A novel approach to optimize material distributions of rotating functionally graded circular disk under minimum and prescribed stresses

Abstract

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.