Functionally Graded Graphene Platelets Reinforced Composite Research Articles

Static and dynamic response of pyramidal lattice sandwich plate with composite face sheets reinforced by graphene platelets

For the pursuit of lightweight structures with excellent mechanical performance, sandwich structures with lightweight cores and strengthened face sheets have become popular in the advanced engineering fields in recent years. In this paper, the nonlinear static and dynamic responses of the sandwich plate constructed with the aluminum pyramidal lattice core and functionally graded graphene platelets reinforced composite (FG-GPLRC) face layers are analyzed. The partial differential equations of the pyramidal lattice sandwich plate considering the geometric nonlinearity are achieved based on the Reddy’s third order shear deformation theory (TSDT), which are solved by the combination of finite element model, Raphson’s method and Newmark numerical integration method. Four different types of the impact loads including the step loading, triangular loading, half-sine loading and exponential loading with the same peak value and duration time are investigated. The influences of the thickness-to-truss radium ratio and the angle of the truss core, as well as the weight fraction and distribution patterns of graphene platelets (GPLs) over the face sheets under different impact loads and different boundary conditions are analyzed. According to the numerical results, it is concluded that the sandwich plate with higher weight fraction of GPLs, lower thickness-to-truss radium ratio, and higher angle of the truss core can exhibit better performance in both static and dynamic loading conditions. The FG-X distribution of GPLs presents the best dynamic performance as compared to the other GPL distributions. The combination of lightweight truss core with the advanced GPLRC face sheets is instructive for potential applications and further research.

Reliability and sensitivity analyses of porous functionally graded graphene platelet reinforced composite plate

The performance of composite is seriously influenced by numerous uncertain factors, in which the uncertainty analysis plays a vital role in composite materials analysis by providing a comprehensive understanding of uncertain factors and their influence on design and performance. In this study, uncertain behaviors of porous functionally graded graphene platelets reinforced composite (FG-GPLRC) plates are first investigated for assessing the safety under bending deformation. The mechanical model for static analysis of the porous FG-GPLRC plate is formulated by Reddy’s higher-order shear deformation theory, and the bending responses are derived by Hamilton’s principle and the Navier method. Material properties and loads are deemed as random variables, and the performance function is determined by the Tsai-Wu criterion. The univariate dimension reduction method and maximum entropy method are employed to estimate the reliability of porous FG-GPLRC plates with diverse distribution patterns. Additionally, the analytical sensitivities of failure probability with respect to material parameters are derived. The analysis results illustrate that the existence of uncertain factors significantly influences the performance and reliability of composites, and the structural reliability can be improved by adding appropriate pores and graphene platelets at the edge layer of the composite plate.

Nonlinear dynamic buckling analysis of the FG-GPLRC cylindrical and sinusoid panels with porous core under time-dependent axial compression

The nonlinear dynamic buckling responses of functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical and sinusoid panels with porous core are presented in this paper. The governing formulations are established by applying the nonlinear higher-order shear deformation theory (HSDT). an approximation technique is used to determine the stress function for complexly curved panels. Euler-Lagrange equations can be used to achieve the nonlinear motion equation. Numerical investigations are considered using the Runge-Kutta method for dynamic responses, and using the Budiansky-Roth criterion for critical dynamic buckling loads. Some discussions on the dynamic buckling responses of panels with porous core can be achieved from the numerical examples.

Vibration characteristics of multilayer functionally graded microplates with variable thickness reinforced by graphene platelets resting on the viscoelastic medium under thermal effects

Due to their improved mechanical properties and adaptability, microplates with tailored variable thickness profiles are becoming essential parts of advanced micro- and nanoelectromechanical systems (MEMS and NEMS). This study conducts a thorough analytical analysis of the vibration properties of thermally loaded, multilayer functionally graded graphene platelet-reinforced composite (FG-GPLRC) microplates of linearly or parabolically varying thickness resting on viscoelastic medium under different boundary conditions. The Halpin–Tsai micromechanical model and the law of mixtures are employed to calculate the effective material characteristics for various reinforcement distributions in the microplate. These distributions encompass uniformly symmetric and asymmetric arrangements. The study utilized the first-order shear deformation theory (FSDT) in conjunction with the modified strain gradient theory (MSGT) and Hamilton's principle to generate the dynamic governing equations for the structure, accounting for size-dependent effects. The resulting equations are afterwards solved using the utilization of the Galerkin technique. This enables the evaluation of the proposed solution's correctness and precision. The impact of various factors on vibration behavior is investigated through numerical analysis. These factors encompass length scale parameters, temperature fluctuations, temperature distribution profiles, boundary conditions, the distribution pattern of the GPL, taper constants in both unidirectional and bidirectional scenarios, the weight fraction of the GPL.

Nonlinear Vibration and Dynamic Buckling of Complex Curved Functionally Graded Graphene Panels Reinforced with Inclined Stiffeners

This paper presents a new semi-analytical approach for the nonlinear vibration and dynamic responses of functionally graded graphene platelet-reinforced composite (FG-GPLRC) panels with complex curvature reinforced by orthogonal and/or inclined stiffeners in the thermal environment resting on the nonlinear viscoelastic foundation with the nonlinearities of von Kármán in the framework of the higher-order shear deformation theory (HSDT). The three curvature types of complexly curved panels are considered to be cylindrical, sinusoid, and parabola panels. Orthogonal and/or inclined stiffeners are modeled utilizing an improved smeared stiffener technique. The stress function form is estimated by applying the like-Galerkin method for complexly curved panels. By applying the Lagrange function and Euler–Lagrange equation, the nonlinear equations of motion of the panels are obtained. The viscous damping effects of the viscoelastic foundation are considered by utilizing the Rayleigh dissipation function. Numerical results are examined utilizing the Runge–Kutta method to acquire the time-deflection curves, and by utilizing the Budiansky–Roth criterion, the critical dynamic buckling loads are determined. From the investigated results, it is possible to evaluate the nonlinear vibration and buckling dynamic responses of three forms of panels with stiffeners.

Multi-patch isogeometric Kirchhoff–Love shell analysis for post-buckling of functionally graded graphene platelets reinforced composite shells

This paper develops a multi-patch isogeometric Kirchhoff–Love shell method for post-buckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) cylindrical, spherical, and conoidal shell structures, which are built with single or multiple NURBS patches. A penalty strategy is employed to weakly couple nonconforming interfaces between adjacent patches. The coupling work induced by enforcing displacement continuity and rotational continuity is added to the equilibrium equation, and the corresponding stiffness matrix is derived in detail. A simplified arc-length method is utilized to capture the complex equilibrium paths including snap-through and snap-back behaviors. Five distribution patterns of the shells including uniform (UD), V-type, A-type, O-type, and X-type are considered. The cylindrical and spherical shells are subjected to concentrated loadings at central points while for conoidal shells the concentrated loadings are enforced at the center points of an edge. The post-buckling of isotropic and laminated shell structures is first studied to validate the developed formulations by comparing the obtained results with those given in existing literature. Then a series of numerical examples considering nonlinear FG-GPLRC shell problems are conducted to explore the effect of various parameters like geometric dimensions, GPL distribution patterns, and shell thickness on the mechanical performance. Finally, the post-buckling of a cylindrical shell subjected to an offset concentrated load, with extremely complicated equilibrium paths, is modeled and analyzed by using the developed multi-patch isogeometric method. The numerical results reveal that the X-type GPL distribution pattern demonstrates better performance in load–deflection responses and provides the largest buckling critical load among the five patterns. Additionally, the increase in height ratio could deteriorate the stability performance of FG-GPLRC conoidal shells.

Investigation of Buckling Behavior of Cracked FG Cylindrical Panels Reinforced by Graphene Platelets

The buckling behavior of a functionally graded graphene-platelet-reinforced composite (FG-GPLRC) was traditionally investigated, mostly with respect to its undamaged structures. In this context, the current study investigated the buckling behavior of an FG-GPLRC cylindrical panel with an anti-symmetric central crack by introducing a 2-D extended natural element method (XNEM). The displacement was basically expressed with the first-order shear deformation theory (FSDT) and approximated using Laplace interpolation functions (for the non-singular displacement part) and crack-tip singular functions (for the singular displacement part) without grid refinement around the crack tips. The complex numerical manipulation on the curved shell surface was resolved by geometrically transforming the curved shell surface to a 2-D planar rectangular NEM grid. The painstaking numerical locking was suppressed by adopting the concept of a stabilized MITC3+ shell element. The validity of the developed numerical method was examined through a benchmark test, and the fundamental buckling loads of cracked FG-GPLRC cylindrical panels were investigated in depth by changing the major parameters. The numerical results also included a comparison with the FG-CNTRC. The numerical results indicated that the developed numerical method effectively predicts the buckling loads with reasonable accuracy, and that the fundamental buckling load of cracked FG-GPLRC cylindrical panels are remarkably influenced by the inclination angle and length of the crack as well as the other associated parameters.

Spectro-geometric solutions for random vibration of functionally graded graphene platelet reinforced conical shells

This study delved into the random vibration characteristics of a conical shell constructed from a functionally graded graphene platelet-reinforced composite (FG-GPLRC) under the influence of basic acceleration excitation. The investigation employed a synthesis of two methodologies: the spectro-geometric method (SGM) and the pseudo-excitation method (PEM). Commencing with the application of the Halpin–Tsai micromechanics approach and the law of mixtures, the effective material characteristics of the FG-GPLRC structure were determined. Subsequently, the displacement field vector for the conical shell structure was established with SGM. By employing the framework of the first-order shear deformation theory (FSDT), the energy function of the FG-GPLRC conical shell was derived, with external random excitation energy being incorporated with PEM. To construct a dynamic model for the conical shell structure, the Rayleigh-Ritz method was applied, subjecting the energy function to variational extremization. This approach yielded a comprehensive dynamic representation. The validity of the proposed model was substantiated through comparison with existing literature and finite element method results. Ultimately, this study explored the influence of graphene material properties and geometric parameters of the conical shell on the random vibration characteristics of the FG-GPLRC conical shell.

Thermal vibration analysis of FG-GPLRC doubly curved shells partially resting on Kerr foundation based on higher-order shear deformation theory

In this paper, we present a novel analytical approach for investigating the influence of non-homogeneous Kerr elastic foundations on the nonlinear dynamical characteristics of functionally graded graphene platelets reinforced composite (FG-GPLRC) doubly curved shells. A new aspect of this study is the investigation of various distributions of the Kerr foundation, either centrally within or along the edges of the nanocomposite shells, a model not previously explored. Three distinct distributions of graphene nanoplatelets reinforcement are examined, utilizing the rule of mixtures and the Halpin-Tsai micromechanical model. The theoretical framework is based on Reddy's third-order shear deformation theory. The equations of motion, formulated as partial differential equations, are efficiently resolved through the application of Galerkin's method. The effectiveness of this approach resides in its utilization of integration to tackle the distribution issue of the elastic foundation, all without the need for deploying intricate algorithms. The validity of our proposed method is established through meticulous comparisons with findings from prior literature. Furthermore, this paper delves into the effect of material properties, thermal conditions, boundary conditions, geometrical parameters, and four configurations of the shells on the vibrational responses. Of notable significance is our thorough investigation of the impact of variations in the distributions, stiffness, and geometrical parameters of the elastic foundation on natural frequencies and the nonlinear transient response of these shells, all of which hold great importance in structural design. We present the obtained results systematically in various formats, including tables, 2D and 3D graphs, and contour plots, providing a comprehensive overview of the research outcomes. These findings have profound implications for the field of engineering, contributing to advancements in novel structural designs and their diverse applications.

Free vibration of functionally graded graphene platelets reinforced composite porous L-shaped folded plate

This paper investigates the free vibration of a functionally graded graphene platelets reinforced composite (FG-GPLRC) porous L-shaped folded plate. According to the folded position, the L-shaped folded plate is divided into three rectangular plates. Based on Mindlin-Reissner plate theory and Hamilton’s principle, the governing equations for free vibration of each subelement are deduced. Utilizing the generalized differential quadrature element (GDQE) method, the governing equations for each subelement are discretized and numerically solved to obtain the natural frequency. The study focuses on discussing the influence of several factors, including porosity distribution, porosity coefficient, plate size, crank angle, boundary conditions, GPL weight fraction, and GPL pattern on the natural frequency. The findings reveal that the incorporation of GPL enhances the mechanical performance of the porous folded plate compared to a pure porous plate. Dispersion of more GPL near the upper and lower layers enhances the stiffness of the FG-GPLRC porous folded plate, leading to higher natural frequency. Additionally, variations in the crank angle have a significant impact on the natural frequency.

Nonlinear buckling and postbuckling analysis of cylindrical and sinusoid FG-GPLRC panels under axial compressive load

This paper presents and analyzes the nonlinear buckling responses of cylindrical and sinusoid Functionally graded graphene platelet reinforced composite (FG-GPLRC) panels under axial compressive load. The higher-order shear deformation theory is applied to establish the governing equations of structures. The stress function is approximated using the like-Galerkin method, and the Galerkin method is applied to solve the governing equations. The critical buckling loads and postbuckling load-deflection curves are expressed in explicit form. The effects of panel types, geometrical parameters, imperfection, and foundation on the critical buckling loads and postbuckling curves of cylindrical and sinusoid FG-GPLRC panels are discussed. Numerical results also evaluate and compare the buckling responses of cylindrical and sinusoid panels.

Nonlinear buckling and postbuckling analysis of cylindrical and sinusoid FG-GPLRC panels under axial compressive load

This paper presents and analyzes the nonlinear buckling responses of cylindrical and sinusoid Functionally graded graphene platelet reinforced composite (FG-GPLRC) panels under axial compressive load. The higher-order shear deformation theory is applied to establish the governing equations of structures. The stress function is approximated using the like-Galerkin method, and the Galerkin method is applied to solve the governing equations. The critical buckling loads and postbuckling load-deflection curves are expressed in explicit form. The effects of panel types, geometrical parameters, imperfection, and foundation on the critical buckling loads and postbuckling curves of cylindrical and sinusoid FG-GPLRC panels are discussed. Numerical results also evaluate and compare the buckling responses of cylindrical and sinusoid panels.

Nonlinear thermo-mechanical axisymmetric stability of FG-GPLRC spherical shells and circular plates resting on nonlinear elastic medium

ABSTRACT An analytical approach for nonlinear thermo-mechanical buckling of functionally graded graphene platelet reinforced composite (FG-GPLRC) circular plates and shallow spherical shells resting on nonlinear elastic medium using the higher-order shear deformation theory (HSDT) and the nonlinearities of von Kármán is established in the present work. Assuming that the structures are axisymmetrically displaced for the central axis and external pressure and thermal loads are applied. The nonlinear elastic medium is used to model the behaviour of hardening or softening medium depending on the positive and negative values of the nonlinear parameter, respectively. By applying the Ritz energy method, the relation expressions of load-deflection are archived to investigate the postbuckling response and critical buckling load of the structures. Special effects on the nonlinear thermo-mechanical behaviour of plates and shells with different medium stiffnesses, different material parameters, and different geometrical dimensions are explored and discussed in numerical results.

Isogeometric approach for thermal buckling analysis of FG graphene platelet reinforced composite trapezoidally corrugated laminated panels

In this research, thermal buckling of trapezoidally corrugated functionally graded graphene platelet reinforced composite (FG-GPLRC) laminated panels are considered and analyzed. Each layer of trapezoidally corrugated panels (TCPs) are reinforced with different value of graphene platelets (GPLs) leading to a piecewise functionally graded (FG) media. The elastic properties of the laminated TCP are evaluated using the Halpin-Tsai scheme. The TCP is modeled by multiple patches. The stability equation of each patch is established using a logarithmic higher order shear deformation theory (HSDT) and then incorporating the isogeometric method. The associated matrices are then transformed appropriately to the global coordinates. Also, the continuity requirements between the boundaries of the patches are satisfied by the bending strip method (BSM). The reliability and accuracy of the proposed method are ascertained through comparison of the computed results with those exist in the open literature as well as those generated by ABAQUS. Afterwards comprehensive parametric studies are provided to show the effects of all influencing factors on the thermal buckling behavior of trapezoidally corrugated FG-GPLRC laminated panels. It is found that with constant corrugation angle and amplitude, when more corrugation units are added to the original panel, the critical buckling temperature difference remains almost constant.

Axisymmetric thermal postbuckling of functionally graded graphene nanocomposite annular plates with various geometric imperfections

This paper presents the axisymmetric thermal postbuckling analysis of functionally graded graphene platelets-reinforced composite (FG-GPLRC) annular plates with various geometric imperfections within the framework of first-order shear deformation theory and von Kármán geometric nonlinearity. An imperfection model composed of trigonometric and hyperbolic functions is used to simulate possible imperfections with different shapes, amplitudes and locations. The 3D Halpin–Tsai model is employed to estimate the effective modulus of graphene nanocomposites. Nonlinear governing equations are derived by the variational principle and are then solved by the generalized differential quadrature method combined with the modified Newton–Raphson iteration. Parametric studies are conducted to highlight the influences of imperfection amplitude, localization degree, location and half-wave number on the thermal postbuckling behaviour of FG-GPLRC annular plates. It is found that the thermal postbuckling resistance is reduced due to the existence of geometric imperfections, and this effect become more/less significant as the imperfection amplitude/half-wave number increases.

A new analytical approach of nonlinear thermal buckling of FG-GPLRC circular plates and shallow spherical caps using the FSDT and Galerkin method

A new analytical approach for nonlinear thermal buckling of Functionally Graded Graphene Platelet Reinforced Composite (FG-GPLRC) circular plates and shallow spherical caps using the first-order shear deformation theory (FSDT) is presented in this paper. The circular plates and shallow spherical caps are assumed to be subjected to uniformly distributed thermal loads. By applying the Galerkin method, the relations between thermal load–deflection are achieved to determine the postbuckling behavior and critical buckling loads of the considered structures. Special effects on the nonlinear thermal behavior of circular plates and shallow spherical caps with five different material distribution laws, different Graphene platelet (GPL) mass fractions, and geometrical dimensions are explored and discussed in numerical examples.

Nonlinear thermo-mechanical buckling and postbuckling of sandwich FG-GPLRC spherical caps and circular plates with porous core by using higher-order shear deformation theory

The main aim of this research is to establish the algorithm for nonlinear thermo-mechanical buckling of sandwich functionally graded graphene platelet reinforced composite (FG-GPLRC) shallow spherical caps and circular plates with porous core under external pressure and/or uniformly distributed thermal load according to the higher-order shear deformation theory considering the von Karman nonlinearities. Sandwich spherical caps and circular plates are made by the porous core and two FG-GPLRC coatings and are assumed to be rested on an elastic foundation modeled by the Pasternak model. The equilibrium equation system in the form of nonlinear algebra can be approximately obtained using the Ritz energy method. The critical buckling loads and postbuckling curves can be explicitly determined. The effects of material parameters, geometrical parameters, porous core, and elastic foundation on thermo-mechanical buckling of sandwich spherical caps and circular plates with porous core and FG-GPLRC coatings are investigated and discussed in detail in the numerical investigation section.

An analytical solution for vibration response of CNT/GPL/fibre/polymer hybrid composite micro/nanoplates

In the present article, a closed-form solution is carried out for the vibration response of CNT/GPL/fiber/polymer hybrid composite macro/micro/nanoplates resting on elastic support. Multi-layered fiber/polymer hybrid plates with either functionally graded carbon nanotube reinforced composite (FG-CNTRC) material or functionally graded graphene platelets reinforced composite (FG-GPLRC) material are two different types of plate considered here. The distribution of reinforcing nanocomposites can be uniform or functionally graded through the plate layers. The governing vibration equations are developed in the framework of the nonlocal elasticity theory of Eringen and using the first-order shear deformation plate theory. In the analytical solution procedure, the partial differential equations of motion are simplified to a series of homogeneous ordinary differential equations using a displacement field for Levy-type of the boundary conditions. The general solution of the obtained equations is expressed in terms of exponential functions. Using that the displacements should satisfy the remaining boundary conditions, the vibrational frequencies are derived. Finally, the influences of different parameters including geometry and material properties such as nonlocal parameter, number and angle of layers, volume fraction, and type of distribution of reinforcing nanocomposites are investigated and discussed. Natural frequencies for various boundary conditions are illustrated. The numerical results illustrate that the effects of the nonlocal parameter on the frequency decrease when one of the boundaries is free, and these effects increase when one of the boundaries is clamped for both FG-CNTRC and FG-GPLRC plates.

Nonlinear free vibration of rotating functionally graded graphene platelets reinforced blades with variable cross-sections

Titanium alloys are widely used for blades due to their favorable combination of high strength, low density and fatigue resistance. Dispersing graphene platelets (GPLs) into titanium alloy in a layer-wise manner to develop novel functionally graded (FG) GPL/titanium alloy blades can achieve further enhanced mechanical performance. This paper first proposes a functionally graded graphene/titanium alloy composite trapezoid plate to investigate the nonlinear free vibration of rotating blades with varying cross-sections. It is assumed that graphene platelets are uniformly dispersed in each layer of titanium alloy, and the weight fraction of GPLs increases from the middle layer to the top layers. The effective Young's modulus, effective Poisson's ratio and mass density are calculated by the modified Halpin-Tsai model and the rule of mixture, respectively. The discretized motion equations of the functionally graded graphene platelets reinforced composite (FG-GPLRC) trapezoid plate are derived by the energy method and Lagrange equations. The Rayleigh-Ritz method and direct iterative process are applied to obtain the linear frequencies and nonlinear frequencies, respectively. A detailed numerical study is carried out to investigate the effects of the material parameters and dimensional parameters on the linear and nonlinear free vibrations of the rotating FG-GPLRC trapezoid plate.

Nonlinear and chaotic vibrations of rotating functionally graded GPL reinforced composite pre-twisted blade subjected to aerodynamic force

The nonlinear and chaotic vibrations of the rotating functionally graded graphene platelet reinforced composite (FG-GPLRC) pre-twisted blade subjected to the aerodynamic force are investigated by taking into account the cantilever boundary condition. The rotating FG-GPLRC pre-twisted blade is simplified to a rotating FG-GPLRC pre-twisted cylindrical panel. The graphene platelets (GPLs) are dispersed uniformly and oriented randomly in every layer while the GPL volume fractions vary from the layer to layer, which leads to four different GPL distribution patterns. Based on the strain–displacement relationship of the pre-twisted cylindrical panel derived by Green strain tensor, the natural frequencies of the rotating FG-GPLRC pre-twisted cylindrical panel are obtained by using the first-order shear deformation theory and Chebyshev–Ritz method. Lagrange’s formulation is used to derive the nonlinear ordinary differential equations of motion. The complex chaotic vibrations of the rotating FG-GPLRC pre-twisted cylindrical panel are investigated by performing numerical simulations on the basis of Runge–Kutta algorithm. The bifurcation diagrams, Lyapunov exponents, time histories, phase portraits and Poincare maps are depicted to detect the periodic and chaotic vibrations of the rotating FG-GPLRC pre-twisted cylindrical panel with different parameters, such as Coriolis force, GPL distribution pattern, steady-state rotating speed, perturbation rotating speed and aerodynamic force. The double-parameter maximum Lyapunov exponent is regarded as an effective method to detect the chaotic regions of the rotating FG-GPLRC pre-twisted cylindrical panel.