Functionally Graded Material Panels Research Articles

Recent developments in modeling and analysis of rotating functionally graded panels: A review

This article presents a comprehensive review on recent developments in the techniques for modeling and exploration of rotating functionally graded material (FGM) panels carried out between periods 2000 to 2023. Special attention is given on literature pertaining to analysis of rotating FGM panels subjected to thermo-mechanical loading. This study scrutinizes the advancements made in analysis of panels such as beam, plate, shell and blades that includes effects like porosity, thermal stress, and piezo-electric in the mathematical model. The present article also highlights the importance and ease in implementation of rule of mixture for calculation of different temperature dependent material properties used in the analysis of rotating FGM panels. An in-depth review of literature clearly indicates the importance of taking thermal effect in the estimation of elastic properties for accurate analysis of rotating FGM panels. Further, a detailed analysis of temperature profile viz., linear/non-linear, is carried out. Finally, the article concludes with the future areas that need to be explored for the analysis of rotating FGM panels.

Vibration and thermomechanical transient response of doubly curved FGM panels with porosities and elastically restrained edges

The present paper aims to analyze the influences of porosities, elevated temperature and elasticity of in-plane boundary conditions on the free vibration and nonlinear transient response of functionally graded material (FGM) doubly curved panels subjected to uniform lateral pressure. Porosities are assumed to exist in the FGM according to even and uneven distributions. Effective properties of porous FGM are determined using a modified rule of mixture. Basic equations in terms of deflection and stress function are derived basing on the classical shell theory taking into account von Kármán–Donnell nonlinearity and initial geometrical imperfection. Analytical solutions for simply supported panels are assumed and Galerkin method along with Runge–Kutta scheme are applied to obtain the deflection–time response for nonlinear dynamic analysis. Numerical results demonstrate that tangential constraints of edges have extremely significant influences on the vibration and transient response of porous FGM panels exposed to an elevated temperature. The analysis also reveals that porosities have negative and positive effects on the dynamic response of FGM panels at reference and elevated temperatures, respectively. Furthermore, when the edges are restrained, initial imperfection importantly influence the behavior tendency of porous FGM panels exposed to preexist thermal environment.

Comparison between linear and nonlinear buckling loads of FGM cylindrical panel with cutout

This paper investigates the influences of effective parameters on the Difference between the Linear and Nonlinear Buckling Loads (DLNBL) of Functionally Graded Material (FGM) perforated cylindrical panel. In this regard, the panel was simulated using spline finite strip method. The linear and nonlinear buckling loads of the panel were obtained from linearized eigenvalue method and nonlinear geometric analysis. A comparison was made between the results obtained from the model developed in this study and those available in the literature to evaluate the validity of the results obtained from the model. Through a parametric study, the influences of different effective parameters such as cutout size, cutout shape, ratio of radius to thickness and power of FGM on the difference between the linear and nonlinear buckling loads of the panel were investigated. Although for the panels without cutout, the DLNBL was about 2 percent, it reached to 40 percent for the panels having cutout. As the cutout area increases or cutout shape changes from circle to long ellipse, the DLNBL increases significantly. Moreover, the DLNBLs obtained for shallow and FGM panels were lower than those for the deep and isotropic panels. The results obtained indicate that the buckling load obtained from linearized eigenvalue method is overestimated by about 40% for the FGM panel having long elliptical cutout. Finally, contour graphs were derived to determine the maximum difference between linear and nonlinear buckling loads of FGM panel based on the shape of cutout, size of cutout and ratio of radius to thickness of the panel. According to these graphs, the linearized eigenvalue method is not a proper method to obtain the buckling load of panels having long elliptical cutout and deep panels having medium elliptical cutout.

Geometrical nonlinear numerical frequency prediction of porous functionally graded shell panel under thermal environment

The nonlinear eigenfrequency responses of a functionally graded material (FGM) panel in a thermal environment are numerically estimated in the present article using the finite element method (FEM). The constituents of the FGM are considered as the function of the temperature. For the evaluation of material properties of the FGM panel, Voigt’s micromechanical model is used in conjunction with three distinct types of material distribution patterns, namely power-law (PL), sigmoid (SM), and exponential (EN). Also, two kinds of porosity distributions, i.e. even (PT-I) and uneven (PT-II) through the panel thickness are considered in the present work. HSDT kinematics and Green–Lagrange nonlinear strain terms are employed to prepare a mathematical model of the FG panel. The governing equation is obtained using Hamilton’s principle, and a direct iterative technique is used to compute the final vibration responses. The convergence and validation are performed to check the stability and accuracy of the proposed model. Afterwards, several numerical examples are solved to demonstrate the proposed model efficacy in terms of currently adopted input parameters on the frequency (nonlinear) responses deliberated in detail.

Static and dynamic analyses of functionally graded sandwich skew shell panels

The present work is an attempt to develop a simple, accurate and widely applicable finite element formulation having a C0 continuity of transverse displacement at nodes, for static and dynamic analyses of functionally graded sandwich skew shell (FGSSS) panels. A layerwise displacement field based on first-order shear-deformation theory for each layer along with Sanders’ approximation has been adopted for the analysis. Compatibility conditions are imposed at the layer interfaces to satisfy displacement continuity. Two different configurations of FGSSS are taken up in the present investigation. In the first configuration, the top and bottom layers of the panel are made of functionally graded material (FGM) and the core is made of pure metal, whereas in the second configuration, the top and bottom layers are made of pure ceramic and pure metal, respectively and the core is considered to be made of FGM. The material properties of both configurations of FGM panels are estimated according to the rule of mixture. It is observed from the analysis that the present finite element formulation is simple, accurate and computationally efficient. Parameters like skew angle, span to thickness ratio, core to facesheet thickness ratio, volume fraction and boundary conditions have a significant effect on static and dynamic behavior of functionally graded sandwich skew shell panels.

Buckling analysis of functionally graded materials by dynamic approach

Laminated composites exhibit difference in the mechanical properties at the interface between two materials resulting in stress concentration. This may lead to damages in the form of delamination, matrix cracking and adhesive bond separation. Functionally Graded Materials (FGM) are formed by gradual variation of two or more material over a particular volume, thereby overcomes these issues. Buckling problems of FGM plates are usually solved by static approach. In some cases, particularly non-uniform loading and geometric discontinuity, the stress concentration usually occurs. In such cases, the solution to the buckling problem by dynamic approach is most suitable. In the dynamic approach, the natural frequencies are calculated by applying in-plane loads. As the intensity of the in-plane load increases, the frequency of the material decreases and finally becomes zero at the onset of buckling. The load at which the natural frequency becomes zero that load is called a buckling load. In this investigation, the vibration and buckling characteristics of FGM panels subjected to uniaxial and biaxial loading conditions have been studied by using the finite element method (F.E.M). In the Finite element (FE) formulation, the effective material properties of FGM plates are assumed to vary in the thickness direction according to the power-law distribution of volume fraction of the constituents. The plate is modelled by using 8-noded serendipity element by incorporating the effect of transverse shear deformation and rotary inertia. The effect of different parameters such as volume fraction index (n), the thickness of the panel (h) and boundary condition of the plate are considered to study the buckling behaviour of the FGM plate under uniaxial loading conditions.

Bending response in smart functionally graded panels using a zigzag theory

Bending response in smart functionally graded material (FGM) panels is presented using a zigzag theory. The functionally graded panel has sensing and actuation capabilities due to the presence of two piezoelectric layers at its outer surfaces. The theory is capable of predicting structural responses in presence of material property continuity as well as discontinuity at the interfaces. Rule of mixtures is used in obtaining effective material properties across thickness of each layer. Governing equations and boundary conditions have been derived using variational principle. Responses in piezoelectric laminated FGM panels have been analyzed using two smart FGM panels of which one panel contains non-symmetric FGM substrate and the other contains symmetric FGM substrate. Effects of variation of the power law index have been studied in thick and moderately thick multilayered smart FGM panels.

Adhesion failure propagation analyses of Spar Wingskin Joints made with curved laminated FRP composite and FGM panels

Spar Wingskin Joint (SWJ) comprises of a thin spar which overlaps and is co-cured to a thick wingskin by suitable adhesive materials. These joints are mostly used in integral modular fabrication of aircraft and fuselage wing structures usually made with curved laminated Fibre Reinforced Polymeric (FRP) composite panels. This paper deals with the analyses of initiation of adhesion failure and its propagation in SWJs subjected to transverse loadings using Finite Element Analyses (FEA) and fracture mechanics approach. Normal and shear stress distributions at different interfacial locations between the adherends and the adhesive have been evaluated. Tsai-Wu coupled stress failure criteria have been used to identify the location of onset of adhesion failure. The critical location for onset of adhesion failure has been found to be at the toe-end of the spar wingskin overlap region. Pre-embedded adhesion failure has been simulated at this location and Strain Energy Release Rate (SERR) components corresponding to Mode I, Mode II and Mode III of adhesion failure have been determined using the principle of Virtual Crack Closure Technique (VCCT). Rate of propagation of adhesion failure has been evaluated by sequential release of Multi-Point Constraint (MPC) and contact finite elements provided at the pre-embedded failure front. It has been observed that Mode I component of SERR primarily governs the process of adhesion failure propagation. The appropriate spar overlap length on the wingskin has been determined in order to prevent adhesion failure. Further, an attempt has been made to improve the structural integrity of the SWJ by reducing the stress concentration at the ends of spar and wingskin overlap. This has been achieved by obtaining a favourable stress distribution over the entire joint structure by using Functionally Graded Materials (FGM) in the spar and wingskin adherend instead of FRP composite panels. Exponential gradation indices have been used for material grading of the spar and wingskin adherends. It has been seen that peel and shear stresses and values of SERR components as well as total SERR reduce significantly by use of FGMs with suitable exponential material grading index.

Non-linear wrinkling of a sandwich panel with functionally graded core – Extended high-order approach

The non-linear response of a sandwich panel with the core that consists of a functionally graded material (FGM) undergoing in-plane loading is investigated. The panel consists of two face sheets, metallic or composite laminated, and an FGM core that is a medium whose mechanical properties change through the depth facilitating a desirable response of the structure. The effect of the FGM core is introduced through the constitutive relations that affect conventional and high-order stress resultants and stress couples in the panel. The formulation employs the Extended High-Order Sandwich Panel Theory (EHSAPT) to assess the effect of the FGM material of the core. A variational approach is adopted to derive the linear and non-linear governing equations with a prescribed FGM distribution through the depth of the core. The wrinkling study of FGM panels includes two loading scenarios where in-plane loads are applied through a rigid edge beam connected to the core only and where the loads are applied through a rigid edge structure attached to both the face sheets and core causing uniform end shortening. The post-wrinkling behavior is also considered to prove that the initial pattern of wrinkles is not affected.

Nonlinear dynamic response and vibration of imperfect eccentrically stiffened sandwich third-order shear deformable FGM cylindrical panels in thermal environments

This study follows an analytical approach to investigate the nonlinear dynamic response and vibration of eccentrically stiffened sandwich functionally graded material (FGM) cylindrical panels with metal–ceramic layers on elastic foundations in thermal environments. It is assumed that the FGM cylindrical panel is reinforced by the eccentrically longitudinal and transversal stiffeners and subjected to mechanical and thermal loads. The material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution. Based on the Reddy’s third-order shear deformation shell theory, the motion and compatibility equations are derived taking into account geometrical nonlinearity and Pasternak-type elastic foundations. The outstanding feature of this study is that both FGM cylindrical panel and stiffeners are assumed to be deformed in the presence of temperature. Explicit relation of deflection–time curves and frequencies of FGM cylindrical panel are determined by applying stress function, Galerkin method and fourth-order Runge-Kutta method. The influences of material and geometrical parameters, elastic foundations and stiffeners on the nonlinear dynamic and vibration of the sandwich FGM panels are discussed in detail. The obtained results are validated by comparing with other results in the literature.

Thermoelastic vibration and maneuver control of smart satellites

PurposeThe purpose of this paper is to analyze and control the thermally induced vibration of orbiting smart satellite panels, which have been modeled as functionally graded material (FGM) beams.Design/methodology/approachIt is assumed that the satellite moves in a circular orbit and has pitch angle rotation maneuver. Rapid temperature changes at day–night transitions in orbit generate time dependent bending moments that induce vibrations in the appendages. So, the heat radiation effects on the appendages should be considered. The thermally induced vibrations of the appendages and the nonlinear heat transfer equation are coupled and should be solved simultaneously. So, the governing equations of the motion are nonlinear and very complicated ones. A robust passivity-based controller is proposed to control the satellite maneuver and appendages vibrations, using piezoelectric sensors/actuators.FindingsAfter the simulation, the effects of the heat radiation, piezoelectric actuators and piezoelectric locations on the response of the system are studied. The results of dynamic response and thermal analysis show that the radiation thermal effects are coupled with structure dynamic. These effects induce the vibration. Also, the effectiveness and the capability of the controller are analyzed. The results of the simulation show that the robust passivity-based control can ensure that the satellite rotates in the desired trajectory and vibrations of the appendages are damped. It demonstrates that the proposed control scheme is feasible and effective.Originality/valueThe paper is the basis of deriving the governing equations, thermal analysis and a robust control system design of a smart satellite with FGM panels.

Experimental and theoretical investigation of the thermo-mechanical deformation of a functionally graded panel

An aluminum/high-density polyethylene (HDPE) functionally graded material (FGM) has been fabricated as a key component of a multifunctional building envelope for energy efficiency and sustainability. Because of the gradual phase change of aluminum and HDPE across the thickness direction, when a free-standing FGM panel is subjected to a temperature variance, it will exhibit considerable curling deformation, which causes challenges to assemble the FGM panel into a flat multifunctional roofing panel and also to assure structural integrity under cyclic temperature change. Therefore, it is crucial to predict the thermo-mechanical behavior of the FGM panel. For this purpose, an axisymmetric refined plate theory was developed in this study for a circular FGM panel subjected to externally applied thermo-mechanical loading. The theoretical solutions are verified with experimental results, it demonstrates that the presented solution can accurately predict the thermo-mechanical behavior of the developed FGM panel and be used in the design of the proposed solar panel.

Manufacture and multi-physical characterization of aluminum/high-density polyethylene functionally graded materials for green energy building envelope applications

An aluminum/high-density polyethylene (HDPE) functionally graded material (FGM) has been fabricated as an essential component of a multifunctional building envelope for high performance of energy efficiency and sustainability. The mass production of the FGM was realized by using coarse aluminum (Al) particles and fine HDPE powder through a vibration-sedimentation process. The gradation of the FGM across its thickness direction was analyzed by developing a modified Rice method, from which five different uniform Al-HDPE samples were made to characterize the material properties of the five sub-layers of the FGM. The mechanical and thermal physical properties of the FGM such as Young's modulus, Poisson ratio, thermal expansion coefficients and thermal conductivities were obtained by various experimental characterizations. A prototype FGM panel with water tubes embedded was fabricated by the vibration and sedimentation combined approach and the thermal efficiency of the FGM panel was evaluated. Under an irradiation level of 620w/m2 and a water flowing rate of 60ml/min, a 22.3°C water temperature increase and an average 18.7°C surface temperature decrease of the FGM panel were achieved, which demonstrates that significant PV conversation efficiency improvement can be realized for both electricity generation and heat collection by the presented FGM panel. The presented fabrication procedures and the associated experimental characterization methods and results can serve as a baseline for quality control of the manufacture of the green energy building envelope materials.

Stress field of a radially functionally graded panel with a circular elastic inclusion under static anti-plane shear loading

The elastic stress field around a circular elastic inclusion in an infinite functionally graded material (FGM) panel that is subjected to a uniform static anti-plane shear loading at infinity is considered. Assuming the rigidity modulus of the FGM panel to be exponential, the analytical solutions of stress and strain distribution around the circular elastic inclusion are obtained by using the variable separation method. Due the generality of the elastic inclusion, other geometrical discontinuities, such as hole and rigid inclusion, can be seen as special cases of circular elastic inclusion when the inclusion rigidity modulus takes a suitable value. Therefore, the present solutions ana- lytically reduce to some classical solution in some special cases. The present analytical solutions are compared with the existing exact solutions to verify them. Finally, the effects of the relative inclusion rigidity modulus ratio and the inhomogeneous rigidity modulus ratio on the stress distribution and the concentration factor are systematically investigated.

Thermal post-buckling and snap-through instabilities of FGM panels in hypersonic flows

The thermo-mechanical behaviors of functionally graded material (FGM) panels are investigated in hypersonic airflows. Present study deals with the three types of material such as power-law FGM (P-FGM), sigmoid FGM (S-FGM) and exponential FGM (E-FGM) models. Based on the first-order shear deformation theory of plate and von Karman strain-displacement relations are adopted in the formulation. Also, the non-linearity is considered as a model for the aerodynamic loads, and thus the pressure is evaluated using the third-order piston theory. Newton–Raphson iterative method is applied to solve the thermal post-buckling behavior in the numerical analysis. In order to validate the modeling and formulation, present results are compared with the previous data. More works reveal that the thermal or aerodynamic loads exceed a critical value, then the panel snaps to the opposite equilibrium position in this study. Especially, snap-through instabilities are more deeply investigated in the thermal post-buckling behavior of FGM panels in hypersonic regimes.

Dynamic analysis and active control of smart doubly curved FGM panels

In this paper, active control and dynamic analysis of shallow doubly curved functionally graded material (FGM) panels integrated with sensor/actuator piezoelectric layers are presented, analytically. Properties of the FGM panel are dictated using a simple power law model across the thickness. Based on the modified Sander’s shell theory combined with first order shear deformation theory, total potential energy of the system is derived. Five mechanical equilibrium equations and two electrical equations are established as the governing equations. The classical negative velocity feedback controller rule is implemented to suppress the vibration response of the panel. For both the active and passive cases, established equations are reduced into new five equations in terms of displacements and rotations. Employing the combined analytical Fourier–Laplace transformation, consistent with the panels with movable simply-supported edges, an accurate closed-form solution is resulted for response of the panel in both active and passive cases in real time domain.

Static and dynamic analysis of an FGM doubly curved panel resting on the Pasternak-type elastic foundation

The static, dynamic, and free vibration analysis of a functionally graded material (FGM) doubly curved panel are investigated analytically in the present paper. The FGM Panel is originated from a rectangular planform and its principle curvatures are considered to be constant. All mechanical properties of the FGM panel are assumed to vary continuously through the thickness according to a power law formulation except Poisson’s ratio, which is kept constant. A Pasternak-type elastic foundation containing damping effects is considered to be in contact with the panel during deformation. The elastic foundation reacts in both compression and tension. Equations of motion are established based on the first order shear deformation and the modified Sanders shell theories. Following the Navier type solution, the established equations are reduced to time-dependent ordinary differential equations. Using the Laplace transform, the time-dependency of the problem is eliminated. The solutions are obtained analytically in the Laplace domain and then are inverted to the time domain following an analytical procedure. Finally, the analytical results are verified with those reported in the literature.

A Review of Nonlinear Aero-Thermo-Elasticity of Functionally Graded Panels

Functionally Graded Materials (FGM) have attracted significant interest as heat-shielding materials for space vehicle, skin sub-structures, gas turbine blades technologies, and many other high-temperature industrial applications. This paper reviews the state-of-the-art in linear and nonlinear aero-thermo-elasticity of FGM panels with emphasis on the authors’ contributions to the topic. An overview of the pertinent literature discussing the linear and nonlinear behavior of flat and curved panels when exposed to high temperature supersonic flow fields is presented first. The effect of material property dependency on temperature is also discussed. The study addresses divergence and flutter and methodologies used to determine these aero-thermo-elastic instabilities. In particular, critical and post-critical behaviors for panels in presence of thermal loads are addressed, along with a series of divergence, flutter, and post-flutter results obtained with linear/nonlinear dynamics approaches. Regular and chaotic motions regime are determined through qualitative tools, such as bifurcation analysis using Poincaré maps, panel time history, phase-space evolutions, and frequency spectra, and with quantitative tools, such as the Lyapunov's exponents and dimensions. Finally, conclusions and directions for further work in the field are presented.

Effect of Elevated Temperature on the Flutter Characteristics of FGM Panel

This paper investigates the stability issues of functionally graded material (FGM) panels subjected simultaneously to both aerodynamic and thermal loads. Finite Element Method is employed to model the panel structures and the supersonic aerodynamics is calculated by the first-order piston theory. The critical buckling temperature elevation of the panels is at first predicted. The nonlinear static analysis of the panels is then implemented at certain interval of temperature elevation before buckling onset to obtain structural stiffness matrix. The flutter speed of the panels with updated stiffness matrix corresponding to a certain temperature elevation is estimated. The results show that the FGM panels can offer beneficial effects, especially prevention from buckling. However, if FGM panels integrated with TPS are to be applied on supersonic vehicles, one should pay more attention to the boundary conditions to guarantee the dynamic stability.

Limit-cycle Oscillations of Functionally Graded Material Plates Subject to Aerodynamic and Thermal Loads

The nonlinear flutter and thermal buckling of a functionally graded material (FGM) plate panel subjected to combined thermal and aerodynamic loads are investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. The thermal load is assumed to be steady-state constant temperature distribution, and the aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The governing nonlinear equations of motion are obtained using the principle of virtual work adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature dependent material properties. The static nonlinear equations are solved by Newton-Raphson numerical technique to get the thermal post-buckling deflection. The dynamic nonlinear equations of motion are transformed to modal coordinates to reduce the computational efforts. The Newmark implicit integration scheme is employed to solve the second order ordinary differential equations of motion. Finally, the buckling temperature, post-buckling deflection and the nonlinear limit-cycle oscillations of an FGM panel are presented, illustrating the effect of volume fraction exponent, dynamic pressure, temperature rise, and boundary conditions on the panel response.