilibrium paths are traced, from which, the maximum pressure (buckling pressure) is determined. Both the analytical and numerical results indicate that the confined FGP-GPL cylinder sustains its highest pressure capacity for the case that the porosity and the GPL are distributed symmetrically to the mid-surface, but non-uniformly through the cross-section. Finally, a full parametric study is mainly focused on the effects of porosity coefficient, and the weight fraction of the GPL on the buckling pressure, the hoop force, the bending moment, the stress and strain distribution on the crown position with the maximum deformation when the critical buckling occurs.

Numerical investigation into dynamic behaviors of axially moving functionally graded porous sandwich nanoplates reinforced with graphene platelets

This paper aims to study the nonlinear transient response of a moving porous sandwich micro-size plate strengthened with graphene platelets (GPLs) under two types of distributed dynamic forces, a pulse load and an impact load. To model closed cell cellular solids stiffened with graphene platelets (GPLs), Gaussian-Random field scheme along with Halpin-Tsai model for microsystems are used, through which mechanical properties of the structures can be obtained. On the basis of the first order shear deformation and von Karman nonlinear theories, the dynamic equations are extracted, and then nonlocal strain gradient theory is recruited to consider small size effects due to non-uniform stress and strain fields. Subsequently, using a hybrid method, kinetic dynamic relaxation technique in conjunction with Newmark’s direct integration method, the time-dependent equation sets are solved. Finally, effects of some key factors such as porosity and GPL coefficients and dispersion patterns, nano-system parameters and the velocity of moving nanoplate on time history of deflections are considered. The results show that as the values of the nanoplate velocity increase, the importance of nonlocality and strain gradient parameter on dynamic deflections become more outstanding. The results can be used to design novel components in marine vessels in nano-scale.

Analytical consideration and numerical verification of the confined functionally graded porous ring with graphene platelet reinforcement

The present work is concerned with the stability behavior of the functionally graded porous (FGP) ring with graphene platelet (GPL) reinforcement. The ring is surrounded by an elastic medium and a point load is introduced at the crown position. Assuming no interface friction between the ring and medium, the buckling load of the ring with a “single-lobe” deformation is obtained analytically. Afterward, the numerical examination is developed by comparing the critical buckling load from the numerical and analytical results. The good comparison indicates the analytical solutions are applicable to the nine cases by combining three porous distributions and three GPL dispersion patterns, respectively. It is explored that the combination of symmetrical pores and symmetrical GPL to the mid-surface can resist the highest external load of the confined FGP–GPL ring, and this case is successfully compared with other closed-form expressions for the homogeneous ring without pores and GPL. Finally, the effects of porosity coefficient, and weight fraction of the GPL are examined and discussed in terms of the load capacity, the hoop force, the bending moment, the hoop stress and strain, and the geometric shapes of the GPL.

Post-buckling analysis of honeycomb core sandwich panels with geometrical imperfection and graphene reinforced nano-composite face sheets

The present research deals with post-buckling analysis of geometrically perfect/imperfect honeycomb core sandwich panels having graphene platelet (GPL) reinforced face sheets based on general higher order plate model. Honeycomb sandwich panels are often made of aluminum material having low weight but also low stiffness. Here, the application of GPL-reinforced nano-composites as face sheets of sandwich panels has been proposed to enhance their mechanical performance. GPL distributions are considered as uniform and linear models in the face sheets. GPL volume and weight fractions are incorporated to Halpin-Tsai modeling of a nano-composite material. Adopting a general higher order plate theory with five field variables, it is possible to satisfy shear deformation influences needless of adding correction factors. Based on Gibson technique, the hexagonal honeycomb core is equalized with a solid core. Post-buckling load of the sandwich panel has been analytically derived and it is showed that the obtained post-buckling load is dependent on the core thickness, face sheet thickness, cell wall thickness of the core, GPL dispersion in the face sheets and also geometrical imperfection.

Active vibration control of GPLs-reinforced FG metal foam plates with piezoelectric sensor and actuator layers

This paper investigates free vibration and dynamic responses of smart FG metal foam plate structures reinforced by graphene platelets (GPLs). We then analyze active control of FG metal foam plates with piezoelectric sensor and actuator layers. To provide numerical solution of underlying problems, we develop a computational approach based on a generalized C0-type higher-order shear deformation theory (C0-HSDT) polygonal finite element formulation (PFEM), which is suitable for modeling both thick and thin plates. To enhance accuracy of solution, we use in PFEM quadratic serendipity shape functions in combination with a generalized C0-HSDT. The FG core layers are constituted by combining between two porosity distributions and three GPL dispersion patterns distributed along the plate's thickness while two piezoelectric layers are perfectly bonded on the both bottom and top surfaces of host plate. The mechanical displacement field is approximated based on C0-HSDT while the electric potential distribution through the thickness for each piezoelectric layer is assumed to be a linear function. For active control, a constant velocity feedback scheme is employed through a closed loop control with piezoelectric sensors and actuators. The effect of the porosity coefficient, weight fraction of GPLs on the plate's behaviors with various porosity distributions and GPL dispersion patterns are evidently demonstrated through numerical examples.

Size-Dependent Vibration of Circular Cylindrical Polymeric Microshells Reinforced with Graphene Platelets

This paper investigates size-dependent vibration of graphene platelet (GPL) reinforced circular cylindrical polymeric microshells. The microshells are composed of multilayers with GPL fillers uniformly dispersed in each individual layer, but GPL weight fraction changes layer-by-layer along the thickness direction. The effective Young’s modulus is predicted by the modified Halpin–Tsai model, while effective Poisson’s ratio and mass density are determined by the rule of mixture. Four different patterns of GPL dispersion are considered to achieve the functionally graded property of the microshells. Based on Love’s thin shell theory and the modified couple stress theory, the governing equations are derived by using Hamilton’s principle. Then, the Navier and Galerkin methods are utilized to solve natural frequencies of GPL reinforced polymeric (GPLRP) microshells. A parametric study is conducted, with a particular focus on the effects of the GPL distribution pattern, the weight fraction, the geometries of the GPL and the microshells, as well as the total number of layers of the microshells.

Nonlinear free vibration of graded graphene reinforced cylindrical shells: Effects of spinning motion and axial load

This paper presents an analytical study on linear and nonlinear free vibration characteristics and dynamic responses of spinning functionally graded (FG) graphene reinforced thin cylindrical shells with various boundary conditions and subjected to a static axial load. The weight fraction of graphene platelet (GPL) nanofillers in each concentric cylindrical layer is constant but follows a layer-wise variation through thickness direction, resulting in position-dependent elastic moduli, mass density and Poisson's ratio along the shell thickness. Based on the Donnell's nonlinear shell theory, the nonlinear partial differential equations of motion for the cylindrical shell are established by using the Hamilton's principle with the effects of centrifugal and Coriolis forces as well as the spin-induced initial hoop tension taken into account. The governing equations for nonlinear vibration of the nanocomposite cylindrical shell with different GPL dispersion patterns are derived from a set of nonlinear ordinary differential equations which are derived by employing the Galerkin approach. Dynamic responses of forward and backward travelling waves are investigated by analyzing the wave form and the frequency spectrum. Special attention is given to the effects of the weight fraction, dispersion patterns and the geometrical size of GPLs, the external axial load and spinning speeds of the cylindrical shell on the linear and nonlinear free vibrations of the nanocomposite cylindrical shell.