GPL-reinforced Composite Research Articles

Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell

In this article, wave propagation behavior of a size-dependent spinning graphene nanoplatelet-reinforced composite (GNPRC) cylindrical nanoshell with porosity is presented. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT), this accurate theory employs exact length scale parameter and nonlocal constant. The governing equations of GNPRC cylindrical nanoshell coupled with piezoelectric actuator (PIAC) are evolved by minimum potential energy principle and solved by the analytical method. For the first time in the current study, wave propagation-porosity behavior of a GNPRC cylindrical nanoshell coupled with PIAC is examined based on NSGT. The results show that, as the angular velocity increases, the difference between the minimum and maximum values of the phase velocity decreases. Another important result of this paper is that, by increasing the radius, extremum values of phase velocity occur in the lower values of the wave number. Finally, the influences of porosity, angular velocity, wave number and different graphene platelet distribution patterns on the phase velocity are investigated using the mentioned continuum mechanics theory. The outputs of the present work can be used in structural health monitoring and ultrasonic inspection techniques.

Torsional Buckling of Functionally Graded Multilayer Graphene Nanoplatelet-Reinforced Cylindrical Shells

Exact solutions for the torsional bifurcation buckling of functionally graded (FG) multilayer graphene platelet reinforced composite (GPLRC) cylindrical shells are obtained. Five types of graphene platelets (GPLs) distributions are considered, and a slope factor is introduced to adjust the distribution profile of the GPLs. Within the framework of Donnell’s shell theory and with the aid symplectic mathematics, a set of lower-order Hamiltonian canonical equations are established and solved analytically. Consequently, the critical buckling loads and corresponding buckling mode shapes of the GPLRC shells are obtained. The effects of various factors, including the geometric parameters, boundary conditions and material properties on the torsional buckling behaviors are investigated and discussed in detail.

Dynamic analysis of multi-layered composite beams reinforced with graphene platelets resting on two-parameter viscoelastic foundation

The aim of the present article is to analyze the free-vibration behavior of multi-layer composite beams reinforced with graphene platelets (GPLs) resting on a viscoelastic foundation. The material properties of GPLs are assumed to vary from layer to layer in the thickness direction. GPLs are dispersed in each layer randomly and four different distribution patterns are employed. Further, all parameter effects on these four are investigated thoroughly. Effective material properties are estimated by the Halpin-Tsai model, and higher-order shear deformation beam theory is utilized to achieve the theoretical formulation of multi-layer graphene-platelets-reinforced composite (GPLRC) beam. Meanwhile, the Navier solution has been used to derive and follow up the governing differential equation of motion and natural frequency. To find out the effect of GPLs on composite structures and effect of the different distribution pattern of GPLs on the frequency of the beam structure and the other parameters, all sections of this study and results are presented based on four GPLs distribution patterns.

Free Vibration Analysis of Graphene Platelets–Reinforced Composites Plates in Thermal Environment Based on Higher-Order Shear Deformation Plate Theory

As a first endeavor, this article presents the free vibration of composite plates reinforced with graphene platelets (GPLs) based on the higher-order shear deformation plate theory. Moreover, it is assumed that the material properties are temperature dependent and are graded in the thickness direction. It is assumed that GPLs randomly spread out in each individual composite layer reinforced with graphene platelets. The theoretical formulation is derived based on higher-order shear deformation plate theory and the initial thermal stresses are evaluated by solving the thermo-elastic equilibrium equations. The Halpin–Tsai micromechanical model is used to evaluate the effective material properties of every layer of composite plates reinforced GPLs. Further, the Navier solution has been used to derive the governing equations of motion and evaluate the natural frequencies and dynamic response of simply supported graphene platelet reinforced composite plates. Four different GPL distribution pattern is modeled to find out its effect on the frequency of the plate and the other parameters. The result asserted that subjoining GPL to composite plates has a significant reinforcing effect on the free vibration of Graphene platelet reinforced composite (GPLRC) plates.

Free vibration and buckling analyses of edge-cracked functionally graded multilayer graphene nanoplatelet-reinforced composite beams resting on an elastic foundation

This study investigates the linear free vibration and elastic buckling behaviors of functionally graded (FG) multilayer graphene platelet (GPL)-reinforced composite beams containing a single edge crack and resting on a Pasternak-type elastic foundation. GPLs are randomly oriented, and their concentration varies layer-wisely through the beam thickness. A modified Halpin-Tsai model is employed to estimate Young’s modulus of the GPL-reinforced composite (GPLRC). The first-order shear deformation beam theory is applied in structural modeling. The bending stiffness of the cracked section is assumed to be equivalent to that of a massless rotational spring, which is related to the stress intensity factor (SIF) at the crack tip. SIFs of the cracked FG multilayer GPLRC beams are calculated by the finite element method. The differential quadrature method is used to discretize the equations of motion of the cracked beams. A parametric study is performed after a validation study for the present approach to illustrate the effects of crack location, crack length, boundary condition, GPL weight fraction, GPL distribution pattern, GPL size and geometry, and foundation stiffnesses on the fundamental frequencies and critical buckling loads.

Buckling and postbuckling of dielectric composite beam reinforced with Graphene Platelets (GPLs)

Buckling and postbuckling behaviors of graphene platelet (GPL) reinforced dielectric composite beams are investigated through theoretical formulation. The effective material properties of the GPL reinforced composite (GPLRC) as required for structural analysis, i.e. tensile modulus, dielectric constant and Poisson's ratio are obtained by using effective medium theory and rule of mixture. Governing differential equations for the composite beam are established through Timoshenko beam theory, von Kármán nonlinear strain-displacement relationship and principle of virtual work. Governing equations are numerically discretized and solved by employing differential quadrature method (DQM), through which several parameters affecting the buckling performances are quantitatively identified. The results demonstrate there exists a critical GPL concentration, above which the electrical field significantly affects the beam's buckling and postbuckling behaviors. The dielectric beam's buckling performances are very sensitive to AC (alternating current) frequency within a certain range. Moreover, it is found the dielectric beam's buckling and postbuckling performances comprehensively depend on the concentration and aspect ratio of GPLs. The present work is envisaged to provide guidelines to develop GPL-based smart composites and structures.

Nonlinear static and dynamic responses of graphene platelets reinforced composite beam with dielectric permittivity

Nonlinear bending and forced vibration of graphene platelets (GPLs) reinforced composite (GPLRC) beam with dielectric permittivity are investigated. The tensile modulus and dielectric permittivity as required for structural analysis are obtained by using effective-medium theory (EMT) while Poisson's ratio and mass density are evaluated by rule of mixture. Based on Timoshenko beam theory, governing equations for nonlinear bending and forced vibration of the GPLRC beam are established and numerically solved through differential quadrature method (DQM). The dependency of the structural behaviours of the GPLRC beams on the attributes of GPL, applied external loading and electrical field are comprehensively studied. The analysis demonstrates that the performances of the GPLRC beam can be designed and actively tuned through adjusting several parameters. The bending and vibration behaviours of the beam are sensitive to smaller beam thickness, larger GPL aspect ratio and electrical voltage. Snap-through behaviour is observed for the bending and vibration of the composite beam within the involved AC frequency range. Reasons underlying the above observations are analysed and discussed to increasingly understand the structural behaviours of graphene reinforced composite structures with dielectric property.

Nonlinear in-plane buckling of fixed shallow functionally graded graphene reinforced composite arches subjected to mechanical and thermal loading

• Nonlinear in-plane buckling of FG- GPLRC arch subjected to uniform radial load and temperature field is investigated. • Analytical solutions for the limit point and bifurcation buckling loads are derived. • Parametric studies of different parameters on the nonlinear equilibrium path and buckling behavior are conducted. • Switches between limit point buckling, bifurcation buckling and no buckling are obtained and discussed. The nonlinear in-plane buckling analysis for fixed shallow functionally graded (FG) graphene reinforced composite arches which are subjected to uniform radial load and temperature field is presented in this paper. The arch is composed of multiple graphene platelet reinforced composite (GPLRC) layers with gradient changes of concentration of graphene platelets (GPLs) in each layer. The principle of virtual work, combined with the effective materials properties estimated by the Halpin-Tsai micromechanics model for GPLRC layer, is used to derive the nonlinear buckling equilibrium equations of the FG-GPLRC arch, and then the analytical solutions for the limit point and bifurcation buckling loads are obtained. Comprehensive parametric studies are conducted to explore the effects of various distribution patterns and geometries of GPL, temperature field and arch geometry on the nonlinear equilibrium path and buckling behavior of the composite arch. The influence of temperature on the geometric parameters which are defined as switches between limit point buckling, bifurcation buckling and no buckling are also discussed. It is found that a higher temperature field can increase the buckling loads of the FG-GPLRC arch but reduce the value of the minimum geometric parameters that switching the buckling modes. The results also show that even a small amount of GPLs filler content can increase the buckling loads of the FG-GPLRC arch considerably, and distributing more GPLs near the surface layers is the best pattern to enhance the buckling performances of FG-GPLRC arches.

Low-velocity impact response of geometrically nonlinear functionally graded graphene platelet-reinforced nanocomposite plates

This paper investigates the low-velocity impact response of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene nanoplatelets (GPLs) in which GPLs are randomly oriented and uniformly dispersed in the polymer matrix within each individual layer with GPL weight fraction following a layer-wise variation along the plate thickness. The micromechanics-based Halpin–Tsai model is used to evaluate the effective material properties of the GPL-reinforced composite (GPLRC), and the modified nonlinear Hertz contact theory is utilized to define the contact force between the spherical impactor and the GPLRC target plate. The equations of motion of the plate are derived within the framework of the first-order shear deformation plate theory and von Karman-type nonlinear kinematics and are solved by a two-step perturbation technique. The present analysis is validated through a direct comparison with those in the open literature. A parametric study is then performed to study the effects of GPL distribution pattern, weight fraction, geometry and size, temperature variation as well as the radius and initial velocity of the impactor on the low-velocity impact response of functionally graded GPLRC plates.

On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell

Due to rapid development of process manufacturing, composite materials with porosity have attracted commercial attention in promoting engineering applications. For this regard, in this research wave propagation-thermal characteristics of a size-dependent graphene nanoplatelet-reinforced composite (GNPRC) porous cylindrical nanoshell in thermal environment are investigated. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT). The governing equations of the laminated composite cylindrical nanoshell in thermal environment have been evolved using Hamilton’s principle and solved with the assistance of the analytical method. For the first time, wave propagation-thermal behavior of a GNPRC porous cylindrical nanoshell in thermal environment based on NSGT is examined. The results show that by increasing the thickness, the effect of porosity on the phase velocity decreases. Another important result is that by increasing the value of the radius, the difference between the minimum and maximum values of the phase velocity increases. Finally, influence of temperature change, wave number, angular velocity and different types of porosity distribution on phase velocity are investigated using the mentioned continuum mechanics theory. As a useful suggestion, for designing of a GPLRC nanostructure should be attention to the GNP weight function and radius, simultaneously.

Analytical mathematical solution for vibrational response of postbuckled laminated FG-GPLRC nonlocal strain gradient micro-/nanobeams

An inhomogeneous beam model incorporating size effects is formulated based on the nonlocal strain gradient theory of elasticity within the framework of a third-order shear deformation beam theory to analyze the size dependency in vibration behavior of postbuckled laminated functionally graded (FG) micro-/nanobeams made from graphene platelet-reinforced composite (GPLRC). The graphene platelets are randomly dispersed in each individual layer in such a way that the weight fraction of the nanofiller varies layerwise on the basis of different patterns of FG dispersion. Based upon the Halpin–Tsai micromechanical scheme, the effective material properties of laminated FG-GPLRC micro-/nanobeams are extracted. With the aid of the Hamilton’s principle, the nonlocal strain gradient equations of motion are constructed. After that, an improved perturbation technique is put to use to capture the small-scale effects on the fundamental frequencies of laminated FG-GPLRC nonlocal strain gradient micro-/nanobeams. The size-dependent natural frequencies of laminated third-order shear deformable FG-GPLRC micro-/nanobeams are obtained as function of applied axial compressive load within both the prebuckling and postbuckling domains. It is seen that in the prebuckling regime, the softening-stiffness effect of the nonlocality causes to reduce the natural frequencies of laminated FG-GPLRC micro-/nanobeam, but the hardening-stiffness influence of strain gradient size effect leads to increase the natural frequencies. However, by moving to the postbuckling regime, this pattern becomes vice versa, as the nonlocal size dependency leads to increase the natural frequencies of micro-/nanobeam while the strain gradient size effect causes to reduce them.

Nonlinear in-plane instability of functionally graded multilayer graphene reinforced composite shallow arches

This paper investigates the in-plane instability of functionally graded multilayer composite shallow arches reinforced with a low content of graphene platelets (GPLs) under a central point load. The GPL weight fraction, which is a constant within each individual GPL reinforced composite (GPLRC) layer, follows a layer-wise variation along the thickness direction. The effective Young’ modulus of the GPLRC is estimated by modified Halpin-Tsai micromechanics model. The virtual work principle is used to establish the nonlinear equilibrium equations for the FG-GPLRC arch fixed or pinned at both ends which are then solved analytically. A parametric study is conducted to examine the effects of distribution pattern, weight fraction, and size of GPL nanofillers and the geometrical parameters of the FG-GPLRC arch on its buckling and postbuckling behaviors. The conditions for multiple limit point buckling to occur in an FG-GPLRC pinned arch are also discussed. It is found that GPL nanofillers have a remarkable reinforcing effect on buckling and postbuckling performances of nanocomposite shallow arches.

New approach to investigate the nonlinear dynamic response and vibration of a functionally graded multilayer graphene nanocomposite plate on a viscoelastic Pasternak medium in a thermal environment

This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene platelets (GPLs) using first-order shear deformation theory and a stress function with full motion equations (not using Volmir’s assumptions). The weight fraction of GPL nanofillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC). The modified Halpin–Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young’s modulus of the GPLRC layers. The plate is assumed to rest on a viscoelastic Pasternak medium and to be subjected to dynamic mechanical load in a thermal environment. Numerical results for the nonlinear dynamic response and vibration of functionally graded (FG) multilayer GPLRC plates are obtained by the Runge–Kutta method. The results show the influences of the GPL distribution pattern, weight fraction, geometry, foundation models, mechanical and temperature loads on the nonlinear dynamic response and vibration, natural frequencies and frequency–amplitude curves of FG multilayer GPLRC plates.

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.

Axial postbuckling analysis of multilayer functionally graded composite nanoplates reinforced with GPLs based on nonlocal strain gradient theory

In this paper, a new size-dependent inhomogeneous plate model is constructed to analyze the nonlinear buckling and postbuckling characteristics of multilayer functionally graded composite nanoplates reinforced with graphene platelet (GPL) nanofillers under axial compressive load. To this purpose, the nonlocal strain gradient theory of elasticity is implemented into a refined hyperbolic shear deformation plate theory. The mechanical properties of multilayer graphene platelet-reinforced composite (GPLRC) nanoplates are evaluated based upon the Halpin-Tsai micromechanical scheme. The weight fraction of randomly dispersed GPLs remain constant in each individual layer, which results in U-GPLRC nanoplate, or changes layerwise in accordance with three different functionally graded patterns, which make X-GPLRC, O-GPLRC and A-GPLRC nanoplates. Via a two-stepped perturbation technique, explicit analytical expressions for nonlocal strain gradient stability paths are established for layerwise functionally graded GPLRC nanoplates. It is demonstrated that both the nonlocal and strain gradient size dependencies are more significant for multilayer GPLRC nanoplates filling by GPL nanofillers with higher length-to-thickness and width-to-thickness ratios.

Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates

This paper deals with the thermal buckling and postbuckling of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene platelets (GPLs). It is assumed that GPL reinforcements are randomly oriented and uniformly dispersed in each individual GPL-reinforced composite (GPLRC) layer but the concentration follows a layer-wise variation across the plate thickness. The modified Halpin-Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young's modulus of GPLRC layers. Within the framework of the first-order shear deformation theory, the nonlinear governing equations are derived by applying the principle of virtual displacements and then solved by using a differential quadrature-based iteration technique. Parametric studies are conducted to examine the influences of GPL distribution pattern, concentration and geometry, as well as in-plane force on the thermal buckling and postbuckling behaviours. Our results show that distributing more GPLs near the surface layers is capable of reinforcing the thermal buckling and postbuckling performances of GPLRC plates. Whether the thermal buckling and postbuckling resistance increases or decreases with the increases in GPL weight fraction, aspect ratio and width-to-thickness ratio is highly dependent on the GPL distribution pattern.

Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates

The present paper investigates the biaxially compressed buckling and postbuckling behaviors of functionally graded multilayer composite plates reinforced with a low content of graphene nanoplatelets (GPLs) that are randomly oriented and uniformly dispersed in the polymer matrix within each individual layer. The material properties of the GPL-reinforced composite (GPLRC), which are graded along the thickness direction due to a layer-wise change in GPL weight fraction, are evaluated through a micromechanics model. Theoretical formulations are based on the first-order shear deformation plate theory and von Kármán-type nonlinear kinematics and include the effect of an initial geometric imperfection. A two step perturbation technique is employed to determine the asymptotic postbuckling solutions and the biaxial compressive postbuckling equilibrium paths of both perfect and imperfect plates simply supported on all edges. The effects of GPL weight fraction, distribution pattern, geometry and size as well as total number of layers on the buckling and postbuckling behaviors of functionally graded GPLRC plates are examined in detail.

A nonlocal strain gradient hyperbolic shear deformable shell model for radial postbuckling analysis of functionally graded multilayer GPLRC nanoshells

The present study addresses the size dependency in nonlinear instability of functionally graded multilayer graphene platelet-reinforced composite (GPLRC) nanoshells under hydrostatic pressure including jointly the nonlocal elastic and strain gradients stress fields. For this objective, the new unconventional continuum theory namely as nonlocal strain gradient theory of elasticity is utilized within the framework of a refined hyperbolic shear deformation shell theory. Via stacking up a number of individual layers, the graphene platelet (GPL) nanofillers are distributed uniformly and three different functionally graded patterns based upon a layerwise change of the GPL weight fraction through the shell thickness direction. The effective material properties corresponding to uniform (U-GPLRC) and X-GPLRC, O-GPLRC, A-GPLRC functionally graded patterns of dispersion are extracted by Halpin-Tsai micromechanical scheme. By employing jointly the boundary layer theory of shell buckling and a two-stepped perturbation technique, explicit analytical expressions are achieved for nonlocal strain gradient stability curves of functionally graded multilayer GPLRC nanoshells. It is indicated that by increasing the value of GPL weight fraction for the U-GPLRC and O-GPLRC nanoshells, the significance of the both nonlocal and strain gradient size dependencies reduces, while for the X-GPLRC and A-GPLRC nanoshells, it increases.

Dynamic instability of functionally graded multilayer graphene nanocomposite beams in thermal environment

This paper studies the dynamic instability of functionally graded multilayer nanocomposite beams reinforced with a low content of graphene nanoplatelets (GPLs) and subjected to a combined action of a periodic axial force and a temperature change. The weight fraction of GPL nanofillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC) layer but follows a layerwise variation across the beam thickness. The Halpin-Tsai micromechanics model is used to estimate the effective Young’s modulus of GPLRC layers. The differential quadrature method is employed to convert the partial differential governing equations into a linear system of Mathieu-Hill equations, from which the principle unstable region of functionally graded multilayer GPLRC beams is determined by Bolotin’s method. Special attention is given to the effects of GPL distribution pattern, weight fraction, geometry and dimension on the dynamic instability behaviour. The thermal buckling and free vibration are also discussed as subset problems. Numerical results show that distributing more GPLs near the top and bottom surfaces can effectively increase the natural frequency and reduce the size of the unstable region. The influences of GPL geometry and dimension tend to be insignificant when the GPL width-to-thickness ratio is larger than 103.

Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams

This paper investigates the buckling and postbuckling behaviours of functionally graded multilayer nanocomposite beams reinforced with a low content of graphene platelets (GPLs) resting on an elastic foundation. It is assumed that GPLs are randomly oriented and uniformly dispersed in each individual GPL-reinforced composite (GPLRC) layer with its weight fraction varying layerwise along the thickness direction. The effective material properties of each layer are estimated by the Halpin-Tsai micromechanics model. The nonlinear governing equations of the beam on an elastic foundation are derived within the framework of the first-order shear deformation beam theory then are converted into a nonlinear algebraic system by using the differential quadrature method. A detailed parametric study is carried out to examine the effects of the distribution pattern, weight fraction, geometry and size of GPL nanofillers, foundation stiffness parameters, slenderness ratio and boundary conditions on the buckling and postbuckling behaviours. The results show that GPLs have a remarkable reinforcing effect on the buckling and postbuckling of nanocomposite beams.