REFINED THEORY FOR THERMOELASTIC STABILITY OF FUNCTIONALLY GRADED CIRCULAR PLATES

Axisymmetric thermal and mechanical buckling of functionally graded circular plates is considered. Equilibrium and stability equations under thermal and mechanical loads are derived based on first-order shear deformation plate theory. Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental ordinary differential equations is established. Buckling analysis of a functionally graded plate under uniform temperature rise, linear and nonlinear gradient through the thickness, and uniform radial compression are considered, and the critical buckling loads are derived for clamped edge plates. The results are compared with the buckling loads obtained for a functionally graded plate based on the classical plate theory given in the literature.     

THERMAL ELASTOPLASTIC ANALYSIS OF PLATES WITH CIRCULAR HOLES

The present paper deals with ehstoplastic thermal stresses in a thin plate with an insulated circular hole. The hole causes a disturbance in temperature distribution when the plate is heated uniformly through the thickness. A finite-difference method is utilized to determine the temperature distribution from the steady-state heat conduction equation. An incremental theory of successive elastic approximations is used in the analysis of the elastoplastic stresses in the plate.     

Three-Dimensional Semi-Analytical Thermo-Elasticity Solution for a Functionally Graded Solid and an Annular Circular Plate

Three-dimensional analysis of a functionally graded (FG) solid and an annular circular plate subjected to thermo-mechanical load with various boundary conditions are carried out in this paper. At first, the temperature gradient can be derived by solving the heat conduction equation exactly and then by applying the differential quadrature method (DQM) along the radial direction and by using the state-space method in the thickness direction to the governing state equations results in a system of first-order differential equations, which can be solved analytically. The thermo-elastic constants of the plate are assumed to vary exponentially through the thickness, and the Poisson ratio is held to be constant. To verify the accuracy of the present work, a comparison is made with previously published results. The effects of temperature change, mechanical load, gradient index, edges conditions and thickness to radial length ratio on the behavior of the plate are examined.     

Analytical solution for an infinite elastic power-law hardening plate containing an elastic circular inhomogeneity and subjected to equi-biaxial tension

This paper presents an clasto-plastic analytical solution for the plane stress inclusion problem of an elastic power-law hardening plate containing an elastic circular inhomogeneity and subjected to equi-biaxial far-field tension. Hencky's deformation theory (for compressible materials) and von Mises' yield criterion are applied, and infinitesimal deformations are assumed. The solution is derived by using a stress formulation and with the help of a modified Nadai's auxiliary-variable method and the extended Michell theorem. All expressions for the stress, strain and displacement components are derived in explicit forms in terms of an auxiliary variable and four constant parameters, which are determined from the given boundary conditions. Three specific solutions of practical interest are presented as limiting cases, one of which is the closed-form solution for the plate containing a traction-free circular hole. Numerical results are also provided to demonstrate quantitatively applications of the solution in the opening and reinforcement design of spherical pressure vessels.     

Asymmetric thermal buckling of annular plates on a partial elastic foundation

In this investigation, the asymmetrical buckling behavior of isotropic homogeneous annular plates resting on a partial Winkler-type elastic foundation under uniform temperature elevation is investigated. First-order shear deformation plate theory is used to obtain the governing equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained under the solution of a plane stress formulation, neglecting the rotations and lateral deflection. Applying the adjacent equilibrium criterion, the linearized stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region, and the second set, which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalized differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved to obtain the critical conditions of the plate and the associated circumferential mode number. Benchmark results are given in tabular and graphical presentations for combinations of simply supported and clamped types of boundary conditions. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and the boundary conditions.     

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.     

Transient Thermo-Mechanical Analysis of Functionally Graded Hollow Circular Cylinders

Thermo-mechanical analysis of functionally graded hollow circular cylinders subjected to axisymmetric mechanical and transient thermal loads is carried out in this study. Thermo-mechanical properties of functionally graded materials (FGM) are assumed to be temperature independent and vary continuously in the radial direction of the cylinder. Employing the Laplace transform, the Galerkin method and series method for ordinary differential equations, solutions for the time-dependent temperature and transient thermo-mechanical stresses are obtained. As an example, a molybdenum/mullite FGM with material properties obeying the exponential law is considered. Effects of heat transfer coefficients and gradient parameters of FGM on the time-dependent temperature and transient thermal stresses are discussed in detail.     

Research on shakedown analysis for functionally graded material plate under thermomechanical loading

Shakedown is an important problem in the design and analysis of functionally graded structures subjected to cyclic, thermal, and mechanical loadings. Subjected to constant mechanical load and cyclic temperature change, static shakedown of a functionally graded material plate and its homogenous counterpart were analyzed in this article with the approach proposed by the authors previously. The functionally graded material plate is composed of an elastoplastic matrix Al and elastic particles SiC, and the particle volume fraction varies through the thickness. The distributions of the effective mechanical and thermal properties of the composites through the thickness are described graded continuously with an exponential law. The results show that a proper and continuously graded distribution of material properties can efficiently improve the shakedown capability of the functionally graded material plate and also show the significance of shakedown analysis and application for functionally graded material plates.     

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.     

On the Behavior of a Rotating Functionally Graded Hybrid Cylindrical Shell with Imperfect Bonding Subjected to Hygrothermal Condition

The static behavior of a rotating cylindrical shell with surface bounded sensor and actuator in an axisymmetric hygrothermal condition is analyzed. The shell is simply supported and could be rested on an elastic foundation. The material properties of the shell and piezoelectric sensor and actuator are assumed to be functionally graded in the radial direction. Using the Fourier series expansion method through the longitudinal direction and the differential quadrature method (DQM) across the radial direction, and governing differential equations are solved. The validity of the present work was verified by comparisons with other published works. Numerical results are presented to illuminate the effects of key parameters on the responses of the hybrid shell.     

螺旋盘管式换热器管板的分析设计

螺旋盘管式换热器的设计标准为ASMEⅧ-1-2010,本文对管板组件进行局部应力分析,按照ASMEⅧ-2进行分析评定。按照标准的规定将管板简化成当量实心圆平板,开孔区设置不同的等效参数。管板组件的应力分析采用两种方法进行,分别为：基于弹性应力分析的应力分类法与基于塑性失效准则的极限载荷分析法。本文旨在促进弹性分析法与极限载荷分析法的联合使用。     

Study of the effective parameters on stress distribution around triangular hole in metallic plates subjected to uniform heat flux

On the basis of the steady-state two-dimensional theory of thermoelasticity, stress field around a triangular hole in an infinite isotropic plate is discussed. A metallic plate subjected to uniform heat flux and thermal-insulated condition along the hole boundary is assumed. The method used for this study is the expansion of Goodier and Florence's method. They used the complex variable method for stress analysis of infinite isotropic plates with an elliptical or circular hole. The rotation angle of the hole, bluntness, aspect ratio of hole size, and angle of heat flux are important parameters considered in this paper.     

Thermal Post-Buckling of Functionally Graded Material Circular Plates Subjected to Transverse Point-Space Constraints

Axisymmetrical thermal post-buckling of functionally graded material (FGM) circular plates with immovably clamped boundary and a transversely central point-space constraint was studied. The material properties of the plate were assumed to vary as power law functions in the thickness direction and the temperature rise field to change only in the thickness direction. Based on von Karman's non-linear plate theory, governing equations in terms of the displacements of the middle plane were established. Temperature rise field was obtained by solving the one-dimensional heat conduction equation associated with specified boundary conditions at the top and bottom surface of the plate. By using the shooting method, thermal post-buckling deformation of the FGM circular plate was obtained before and after the plate contacting the point-space constraint. The changes in the characteristics of the deformation and the internal forces of FGM plates were discussed. The effects of gradients of material properties and non-uniform temperature rise parameters on the thermal post-buckling behaviors of FGM circular plates were also examined.     

Thermoelastic Buckling Analysis of Functionally Graded Circular Plates Integrated with Piezoelectric Layers

Thermal buckling of circular plates made of functionally graded materials with surface-bounded piezoelectric layers are studied. The material properties of the FG plates are assumed to vary continuously through the plate thickness by distribution of power law of the volume fraction of the constituent materials. The general thermoelastic nonlinear equilibrium and linear stability equations for the piezoelectric FG plate are derived using the variational formulations. Buckling temperatures are derived for solid circular plates under uniform temperature rise, nonlinear and linear temperature variation through the thickness for immovable clamped edge of boundary conditions. The effects of piezo-to-host thickness ratio, applied actuator voltage, boundary condition, and power law index of functionally graded plates on the buckling temperature of plate are investigated. The results are verified with the data in literature.     

Effect of uniform heat flux on stress distribution around a triangular hole in anisotropic infinite plates

The presence of a hole in an anisotropic plate under uniform heat flux causes thermal stress around the hole. In this study, on the basis of two-dimensional thermoelastic theory and using Lekhnitskii’s complex variable technique, the stress analysis of an anisotropic infinite plate with a circular hole under a uniform heat flux is developed to the plate containing a triangular hole. For this purpose, an infinite plate containing a triangular hole is mapped to the outside of a unit circle using a conformal mapping function. Stress and displacement distributions around the triangular holes in an anisotropic infinite plate are investigated in thermal steady-state condition. The plate is under uniform heat flux at infinity and Neumann boundary conditions and thermal-insulated condition on the hole boundary are considered. The rotation angle of the hole, fiber angle, the angle of heat flux, bluntness, and the aspect ratio of hole size are investigated in the present study. The accuracy of the analytical results is also confirmed by finite element analysis.     

Elastoplastic analysis of FGM plate with a central cutout of various shapes under thermomechanical loading

The present work aims to study the elastoplastic buckling, postbuckling, and failure behavior of perforated Ni/Al₂O₃ functionally graded material (FGM) plate with various shaped cutouts (i.e., circular, square, diamond, and elliptical) of various sizes under thermomechanical loading conditions using finite element method (FEM). The nonlinear FEM formulation is based on the first-order shear deformation theory and von Kármán’s nonlinear kinematics in which the material nonlinearity is incorporated. The nonlinear temperature-dependent thermoelastic material properties of FGM plate are varied in the thickness direction by controlling the volume fraction of the constituent materials (i.e., ceramic and metal) as per a power law, and Mori–Tanaka homogenization scheme is applied to evaluate the properties at a particular thickness coordinate of FGM. In accordance with the Tamura–Tomota–Ozawa model (TTO model), the ceramic phase of FGM is considered to be elastic, whereas the metal phase is assumed to be elastoplastic. Further, the elastoplastic analysis of FGM is assumed to follow J₂ plasticity with isotropic hardening. After validating the present formulation with the results available in the literature, various numerical studies are conducted to examine the effects of material inhomogeneity, thermal loading, cutout shape, and size on the elastoplastic buckling, postbuckling, and failure behavior of perforated FGM plate. It is observed that for smaller cutout sizes, the FGM plate with square shape cutout possesses maximum value of ultimate failure load; however, for larger cutout size, the FGM plate with diamond cutout depicts highest ultimate failure load. Furthermore, for all cutout shapes, the ultimate failure load of FGM plate decreases with an increase in cutout size. It is also revealed that irrespective of shape and size of cutout, the material plastic flow has considerable effect on postbuckling path of FGM plate, and under thermomechanical loading conditions, the FGM plate shows destabilizing response after the point of maximum postbuckling strength.     

TRANSIENT THERMAL SINGULAR STRESSES OF MULTIPLE CRACKING IN A W-Cu FUNCTIONALLY GRADED DIVERTOR PLATE

We consider the transient thermal singular stresses of multiple cracking in a functionally graded divertor plate due to a thermal shock. The plate is made of a graded layer bonded between a homogeneous substrate and a homogeneous coating, and it is subjected to a cycle of heating and cooling on the coating surface of the plate. The surface layer contains a parallel array of embedded or edge cracks perpendicular to the boundaries. The thermal and elastic properties of the material are dependent on the temperature and the position. Finite element calculations are carried out, and the transient thermal stress intensity factors are shown graphically.     

SOLUTION OF DISPLACEMENT BOUNDARY VALUE PROBLEM UNDER UNIFORM HEAT FLUX

The general solution of the displacement boundary value problem is obtained for an infinite plate with an arbitrary shaped hole under uniform heat flux in any direction. The complex stress functions, the dislocation method, and a rational mapping function are used and the closed solution is obtained. An infinite plate with a circular hole and a slit is analyzed under the condition of the constrained displacements. The singularity at the tip of the slit of the constrained displacement is investigated     

Nonlinear dynamic response of eccentrically stiffened FGM plate using Reddy’s TSDT in thermal environment

The nonlinear dynamics of an eccentrically stiffened functionally graded material (ES-FGM) plates resting on the elastic Pasternak foundations subjected to mechanical and thermal loads is considered in this article. The plates are reinforced by outside stiffeners with temperature-dependent material properties in two cases: uniform temperature rise and through the thickness temperature gradient. Both stiffeners and plate are deformed under temperature. Using Reddy’s third-order shear deformation plate theory, stress function, Galerkin and fourth-order Runge–Kutta methods, the effects of material and geometrical properties, temperature-dependent material properties, elastic foundations, and stiffeners on the nonlinear dynamic response of the ES-FGM plate in thermal environments are studied and discussed. Some obtained results are validated by comparing with those in the literature.     

Nonlinear dynamic response and vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shear deformable plates with temperature-dependent material properties and surrounded on elastic foundations

Based on Reddy’s third-order shear deformation plate theory, the nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates on elastic foundations subjected to dynamic loads and temperature are presented. The plates are reinforced by single-walled carbon nanotubes which vary according to the linear functions of the plate thickness. The plate’s effective material properties are assumed to depend on temperature and estimated through the rule of mixture. By applying the Airy stress function, Galerkin method and fourth-order Runge–Kutta method, nonlinear dynamic response and natural frequency for imperfect FG-CNTRC plates are determined. In numerical results, the influences of geometrical parameters, elastic foundations, initial imperfection, dynamic loads, temperature increment, and nanotube volume fraction on the nonlinear vibration of FG-CNTRC plates are investigated. The obtained results are validated by comparing with those of other authors.