Optimum material distributions for minimizing stresses in a rotating functionally graded material circular disk

Abstract

Functionally graded materials (FGMs) are an advanced type of composite material having varying material distribution from one to another surface, for which these FGMs become nonhomogeneous in the case of both material characteristics and microstructures. The present study considers a thin circular rotating disk of functionally graded material with a concentric circular hole. The disk is subjected to a thermal load and an inertial force due to the rotation of the disk. The analysis is carried out under plane stress condition. Material properties of the FGM disk are assumed to vary along the radial direction only. In this study, an optimization model is developed for evaluating optimum material distributions in a rotating FGM circular disk corresponding to minimum/prescribed stresses. Further, a mathematical model of direct problem is also developed to calculate stresses and displacements induced in the FGM disk corresponding to a prescribed material distribution. Based on two-dimensional thermoelasticity theories, the problem is formulated in terms of a second-order differential equation. Since a close-form solution of the differential equation is not possible, a standard finite element approach is adopted for the solution of the optimization and direct problems. The models developed in the present study are validated by comparing the results with those available in literature. To demonstrate the developed models, numerical results are obtained for an FGM disk consisting of Al and Al_2 O_3. From the numerical results of direct problem, it is found that the stresses are greatly influenced by material distribution. The results of optimization model ensure that an FGM disk can be designed with optimum material distribution realizing the minimum/prescribed stress profile in the disk. It is also revealed that the stress profile, temperature field, angular speed, and radial thickness of the disk all have significant effects on optimum material distribution of the FGM disk.