Stress and deformation of functionally graded rotating disk based on modified rule of mixture

Abstract The present study reports the linear elastic analysis of variable thickness functionally graded rotating disks. Disk material is graded radially by varying the volume fraction ratios of the constituent components. Three types of distribution laws, namely power law, exponential law and Mori–Tanaka scheme are considered on a concave thickness profile rotating disk, and the resulting deformation and stresses are evaluated for clamped-free boundary condition. The investigation is carried out using element based grading of material properties on the discretized elements. The effect of grading on deformation and stresses is investigated for each type of material distribution law. Further, a comparison is made between different types of distributions. The results obtained show that in a rotating disk, the deformation and stress fields can be controlled by the distribution law and grading parameter n of the volume fraction ratio.

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Thermo-mechanical analysis and optimization of functionally graded rotating disks

The Journal of Strain Analysis for Engineering Design ◽

10.1177/0309324720904793 ◽

2020 ◽

Vol 55 (5-6) ◽

pp. 159-171

Author(s):

Hassan Mohamed Abdelalim Abdalla ◽

Daniele Casagrande ◽

Luciano Moro

Keyword(s):

Finite Element ◽

Equivalent Stress ◽

Rotating Disk ◽

Mechanical Analysis ◽

Theory Of Elasticity ◽

Functionally Graded ◽

Rotating Disks ◽

Maximum Equivalent Stress ◽

Quadratic Programming Method ◽

Stress Uniformity

The behavior of thermo-mechanical stresses in functionally graded axisymmetric rotating hollow disks with variable thickness is analyzed. The material is assumed to be functionally graded in the radial direction. First, a two-dimensional axisymmetric model of the functionally graded rotating disk is developed using the finite element method. Exact solutions for stresses are then obtained assuming that the plane theory of elasticity holds. These solutions are in accordance with finite element ones, thus showing the validity of the assumption. Finally, in order to reduce the maximum equivalent stress along the radius, the optimization of the material distribution is addressed. To avoid subsequent finite element simulations in the optimization process, which can be computationally demanding, a nonlinear constrained optimization problem is proposed, for which the solution is obtained numerically by the sequential quadratic programming method, showing prominent results in terms of equivalent stress uniformity.

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A semianalytical finite element method for stress and deformation analyses of bi-directional functionally graded truncated conical shells

Mechanics Based Design of Structures and Machines ◽

10.1080/15397734.2019.1636657 ◽

2019 ◽

Vol 48 (4) ◽

pp. 433-458 ◽

Cited By ~ 5

Author(s):

Chih-Ping Wu ◽

Hao-Yang Huang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Functionally Graded ◽

Conical Shells ◽

Stress And Deformation ◽

Element Method

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

Journal of Engineering Materials and Technology ◽

10.1115/1.4036242 ◽

2017 ◽

Vol 139 (3) ◽

Cited By ~ 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.

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Thermoelastic creep analysis of a functionally graded various thickness rotating disk with temperature-dependent material properties

International Journal of Pressure Vessels and Piping ◽

10.1016/j.ijpvp.2013.05.001 ◽

2013 ◽

Vol 111-112 ◽

pp. 63-74 ◽

Cited By ~ 18

Author(s):

S.A. Hosseini Kordkheili ◽

M. Livani

Keyword(s):

Material Properties ◽

Rotating Disk ◽

Functionally Graded ◽

Temperature Dependent ◽

Creep Analysis

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Vibration Response of Functionally Graded Rotating Disk With a Circumferential Crack

Volume 8: Dynamic Systems and Control, Parts A and B ◽

10.1115/imece2010-39408 ◽

2010 ◽

Author(s):

Rui Liu ◽

Hamid Nayeb-Hashemi

Keyword(s):

Critical Speed ◽

Crack Depth ◽

Rotating Disk ◽

Vibration Characteristics ◽

Functionally Graded ◽

Mode Shapes ◽

Campbell Diagram ◽

Circumferential Crack ◽

Inner Radius ◽

The Galerkin Method

In this study, the vibration characteristics of a functionally graded rotating hollow disk with the circumferential surface crack are investigated. In order to simplify the problem, the circumferential crack of the rotating hollow disk is modeled as circumferential step indentation. The Galerkin Method is used to obtain the radial and hoop stresses for disks with clamped edge at the inner radius. Finite Difference scheme is adopted to solve the partial differential equation of motion of the rotating hollow disk to obtain the mode shapes and the Campbell Diagram. The first critical speed, which is one of the important parameters limiting the performance of the rotating disk, was obtained from the Campbell Diagram. The results show that the crack will reduce the stiffness and the critical speed of the rotating disk. Critical speed increases with decreasing the distance from inner radius to the crack and decreases with increasing crack depth. Furthermore, considering the functionally graded disk, the distribution of elastic modulus does not change significantly the effects of circumferential cracks on the vibration characteristics of the rotating.

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