STEADY-STATE THERMOELASTIC ANALYSIS OF A FUNCTIONALLY GRADED ROTATING ANNULAR DISK

2006 ◽  
Vol 06 (04) ◽  
pp. 559-574 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Steady State ◽  
Material Properties ◽  
Radial Direction ◽  
Rotating Disk ◽  
Functionally Graded ◽  
Stress Strain ◽  
Annular Disk ◽  
Thermoelastic Analysis ◽  
Thermal Bending ◽  
Temperature Loads

This paper is concerned with the thermoelastic analysis of a functionally graded rotating annular disk subjected to a nonuniform steady-state thermal load. Material properties are assumed to be temperature independent and continuously varying in the radial direction of the annular disk. The variations of Young's modulus, material density, thermal expansion and conductivity coefficients are represented by a novel exponential-law distribution through the radial direction of the disk, but Poission's ratio is kept constant. The governing differential equations are exactly satisfied at every point of the disk. Exact solutions for the temperature and stress fields are derived in terms of an exponential integral and Whittaker's functions. Presented are some results for stress, strain and displacement components due to thermal bending of the rotating disk. The effects of angular velocity, inner and outer temperature loads and material properties on the stress, strain and displacement components are discussed.

scholarly journals Mechanical and Thermal Stresses in a FGPM Hollow Cylinder due to Radially Symmetric Loads

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
M. Jabbari ◽  
M. Meshkini ◽  
M. R. Eslami
Keyword(s):  
Fourier Series ◽  
Heat Conduction ◽  
Steady State ◽  
Material Properties ◽  
Radial Direction ◽  
Thermal Stresses ◽  
Functionally Graded ◽  
Power Functions ◽  
One Dimensional ◽  
Complex Fourier Series

The general solution of steady-state on one-dimensional Axisymmetric mechanical and thermal stresses for a hollow thick made of cylinder Functionally Graded porous material is developed. Temperature, as functions of the radial direction with general thermal and mechanical boundary-conditions on the inside and outside surfaces. A standard method is used to solve a nonhomogenous system of partial differential Navier equations with nonconstant coefficients, using complex Fourier series, rather power functions method and solve the heat conduction. The material properties, except poisson's ratio, are assumed to depend on the variable , and they are expressed as power functions of .

Thermoelastic analysis of three-dimensional functionally graded rotating disks based on finite volume method

2013 ◽  
Vol 228 (4) ◽  
pp. 583-598 ◽  
Author(s):  
Jing-Feng Gong ◽  
Ping-Jian Ming ◽  
Ling-Kuan Xuan ◽  
Wen-Ping Zhang
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Material Properties ◽  
Three Dimensional ◽  
Least Square Method ◽  
Rotating Disk ◽  
Functionally Graded ◽  
Least Square ◽  
Thermoelastic Analysis ◽  
Volume Method

In this study, a finite volume method for the steady thermoelastic analysis of the functionally graded materials is presented. The method is validated in a benchmark case from the published paper. By incorporating the variation of material properties in the discretization process, the method is able to avoid discontinuous distributions of stresses. Two different formulations for the calculation of variable gradients are assessed. The numerical results show that the least square method achieves better performances than the Gaussian method but least square method costs slightly more iteration and computer memory under different mesh types. Then the method is applied to analyze thermoelastic problems of the functionally graded circular rotating disk under different conditions. The effects of thickness, material properties, reference temperature and temperature difference between the inner and outer surfaces on the thermoelastic performance of the disk have been studied.

Displacement and Stress Fields in a Functionally Graded Fiber-Reinforced Rotating Disk With Nonuniform Thickness and Variable Angular Velocity

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Y. Zheng ◽  
H. Bahaloo ◽  
D. Mousanezhad ◽  
A. Vaziri ◽  
H. Nayeb-Hashemi
Keyword(s):  
Radial Direction ◽  
Volume Fraction ◽  
Rotating Disk ◽  
Outer Radius ◽  
Functionally Graded ◽  
Circumferential Direction ◽  
Stress Fields ◽  
Fiber Reinforced ◽  
Inner Radius ◽  
Nonuniform Thickness

Displacement and stress fields in a functionally graded (FG) fiber-reinforced rotating disk of nonuniform thickness subjected to angular deceleration are obtained. The disk has a central hole, which is assumed to be mounted on a rotating shaft. Unidirectional fibers are considered to be circumferentially distributed within the disk with a variable volume fraction along the radius. The governing equations for displacement and stress fields are derived and solved using finite difference method. The results show that for disks with fiber rich at the outer radius, the displacement field is lower in radial direction but higher in circumferential direction compared to the disk with the fiber rich at the inner radius. The circumferential stress value at the outer radius is substantially higher for disk with fiber rich at the outer radius compared to the disk with the fiber rich at the inner radius. It is also observed a considerable amount of compressive stress developed in the radial direction in a region close to the outer radius. These compressive stresses may prevent any crack growth in the circumferential direction of such disks. For disks with fiber rich at the inner radius, the presence of fibers results in minimal changes in the displacement and stress fields when compared to a homogenous disk made from the matrix material. In addition, we concluded that disk deceleration has no effect on the radial and hoop stresses. However, deceleration will affect the shear stress. Tsai–Wu failure criterion is evaluated for decelerating disks. For disks with fiber rich at the inner radius, the failure is initiated between inner and outer radii. However, for disks with fiber rich at the outer radius, the failure location depends on the fiber distribution.

Thermoelastic Dynamic Behaviors of a FGM Hollow Cylinder Under Non-Axisymmetric Thermo-Mechanical Loads

2012 ◽  
Vol 29 (1) ◽  
pp. 109-120 ◽  
Author(s):  
H. Xie ◽  
H.-L. Dai ◽  
Y.-N. Rao
Keyword(s):  
Hollow Cylinder ◽  
Material Properties ◽  
Radial Direction ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Two Dimensional ◽  
Governing Equations ◽  
Mechanical Loads ◽  
Temperature Boundary

AbstractThis paper is concerned with two-dimensional (r, θ) thermoelastic dynamic responses of a long functionally graded hollow cylinder subjected to asysmmetrical thermal and mechanical loads. The material properties, except the Poisson's ratio, are assumed to be temperature independent and vary exponentially and continuously in the radial direction. By means of finite difference method and Newmark method, the motion governing equations of the long FGM hollow cylinder are solved. Comparisons between this paper's results and the corresponding analytical results validate the proposed solution. In addition, the effects of the volume fraction, temperature boundary conditions on the hollow cylinder's deformations and stresses distributions are examined, and many other valuable thermoelastic dynamic characteristics are revealed.

scholarly journals Numerical solution of thermal elastic-plastic functionally graded thin rotating disk with exponentially variable thickness and variable density

2019 ◽  
Vol 23 (1) ◽  
pp. 125-136 ◽  
Author(s):  
Sanjeev Sharma ◽  
Sanehlata Yadav
Keyword(s):  
Strain Hardening ◽  
Functionally Graded Material ◽  
Circumferential Stress ◽  
Rotating Disk ◽  
Functionally Graded ◽  
Linear Strain ◽  
Annular Disk ◽  
Elastic Plastic ◽  
Non Linear ◽  
Graded Material

Thermal elastic-plastic stresses and strains have been obtained for rotating annular disk by using finite difference method with Von-Mises? yield criterion and non-linear strain hardening measure. The compressibility of the disk is assumed to be varying in the radial direction. From the numerical results, we can conclude that thermal rotating disk made of functionally graded material whose thickness decreases exponentially and density increases exponentially with non-linear strain hardening measure (m = 0.2) is on the safe side of the design as compared to disk made of homogenous material. This is because of the reason that circumferential stress is less for functionally graded disk as compared to homogenous disk. Also, plastic strains are high for functionally graded disk as compared to homogenous disk. It means that disk made of functionally graded material reduces the possibility of fracture at the bore as compared to the disk made of homogeneous material which leads to the idea of stress saving.

scholarly journals Two-Dimensional Stress Analysis of Thick Hollow Functionally Graded Sphere Under Non-Axisymmetric Mechanical Loading

2021 ◽  
Vol 6 (4) ◽  
pp. 1115-1126
Author(s):  
Sandeep Kumar Paul ◽  
Manoj Sahni
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Mechanical Loading ◽  
Radial Direction ◽  
External Pressure ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Legendre Series ◽  
Spherical Coordinate ◽  
Nonlinear Variation

In this paper, a functionally graded thick hollow sphere is considered for the analysis of two-dimensional steady state mechanical stress in the radial and circumferential directions under mechanical loading. Modulus of elasticity is varying with continuous nonlinear variation along the radial direction and Poisson’s ratio is kept as constant. The Legendre series and Euler differential equation are used to solve Navier equations. Geometry of the sphere is assumed in spherical coordinate system. Applying mechanical boundary conditions at inner and outer radii, we have carried out the analytical solutions for stresses, strains and displacements. In the numerical example, only internal pressure is varying along circumferential direction and external pressure is kept as zero. Displacements and mechanical stresses are presented graphically and the results are discussed numerically.

A high-order control volume finite element method for thermoelastic analysis of functionally graded solids with mixed grids

2018 ◽  
Vol 233 (11) ◽  
pp. 3994-4013
Author(s):  
Qi Liu ◽  
Yan Yu ◽  
Pingjian Ming
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Properties ◽  
Control Volume ◽  
Functionally Graded ◽  
High Order ◽  
Shape Functions ◽  
Quadrilateral Element ◽  
Thermoelastic Analysis ◽  
Control Volume Finite Element

In this article, a new two-dimensional control volume finite element method has been developed for thermoelastic analysis in functionally graded materials. A nine-node quadrilateral element and a six-node triangular element are employed to deal with the mixed-grid problem. The unknown variables and material properties are defined at the node. The high-order shape functions of six-node triangular and nine-node quadrilateral element are employed to obtain the unknown variables and their derivatives. In addition, the material properties in functionally graded structure are also modeled by applying the high-order shape functions. The capabilities of the presented method to heat conduction problem, elastic problem, and thermoelastic problem have been validated. First, the defined location of material properties is found to be important for the accuracy of the numerical results. Second, the presented method is proven to be efficient and reliable for the elastic analysis in multi-phase materials. Third, the presented method is capable of high-order mixed grids. The memory and computational costs of the presented method are also compared with other numerical methods.

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