Linear And Nonlinear Thermoelastic Analysis Of Functionally Graded Materials Axisymmetric Rotating Disks

Functionally graded materials (FGMs) are non-homogeneous materials where the volume fraction of two or more materials is varied, as a power-law distribution, continuously as a function of position along certain dimension(s) of the structure. FGMs are usually made of a mixture of ceramic and metals. The ceramic constituent of the material provides the high temperature resistance due to its low thermal conductivity and the ductile metal constituent, on the other hand, prevents fracture caused by stress due to high temperature gradient in a very short period of time. These materials, usually designed to operate in high temperature environments, find their applications in automotive and aerospace as turbine rotors, flywheels, gears, tubes, disk brakes and energy storage devices. In all these applications, the performance of the components in terms of efficiency, service life and power transmission capacity depends on the material, thickness profile, speed of rotation and operating conditions. Normally, these components are fabricated by using homogeneous metal. In the present work, components made of FGM are to be considered and they are axisymmetric disks subjected to body force, bending and thermal loads. The displacement and stress fields of these components are determined both analytically and numerically. The effect of geometry and material-property nonlinearity on small and large deflections in functionally graded rotating disks is investigated by studying their elastic behavior under thermo mechanical loads. Six types of thickness profiles, namely uniform, linear, concave, convex, hyperbolic convergent and hyperbolic divergent are considered. Material properties such as Young’s modulus,, mass density,hEρ, and the thermal conductivity,α,are assumed to be represented by two power law distributions along the radial direction. Material properties are also assumed to be temperature-dependent for more accurate and realistic results. A theoretical formulation for bending analysis of functionally graded (FG) rotating disks based on First Order Shear Deformation Theory (FSDT) is presented. A semi analytical solution for displacement field is obtained. New linear and nonlinear equilibrium equations for FG axisymmetric rotating disk with bending and thermal loading are developed and presented. The disk has material properties varying through the thickness of the disk graded according to a power-law distribution of the volume fraction of the constituents. FSDT and von Karman theory are used and both small and large deflections are considered. In the case of small deflection, an exact solution for displacement field is given. For large deflection, power series solutions are employed to solve for displacement field. The results for displacement and stresses are normalized with respect to the corresponding disk with homogeneous material geometry and certain value of properties of disk with the same unit respectively. All the results shown are thus independent of the physical dimension of the component. As for practical applications, rotating disks with typical dimensions up to 2 meter diameter are considered. The results for free-free FG rotating disk show that there exist combinations of values of parameters related to thickness profiles for which the radial stress can attain its maximum at radial distance greater than half of the radius, to be more specific at if the ratio of inner to outer radius is assumed to be 0.2, and also the ratio of thickness to outer radius is 0.2 while material properties change in radial direction. The results for FG disk with variable thickness under thermomechanical loading show that an efficient and optimal design of the disk requires variable section thicker at the hub and tapering to smaller thickness at the periphery and also that the temperature-dependent material properties must be considered in high temperature environment. Applying FSDT, while material properties change in radial direction, it is seen that for the specific value of the grading index n(), the moment resultants in a FG solid disk with convex or constant thickness profile are lower throughout than those in pure material disk. In case of changing material properties in thickness direction by using large deflection theory, it is observed that the radial stresses in a full-metal disk due to thermal load, body force and vertical pressure are smaller than those in a full-ceramic disk. It is found that the small deflection theory gives large errors in the results for FG disks if the ratio of maximum deflection to thickness is close to 0.4 for a homogeneous (full-ceramic in this study) disk.

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