Functionally Graded Panels Research Articles

Theoretical thermoelastic frequency prediction of multi (uni/bi) directional graded porous panels and experimental verification

A novel finite element algorithm has been developed to analyse the eigenvalue characteristics of porous functionally graded (FG) curved panel under a thermal environment, considering the material gradings along the length and thickness, i.e. unidirectional (1D) and bidirectional (2D). In this research, exponential (EN), sigmoid (SM) and power-law (PL) gradings and porosity variations, i.e. even (POT-I) and uneven (POT-II), are adopted. The finite element (FE) computational algorithm has been prepared using a mathematical model of the FG panel based on the higher-order theory (HSDT). The structural governing equation is derived via Hamilton’s principle and solved numerically (FE solutions) to predict the eigenvalues. The obtained solution’s convergence is verified to establish the necessary stability. The difference between the present and published results is below 3.7%, and that between the present and experimental results is under 9.1%, which shows the accuracy of the developed model. A few natural fibre-reinforced (linearly varying through the thickness) polymeric layered FG plates are prepared for experimental validation. Finally, regarding the applicability of the proposed computational FE algorithm, a few parametric studies have been conducted to examine the effect of input variables on the thermal frequencies of the graded panel.

Nonlinear Vibration Analysis of Multidirectional Porous Functionally Graded Panel Under Thermal Environment

Nonlinear thermal frequency characteristics of multidirectional doubly curved, functionally graded (FG) panels are examined numerically in the current paper using the finite element method. The material properties of the FG panel are computed using individual temperature-dependent properties of the FG constituents and by using Voigt’s micromechanical model in conjunction with different types of material distribution patterns. Also, two types of porosity distributions through the panel thickness are considered in the present work. Higher-order shear deformation theory kinematics and Green–Lagrange nonlinearity are used to create a mathematical model. The graded panel’s governing equation is obtained and solved using Hamilton’s principle and the direct iterative method. The stability and correctness of the proposed model have been checked via a convergence and validation study. Several numerical examples are solved and discussed in the paper to show the efficacy of the proposed model.

Thermo-elastic free vibration analysis of functionally graded flat panel with temperature gradient along thickness

In this paper, the free vibration behavior of functionally graded (FG) flat panels subjected to temperature gradient along the thickness direction is investigated by utilizing the temperature independent as well as dependent material properties. The FG panels are modeled using ANSYS commercial package in the framework of first-order shear deformation theory. The convergence and the validity of the present model have been established by comparing the present results with the benchmark results available in published literature. Subsequently, the influence of elevated temperature load, aspect ratio, thickness ratio, and support conditions on the non-dimensional fundamental frequency is investigated by varying the gradient index of the FG panel. The temperature and the consideration of the temperature dependence of the material properties is found have significant influence on the fundamental frequency of the FG panel. The effect of other design parameters on the natural frequency of the FG flat panel under thermal environment has also been examined and discussed in detail.

Nonlinear vibration characteristics of shear deformable functionally graded curved panels with porosity including temperature effects

In this study, nonlinear thermo-elastic vibration characteristics of shear deformable functionally graded (FG) curved porous panels have been analyzed using the finite element method. The present formulation is based on the higher-order shear deformation nonlinear shell theory. The FG panels' material properties are varied continuously in the thickness direction by a simple power law distribution in terms of the constituents’ volume fractions. The distribution of the porosity along the thickness direction is considered as even and uneven distribution. Comparison and convergence studies have been performed to validate the present nonlinear formulation. Parametric studies have been performed to study the effect of different influencing parameters on the frequency ratio of the curved FG panels, i.e., porosity, temperature rise, volume fraction indices, and side-to-thickness ratios. The benchmark solutions for the problems of large amplitude vibration characteristics have been accomplished with the present model.

Structural analysis of size-dependent functionally graded doubly-curved panels with engineered microarchitectures

Advances in multi-material 3D printing technologies have opened a new horizon for design and fabrication of architected multi-materials in multiple length scales from nano-/microscale to meso-/macroscales. In this study, we apply modified couple stress and first-order shear deformation theories for a size-dependent structural analysis of 3D printable functionally graded (FG) doubly-curved panels where their microarchitecture can be engineered to improve their structural performance. This non-classical model incorporates the microstructure-dependent size effects for the structural performance through the introduction of a length scale in the kinematics of deformation. The volume fraction of matrix in the dual-phase (inclusion and matrix) FG size-dependent panels varies continuously through the thickness. The microarchitecture of inclusion and matrix in FG panels is engineered to show its effect on the structural responses. We implement the standard mechanics homogenization technique via finite element simulation to accurately predict the effective mechanical properties of FG materials for different topologies of engineered microarchitecture to show the significance of selecting appropriate micromechanical modeling for analyzing FG structures. Governing equations derived by variational Hamilton’s principle are solved by applying the Galerkin method for different sets of boundary conditions. We investigate the effects of material length scale, material composition, heterogeneous material distribution, particulate topology, length-to-thickness ratio, and panel curvature on the structural performance. It is found that the fundamental frequencies of size-dependent two-phase FG doubly-curved panels with square-shape inclusions are higher than for those with other topologies, which sheds lights on the engineering of the inclusion shape in advanced architected materials to optimize their structural performance.

Free vibration of moderately thick functionally graded parabolic and circular panels and shells of revolution with general boundary conditions

PurposeThe purpose of this work is to apply the Fourier–Ritz method to study the vibration behavior of the moderately thick functionally graded (FG) parabolic and circular panels and shells of revolution with general boundary conditions.Design/methodology/approachThe modified Fourier series is chosen as the basis function of the admissible functions of the structure to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges, and the vibration behavior is solved by means of the Ritz method. The complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of FG parabolic and circular panels at the common meridian of θ = 0 and 2π. The convergence and accuracy of the present method are verified by other contributors.FindingsSome new results of FG panels and shells with elastic restraints, as well as different geometric and material parameters, are presented and the effects of the elastic restraint parameters, power-law exponent, circumference angle and power-law distributions on the free vibration characteristic of the panels are also presented, which can be served as benchmark data for the designers and engineers to avoid the unpleasant, inefficient and structurally damaging resonant.Originality/valueThe paper could provide the reference for the research about the moderately thick FG parabolic and circular panels and shells of revolution with general boundary conditions. In addition, the change of the boundary conditions can be easily achieved by just varying the stiffness of the boundary restraining springs along all the edges of panels without making any changes in the solution procedure.

Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions

In this paper, porosity-dependent aero-hygro-thermal instability of functionally graded (FG) panels is investigated by developing a higher-order refined shear deformable theory for the first time. Porosities are randomly distributed around the cross section of FG panel. Hygro-thermo-elastic material properties of porous FG panel are described using a modified power-law function accounting for even and uneven porosity distributions. Based on the presented refined shear deformation theory, it is possible to examine instability regions of thicker FG panels without using a shear correction factor. Employing extended Hamilton’s principle, the governing equations of FG panel under supersonic airflow simulated via first-order piston theory are obtained. It is concluded that porosity volume fraction, type of porosities, hygro-thermal environment, material gradation and slenderness ratio have major roles on the prediction of divergence and flutter boundaries of porous FG panels.

Dynamic relaxation method for nonlinear buckling analysis of moderately thick FG cylindrical panels with various boundary conditions

Using new approach proposed by Dynamic relaxation (DR) method, buckling analysis of moderately thick Functionally graded (FG) cylindrical panels subjected to axial compression is investigated for various boundary conditions. The mechanical properties of FG panel are assumed to vary continuously along the thickness direction by the simple rule of mixture and Mori-Tanaka model. The incremental form of nonlinear formulations are derived based on First-order shear deformation theory (FSDT) and large deflection von Karman equations. The DR method combined with the finite difference discretization technique is employed to solve the incremental form of equilibrium equations. The critical mechanical buckling load is determined based on compressive load-displacement curve by adding the incremental displacements in each load step to the displacements obtained from the previous ones. A detailed parametric study is carried out to investigate the influences of the boundary conditions, rule of mixture, grading index, radius-to-thickness ratio, length-to-radius ratio and panel angle on the mechanical buckling load. The results reveal that with increase of grading index the effect of radius-to-thickness ratio on the buckling load decreases. It is also observed that effect of distribution rules on the buckling load is dependent to the type of boundary conditions.

Nonlinear Thermomechanical Behavior of Functionally Graded Material Cylindrical/Hyperbolic/Elliptical Shell Panel With Temperature-Dependent and Temperature-Independent Properties

In this article, the nonlinear bending behavior of functionally graded (FG) curved (cylindrical, hyperbolic, and elliptical) panel is investigated under combined thermomechanical loading. In this study, two temperature fields (uniform and linear) across the thickness of shell panel are considered. The panel model is developed mathematically using higher-order shear deformation midplane kinematics with Green–Lagrange-type nonlinear strains. The individual constituents of functionally graded material (FGM) are assumed to be temperature-dependent (TD) and graded continuously using the power-law distribution. The effective material properties of FG shell panel are evaluated based on Voigt's micromechanical model. The governing equation of the panel structure is obtained using the variational principle and discretized through suitable finite-element (FE) steps. A direct iterative method is employed to compute the desired responses of the curved panel structure. The efficacy of the present nonlinear model has been shown by comparing the responses with those available published literature and commercial FE tool ansys. Finally, the model has been extended to examine the effect of various parameters (volume fractions, temperature, thickness ratios, curvature ratios, aspect ratios, and support conditions) on the nonlinear bending behavior of curved FG panel by solving wide variety of numerical illustrations.

Aerothermoelastic Analysis of Functionally Graded Plates Using Generalized Differential Quadrature Method

In the present paper, the aerothermoelastic behavior of Functionally Graded (FG) plates under supersonic airflow is investigated using Generalized Differential Quadrature Method (GDQM). The structural model is considered based on the classical plate theory and the von Karman strain-displacement relations are utilized to involve the nonlinear behavior of the plate. To consider the supersonic aerodynamic loads on the plate, the first order piston theory is applied. The material properties of the FG panel are assumed to be temperature independent and alter in the thickness direction according to a power law distribution. The temperature distribution on the surface of the plate is assumed to be constant and in the thickness direction is obtained by one-dimensional steady conductive heat transfer equation. The discretized governing equations via GDQM are solved by the fourth order Runge-Kutta method. Comparison of the obtained results with those available in literature confirms the accuracy and ability of the GDQM to perform the aerothermoelastic analysis of FG plates. Also, the effect of some important parameters such as Mach number, in-plane thermal load, plate aspect ratio and volume fraction index on the plate aerothermoelastic behavior is examined.

Bifurcation analysis of FG curved panels under simultaneous aerodynamic and thermal loads in hypersonic flow

This study presents a numerical analysis for aerothermoelastic behavior of functionally graded (FG) curved panels in hypersonic airflow regime. The classical plate theory is used to model the structural treatment and the von Karman strain–displacement relations are utilized to involve the structural nonlinearity. To incorporate the applied hypersonic aerodynamic loads, third-order piston theory is employed to model unsteady aerodynamic pressure in this flow regime. The material properties of a FG panel are supposed to be temperature-dependent and vary continuously through the thickness direction according to power-law distribution of the volume fraction of the constituents. The temperature distribution in the thickness direction is calculated by the solution of one-dimensional steady-state heat conduction equation. The Generalized Differential Quadrature (GDQ) method in conjunction with the fourth order Runge–Kutta method is implemented for discretization and solution of the equations. The effects of several significant parameters including Mach number, curvature, dynamic pressure, surface temperature and volume fraction index on the FG curved panel aerothermoelastic behavior and route to chaos are examined. Comparison of the obtained results with those available in the literature demonstrates the accuracy and reliability of the GDQ method to analyze the aerothermoelastic behavior of FG curved panels in hypersonic flow.

Investigation of Aerothermoelastic Behaviors of Functionally Graded Panels in Supersonic Flows

Considering the potentials of Functionally Graded Panels (FGPs) in aerospace field, it is necessary to study the aerothermoelastic behaviors of FGPs in supersonic flows. In this study, Piston Theory Aerodynamics (PTA) and Eckert reference enthalpy method are used to model aerodynamic force and heating, respectively. The 2-D heat conduction equation is solved and the impact of elevated temperature on the mechanical properties of FGPs is considered to build an aerothermoelastic two-way coupling model of FGPs, and Finite Element Method (FEM) is used to approach the solution. As the results, it is found that there exist three different regions in the bifurcation diagram, namely, thermal buckling region, critical region and flutter region. Due to the inhomogeneous distribution of thermal expansion coefficient, the panel buckles up first and then buckles down via vibration, as thermal buckling happens. Also, irregular vibrations are observed in the critical region of bifurcation diagram. In the flutter region, the dynamic behavior of FGPs is discontinuous and very sensitive to initial conditions. With the impact of aerothermoelastic two-way coupling, different FGPs behaviors lead to the differences in temperature distribution. In particular, the final buckling position and vibration center move to lower positions, and lower temperature region near leading edge is left in the FGPs, because of thermal moment. Also, regular vibrations, rather than irregular vibrations, are easy to extract more principal and regular POD (Proper Orthogonal Decomposition) modes. The results presented could be applied to the analysis and design of Functionally Graded Panels in supersonic flows.

Thermal post-buckling and the stability boundaries of structurally damped functionally graded panels in supersonic airflows

Abstract In this study, the thermal post-buckling behaviors and linear flutter analysis of structurally damped functionally graded (FG) panels under a supersonic airflow are investigated. The material properties are assumed to be temperature-dependent and vary in the thickness direction of the panel. First-order shear-deformation theory (FSDT) is applied to model the panel, and the von Karman strain–displacement relations are adopted to consider the geometric nonlinearity. In addition, the damping is modeled as the Rayleigh damping, and first-order piston theory is applied for the supersonic aerodynamic load. Results are obtained for the thermal post-buckling behavior, and linear flutter analysis of FG panels with a damping effect is performed to search for the origin of the flutter. The numerical data are validated through a comparison with the previous works, and the effects of structural damping are discussed in detail for various cases.

Thermal Post-Buckling Analysis of Functionally Graded Panels in Hypersonic Airflows

In this study, thermal post-buckling characteristics of functionally graded (FG) panels in hypersonic airflows are investigated. The volume fraction and the material properties of FGMs are continuously changed from ceramic to metal in the thickness direction agreeably to a simple power law distribution and a linear rule of mixture, respectively. Using the principle of virtual work, the governing equations are derived and the finite element method is applied to obtain the solutions. Based on the first-order shear deformation theory (FSDT), the FG panels are modeled by the von Karman strain-displacement relation for the structural non-linearity. Also, the third-order piston theory is employed to consider the aerodynamic non-linearity.

Nonlinear thermal flutter of functionally graded panels under a supersonic flow

Abstract Thermal flutter characteristics of functionally graded (FG) ceramic/metal panels under the thermal and aerodynamic loads are investigated. The volume fractions of the constitutive materials are determined by a simple power-law distribution, and material properties are assumed to be a linear rule of mixture. The panels are considered as rectangular plates based on the first-order shear deformation theory, and the von Karman strain–displacement relations are used to account for the geometric nonlinearity. The first-order piston theory is adopted to represent aerodynamic pressures induced by supersonic airflows. The principle of virtual work is applied to derive equations of motion, and a finite element method is used to obtain numerical solutions. The Newton–Raphson method is adopted to obtain approximate solutions of the nonlinear governing equations. Flutter boundaries are defined by eigenvalue analysis, and the Guyan reduction is used to reduce degree of freedom. Flutter motions of FG panels are investigated using the Newmark method. The effects of volume fraction distributions, boundary conditions, temperature changes and aerodynamic pressures on panel flutter characteristics are analyzed in detail.

Structural stability of functionally graded panels subjected to aero-thermal loads

Abstract Static and dynamic stabilities of functionally graded (FG) panels which are subjected to combined thermal and aerodynamic loads are investigated. The volume fractions of constituent materials composing the FG panels are assumed to be given by a simple power law distribution. Material properties of the FG panels are obtained by a linear rule of mixture. Panels are considered as rectangular plates which are based on the first-order shear deformation theory. The von Karman strain–displacement relation is used to account for geometric nonlinearity, which is caused by a large deformation. The first-order piston theory is used to simulate supersonic aerodynamic loads acting on the panels. Equations of motion are derived by the principle of virtual work and numerical solutions are obtained by a finite element method. The Newton–Raphson method is applied to get solutions of the nonlinear governing equations. Flutter boundaries are defined by linear flutter analysis and the Guyan reduction is applied to reduce degree of freedom for eigenvalue analysis. The influence of the material constitution, asymmetric characteristics of FG panels on thermal buckling and flutter characteristics are examined. Static and dynamic stability margins of FG panels are defined for various volume fractions.