Figure - available from: Mathematical Problems in Engineering
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(a) Schematic diagram of functionally graded circular disk models. (b) Notations of finite control volumes.
Source publication
A rotating functionally graded circular disk undergoing a contact load is taken into account to investigate the thermoelastic characteristics. By considering contact force, a pair of partial differential equations is induced as the governing equations based on Hooke’s law. The behavior of circular disk modes is described with the variations of cont...
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Citations
... Neghdabadi and Kordkheili [14] developed finite element analysis to represent thermoelastic characteristics in FGM plates and shells. Go [15][16][17] investigated temperature distribution, strain and stress in a circular disk under the effect of angular velocity, contact force and thickness by using finite element and finite volume method. Sharma et al. [18][19][20][21] studied thermoelastic characteristics in the FGM disk and a cylinder with the help of a finite element method under exponentially and linearly varying material properties. ...
This study represents a numerical analysis of stress and strain in the functionally graded material (FGM) hollow cylinder subjected to two different temperature profiles and inhomogeneity parameter. The thermo-mechanical properties of a cylinder are assumed to vary continuously as power law function along the radial coordinate of a cylinder. Based on equilibrium equation, Hooke's law, stress-strain relationship in the cylinders, and other theories from mechanics second order differential equation is obtained that represents the thermoelastic field in hollow FGM cylinder. To find a numerical solution of governing differential equation, the finite element method (FEM) with standard discretization approach is used. The analysis of numerical results reveals that stress and strain in the FGM cylinder are significantly depend upon variation made in temperature profile and inhomogeneity parameter n . The results show good agreement with results available in the literature. It is shown that thermoelastic characteristics of the FGM cylinder are controlled by controlling the value of the above discussed parameters. Moreover, these results are very useful in various fields of engineering and science as FGM cylinders have a wide range of applications in these fields.
... Hu et al. [37] investigated in uence of various parameters on natural vibration in rotating functionally graded ring plate. Go [38] made thermoelastic characteristics analysis numerically under variable contact force and homogeneous thickness. Thakare and Warbhe [39] studied temperature distribution and stress distribution in thick hollow cylinder for homogeneous and inhomogeneous material properties. ...
In this research paper, displacement, stresses and strains are presented for rotating FGM disk with variable thickness by using finite element method (FEM). Thermo-elastic material properties and thickness of FGM disk continuously vary as exponential and power law function in radial direction along radius of disk. The value of Poisson's ratio is taken as constant. The problem of thermo-elasticity is converted into second order governing differential equation in terms of radial coordinate. This conversion is based upon equilibrium equation for disk and stress-strain relationship. The influence of variable thickness, angular velocity and functionally graded materials is discussed on thermo-elastic characteristics of rotating disk for exponential variation of material properties. Further, these thermo-elastic characteristics of disk are plotted for various values of non-homogeneity parameter under power law distribution of material properties. Thus, the investigations done in this research paper may be useful for industrial area in construction an appropriate FGM disk by controlling above mentioned parameters.
This study focuses on the optimization of a rotating disk composed of functionally graded material (FGM), which is subjected to both inertial and thermal loads. The novelty of this study lies in the fact that the optimum material distribution for achieving minimum and prescribed stress profiles in the FGM disk is not limited to the priori assumed functional variation, unlike the case in the majority of existing literature. An optimization model is developed to solve the inverse problem and obtain the volume fraction or material distribution of the FGM disk corresponding to the minimum and prescribed stress profiles. First, the problem is formulated utilizing second-order differential equations in accordance with theories of two-dimensional thermoelasticity. Then, the second-order governing differential equation, with the design variables being the volume fractions across the disk, is used in an objective function. Finally, the determination of the global minimum value of the objective function is achieved by the differential evolution method through the utilization of a standard finite element approach for solving the differential equation. Thus, the volume fraction distribution of the disk corresponding to the objective function is obtained. The present investigation pertains to two distinct forms of the objective function, specifically, an objective function for minimum stress and another for prescribed stress. In addition, a mathematical model of the direct problem is developed to analyze the minimum stress profile of the FGM disk, with the optimum material distribution derived from the optimization model provided as input. The models are validated through a comparison of their results with those found in existing literature. The numerical results of this study ensure that it is feasible to design an FGM disk with optimum material distribution, achieving the minimum and prescribed stress profile within the disk. It is also revealed that the optimum material distribution is significantly influenced by the stress profile, temperature field, angular speed, and radial thickness of the disk.
In this work, a FGM thick wall tube under both thermal and mechanical loadings is studied by referring to the Mori-Tanaka method. The studied FGM tube is assumed to be made of two distinct linear elastically deformable materials equipped with unique volume fractions. Specially, its material parameters are firstly evaluated in the scheme of the Mori-Tanaka method which can more accurately depict the effective material properties of FGMs composites. Later, we derive the ordinary differential equation (ODE) of the displacement along radial direction, based on which we determine the approximate analytical results of displacement and later derive explicit forms of stress components along all the radial, axial and circumferential directions. After comparison, we found that the derived analytical results agree well with that obtained through numerical method. Moreover, for the same researching problem we found the Mori-Tanaka method could outperform the Voigt method. Further, the results are valid for materials with different Poisson’s ratios rather than constant Poisson’s ratios usually used in the existing references. Finally, parametric studies are also conducted by exploring the variations of the displacement and stress components affected by different volume fractions and distinct thermal conductivities and expansion coefficients.
