Thermal stability of eccentrically stiffened FGM plate on elastic foundation based on Reddy's third-order shear deformation plate theory

This article studies the nonlinear thermal buckling and postbuckling of eccentrically stiffened functionally graded plates on elastic foundation subjected to mechanical, thermal, and thermomechanical loads. The noticeable point of this study is using the Reddy's higher order shear deformation plate theory and a general formula for the forces and moments of eccentrically stiffened functionally graded material (FGM) plate, which takes into account the influence of temperature on both the FGM plate and stiffeners. The article used the Galerkin method, stress function, and iterative method to determine the thermal buckling loads and postbuckling response of the eccentrically stiffened FGM plates in three different cases of boundary conditions. The effects of material, temperature-dependent material properties, elastic foundations, boundary conditions, outside stiffeners, and temperature on the buckling and postbuckling loading capacity of the FGM plates in thermal environments are analyzed and discussed. A good agreement is obtained by comparing the present analysis with other available literature.     

Dynamic Thermal Postbuckling Analysis of Piezoelectric Functionally Graded Cylindrical Shells

Dynamic thermal postbuckling behavior of functionally graded cylindrical shells with surface-bonded piezoelectric actuators subjected to the combined action of thermal load and applied actuator voltage is analyzed using an incremental numerical technique. The shell is graded across the thickness according to a power law form function. The material properties of the functionally graded cylindrical shells are considered to be temperature dependent. The theoretical formulations are based on the classical shell theory with Sanders' nonlinear kinematic relations. Then, using Hamilton's principle, equations of motion are derived for the piezoelectric FGM cylindrical shell. A finite difference based method combined with the Runge–Kutta method is employed to predict the postbuckling equilibrium paths, and the dynamic buckling temperature difference is detected according to Budiansky's stability criterion. Numerical results are presented to demonstrate the effects of the applied actuator voltage, shell geometry, volume fraction exponent of FGM, and the temperature dependency of the material properties on the postbuckling behavior of the shell. The results for simpler states are validated with the known data in the literature.     

Thermal Buckling of Functionally Graded Plates Resting On Elastic Foundations Using the Trigonometric Theory

In this article, thermal buckling analysis of functionally graded material (FGM) plates resting on two-parameter Pasternak's foundations is investigated. Equilibrium and stability equations of FGM plates are derived based on the trigonometric shear deformation plate theory and includes the plate foundation interaction and thermal effects. The material properties vary according to a power law form through the thickness coordinate. The governing equations are solved analytically for a plate with simply supported boundary conditions and subjected to uniform temperature rise and gradient through the thickness. Resulting equations are employed to obtain the closed-form solution for the critical buckling load for each loading case. The influences of the plate aspect ratio, side-to-thickness ratio, gradient index, and elastic foundation stiffnesses on the buckling temperature difference are discussed.     

Thermal buckling analysis of functionally graded sandwich plates

Thermal buckling of functionally graded sandwich plates are presented in this article. Two common types of FGM sandwich plates, namely, homogeneous face layers with FGM core and FGM face layers with homogeneous core are considered. Material properties and thermal expansion coe?cient of FGM layers are assumed to vary continuously through-the-thickness according to a simple power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FGM sandwich plate with simply supported boundary conditions are derived using the higher-order shear deformation plate theory. The influence of the plate aspect ratio, the relative thickness, the gradient index, and the thermal loading conditions on the critical buckling temperature of FGM sandwich plates are investigated. The thermal loads are assumed to be uniform, linear, and nonlinear distribution through-the-thickness. A new simple solution for thermal buckling of FGM sandwich plates under nonlinear temperature rise is presented.     

Thermomechanical postbuckling behavior of CNT-reinforced composite sandwich plate models resting on elastic foundations with elastically restrained unloaded edges

Buckling and postbuckling behaviors of two models of sandwich plate reinforced by carbon nanotubes (CNTs) resting on elastic foundations and subjected to uniaxial compressive and thermomechanical loads are investigated in this paper. Material properties of all constituents are assumed to be temperature dependent and effective properties of CNT-reinforced composite layer are determined according to extended rule of mixture. Governing equations are established within the framework of first-order shear deformation theory taking into account von Kármán nonlinearity, initial geometrical imperfection, plate-foundation interaction and tangential elastic constraints of unloaded edges. Three types of loading are considered including uniaxial compression, preexisting thermal load combined with uniaxial compression and preexisting mechanical load combined with thermal load. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and the Galerkin method is used to derive nonlinear load-deflection relations from which buckling loads and postbuckling equilibrium paths are determined. The most important findings are that tangential constraints of unloaded edges significantly lowers buckling loads and postbuckling load capacity of sandwich plates and, in contrast, buckling loads and postbuckling strength are considerably enhanced as sandwich plate is constructed from CNT-reinforced composite core layer and homogeneous face sheets.     

Thermal buckling and postbuckling analysis of piezoelectric FGM beams based on high-order shear deformation theory

This article deals with the thermal buckling and postbuckling of functionally graded material (FGM) beams with surface-bonded piezoelectric actuators based on physical neutral surface concept and high-order shear deformation theory including von Kármán strain–displacement relationships. The beams are exposed to a uniform temperature field and electric field, the material properties of FGM layers are temperature-dependent and vary in the thickness direction. The approximate solutions of piezoelectric FGM beams for thermal buckling and postbuckling are obtained by a two-step perturbation method, meanwhile, the analytical solutions of Timoshenko beam model and Euler beam model are also presented. The validity of the present work can be confirmed by comparisons with previous results. The effects of the applied actuator voltage, beam geometry as well as volume fraction index of FGM beam on the critical buckling temperature, and postbuckling load–deflection relationships are investigated.     

Effect of Initial Imperfections on Thermal Buckling of Functionally Graded Plates

ABSTRACT

Thermal buckling analysis of rectangular functionally graded plates with initial geometrical imperfections is presented in this article. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the first-order shear deformation plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through the thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading, namely: uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect functionally graded plate. The influence of transverse shear on thermal buckling load is discussed.     

Dynamic Thermal Postbuckling Analysis of Shear Deformable Piezoelectric-FGM Cylindrical Shells

Dynamic thermal postbuckling behavior of functionally graded cylindrical shells with surface-bonded piezoelectric actuators subjected to the combined action of thermal load and applied actuator voltage is studied. The shell material is graded across the thickness according to a power law. The material properties of the functionally graded cylindrical shells are considered to be temperature dependent. The theoretical formulations are based on the Sanders nonlinear kinematic relations, which account for the transverse shear strains, and the third-order shear deformation shell theory is employed. Hamilton's principle is used to derive the equations of motion governing piezoelectric FGM cylindrical shells. A finite difference approximation combined with the Runge-Kutta method is employed to predict the postbuckling equilibrium paths, and the dynamic buckling temperature difference is detected according to Budiansky's stability criterion. Numerical results are presented to demonstrate the effects of the applied actuator voltage, shell geometry, volume fraction exponent in the power-law variation of the FGM, and the temperature dependency of the material properties on the postbuckling behavior of the shell. The results for simpler states are validated with the known results in the literature.     

Thermal Buckling Analysis of a Mindlin Rectangular FGM Microplate Based on the Strain Gradient Theory

This article is aimed at developing a nonclassical Mindlin rectangular functionally graded material (FGM) microplate based on the strain gradient theory (SGT) to study the thermal buckling behavior of microplates with different boundary conditions. This theory comprises material length scale parameters to interpret size effects. The developed model encompasses classical and modified couple stress Mindlin microplate models, if all the material length scale parameters or two of them are taken to be zero, respectively. The Mindlin rectangular FGM microplate is considered to be made of a mixture of metal and ceramic of which the volume fraction is described through a power low function. According to Hamilton's principle and the generalized differential quadrature (GDQ) method, the stability equations and associated boundary conditions are obtained and discretized, respectively. Current formulations provide a possibility to have all types of boundary conditions which herein, FGM microplates with three commonly used boundary conditions are considered. Three different types of thermal loads including uniform, linear and nonlinear temperature rises along the thickness of FGM microplates are considered. The dimensionless critical buckling temperature difference (DCBTD) predicted by SGT is compared with that of modified couple stress theory (CST) and classical theory (CT) which it is found that CST and CT underestimate the DCBTD. Also, effects of the boundary conditions, length scale parameter and material gradient index of FGM microplates on the DCBTD are judiciously investigated.     

The buckling of FGM truncated conical shells subjected to axial compressive load and resting on Winkler–Pasternak foundations

In this study, the buckling analysis of the simply supported truncated conical shell made of functionally graded materials (FGMs) is presented. The FGM truncated conical shell subjected to an axial compressive load and resting on Winkler–Pasternak type elastic foundations. The material properties of functionally graded shells are assumed to vary continuously through the thickness. The modified Donnell type stability and compatibility equations are solved by Galerkin’s method and the critical axial load of FGM truncated conical shells with and without elastic foundations have been found analytically. The appropriate formulas for homogenous and FGM cylindrical shells with and without elastic foundations are found as a special case. Several examples are presented to show the accuracy and efficiency of the formulation. Finally, parametric studies on the buckling of FGM truncated conical and cylindrical shells on elastic foundations are being investigated. These parameters include; power-law and exponential distributions of FGM, Winkler foundation modulus, Pasternak foundation modulus and aspect ratios of shells.     

Thermal buckling and postbuckling responses of geometrically imperfect FG porous beams based on physical neutral plane

Abstract

Considering the third-order shear deformation and physical neutral plane theories, thermal postbuckling analysis for functionally graded (FG) porous beam are performed in this research. The cases of shear deformable functionally graded materials (FGM) beams with initial deflection and uniformly distributed porosity are considered. Geometrically imperfect FG porous beams with two different types of immovable boundary conditions as clamped–rolling and clamped–clamped are analyzed. Thermomechanical nonhomogeneous material properties of the FG porous beam are assumed to be temperature and position dependent. FG porous beams are subjected to different types of thermal loads as heat conduction and uniform temperature rise. Heat conduction equation is solved analytically using the polynomial series solution for the one-dimensional condition. The governing equilibrium equations are obtained by applying the virtual displacement principle. Assuming von Kármán type of geometrical nonlinearity, equilibrium equations are nonlinear and are solved using an analytical method. A two-step perturbation technique is used to obtain the thermal buckling and postbuckling responses of FG porous beams. The numerical results are compared with the case of perfect FGM Timoshenko beams without porosity distribution based on the midplane formulation. Parametric studies of the perfect/imperfect FG porous beams for two types of thermal loading and boundary conditions are provided.     

Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations

This paper investigates the nonlinear dynamic response of thick functionally graded materials (FGM) plates using the third-order shear deformation plate theory and stress function. The FGM plate is assumed to rest on elastic foundations and subjected to thermal and damping loads. Numerical results for dynamic response of the FGM plate are obtained by Runge–Kutta method. The results show the influences of geometrical parameters, the material properties, the elastic foundations, and thermal loads on the nonlinear dynamic response of FGM plates.     

Mechanical Behavior of Rectangular Plates with Functionally Graded Coefficient of Thermal Expansion Subjected to Thermal Loading

This study analyzed an elastic, rectangular, and simply supported functionally graded material (FGM) plate with medium thickness subjected to linear temperature change in the z direction. Young's modulus and Poisson ratio of the FGM plates are assumed to remain constant throughout the entire plate. However, the coefficient of thermal expansion of the FGM plate varies continuously throughout the thickness direction in relation to the volume fraction of constituents defined by power-law, sigmoid, or exponential functions. The series solutions for the power-law FGM (P-FGM), sigmoid FGM (S-FGM), or exponential FGM (E-FGM) plates subjected to thermal loading are obtained based on the classical plate theory and Fourier series expansion. The analytical solutions for P-, S-, and E-FGM plates are verified by numerical results obtained with the finite element technique.     

AEROTHERMOELASTIC PHENOMENA OF AEROSPACE AND COMPOSITE STRUCTURES

The thermal postbuckling and aerodynamic-thermal load analysis of cylindrical laminated panels has been performed using the finite element method. To consider large deflections due to thermomechanical loads, the von Karman nonlinear displacement-strain relationships based on layerwise theory are applied. The cylindrical arc-length method is used to take account of the snapping phenomena. The panel flutter analysis of cylindrical panels subject to thermal stresses is carried out using Hans Krumhaar's supersonic piston theory. For the enhancement of the postbuckling and panel flutter behavior subjected to thermal load, the shape memory alloy hybrid composite (SMAHC) panel is investigated.     

THERMAL BUCKLING AND POSTBUCKLING OF SYMMETRICALLY LAMINATED COMPOSITE PLATES

The thermal buckling and postbuckling response of symmetrically laminated composite plates are discussed. Using variational methods in conjunction with a Ray-leigh-Ritz formulation, thermal buckling and postbuckling are investigated for two laminates, a ( ±45/0/90) _s and a ( ± 45/0₂ ) _s, under two different simple support conditions, fixed and sliding. These laminates are subjected to the condition of a uniform temperature change. The effects of the principal material axes not being aligned with the edges of the plate, referred to here as material axis skewing, are also investigated. Although differences between buckling temperatures for the two support conditions were small, support conditions can have a large influence on thermal postbuckling response. In general, plates with fixed simple supports defied more than plates with sliding simple supports. In addition, support conditions can influence modal interaction. Skewing of the material axis decreases the buckling temperatures of both laminates and, like fixed support conditions, causes increased postbuckling deflections. Skewing also influences modal interaction.     

Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation

Buckling and post-buckling thermomechanical deformations of a functionally graded material (FGM) Timoshenko beam resting on a two-parameter non-linear elastic foundation and subjected to only a temperature rise have been numerically investigated with the shooting method. The material properties are assumed to vary only in the thickness direction according to a power law function. Through-the-thickness temperature distribution is determined by numerically solving the one-dimensional heat conduction equation. Geometric non-linearities in the strain-displacement relations and the non-linear traction-displacement relations at the interface between the beam and the foundation are considered. For clamped-clamped and immovable simply supported beams, critical values of the ratio of temperatures of the top and the bottom surfaces of the beam for transitions in buckling modes to occur are determined. Post-buckled equilibrium paths and configurations of the heated FGM beam are illustrated for different values of the elastic foundation stiffness parameters, exponent in the power law variation of material properties and the slenderness ratio. Results for the Timoshenko beam are compared with those of the corresponding homogeneous Euler–Bernoulli beam available in the literature.     

Thermal Buckling of Imperfect Functionally Graded Cylindrical Shells Based on the Wan–Donnell Model

ABSTRACT

A thermal buckling analysis of an imperfect functionally graded cylindrical shell is considered using the Wan–Donnell model for initial geometrical imperfections. Derivation of the equations is based on the first-order classical shell theory using the Sanders nonlinear kinematic relations. Results for the buckling loads are obtained in the closed form. The effects of shell geometry and volume fraction exponent of functionally graded material on the buckling load are investigated. The results are validated with known data in the literature.     

Thermal Buckling of Piezolaminated Plates Subjected to Different Loading Conditions

A thermal buckling analysis is presented for simply supported rectangular laminated composite plates that are covered with top and bottom piezoelectric actuators, and subjected to the combined action of thermal load and constant applied actuator voltage. The thermomechanical properties of composite and piezoelectric materials are assumed to be linear functions of the temperature. The formulations of the equations are based on the higher-order laminated plate theory of Reddy and using the Sanders nonlinear kinematic relations. The closed-form solutions for the buckling temperature are obtained through the Galerkin procedure and solving the resultant eigenvalue problem, which are convenient to be used in engineering design applications. Numerical examples are presented to verify the proposed method. The effects of the plate geometry, fiber orientation in composite layers, lay-up configuration, different utilized piezoelectric materials, temperature dependency of material properties, thermal conductivity, and energy generation on the buckling load are investigated.     

Nonlinear thermal stability of eccentrically stiffened FGM double curved shallow shells

This article presents analytical solutions for the nonlinear static and dynamic stability of imperfect eccentrically stiffened functionally graded material (FGM) higher order shear deformable double curved shallow shell on elastic foundations in thermal environments. It is assumed that the shell’s properties depend on temperature and change according to the power functions of the shell thickness. The shell is reinforced by the eccentrically longitudinal and transversal stiffeners made of full metal. Equilibrium, motion, and compatibility equations are derived using Reddy’s higher order shear deformation shell theory and taking into account the effects of initial geometric imperfection and the thermal stress in both the shells and stiffeners. The Galerkin method is applied to determine load–deflection and deflection–time curves. For the dynamical response, motion equations are numerically solved using Runge–Kutta method. The nonlinear dynamic critical buckling loads are found according to the criterion suggested by Budiansky–Roth. The influences of inhomogeneous parameters, dimensional parameters, stiffeners, elastic foundations, initial imperfection, and temperature increment on the nonlinear static and dynamic stability of thick FGM double curved shallow shells are discussed in detail. Results for various problems are included to verify the accuracy and e?ciency of the approach.     

Thermo-Elasticity Solution of Functionally Graded Plates Integrated with Piezoelectric Sensor and Actuator Layers

Based on theory of piezoelasticity, a functionally graded material (FGM) host plate under applied electric field and thermal or mechanical load is studied. The thermo-elastic constants of the plate vary continuously throughout the thickness direction in the form of an exponential function and the Poisson ratio is held constant. Analytical solutions for the temperature, stress and displacement fields for the plate with simply supported edges are derived by using the Fourier series expansions and state-space method. The theory is assessed by comparison with the previously published results. The effects of surface boundary conditions, gradient index, applied voltage, aspect ratio and length-to-thickness ratio on the behavior of the FGM plate are examined.