Classical and modern optimization methods in minimum weight design of elastic rotating disk with variable thickness and density

Abstract

Rotating disks work mostly at high angular velocity and this results a large centrifugal force and consequently induce large stresses and deformations. Minimizing weight of such disks yields to benefits such as low dead weights and lower costs. This paper aims at finding an optimal disk profiles for minimum weight design using the Karush-Kuhn-Tucker method (KKT) as a classical optimization method, simulated annealing (SA) and particle swarm optimization (PSO) as two modern optimization techniques. Some semi-analytical solutions for the elastic stress distribution in a rotating annular disk with uniform and variable thickness and density proposed by the authors in the previous works have been used. The von Mises failure criterion of optimum disk is used as an inequality constraint to make sure that the rotating disk does not fail. The results show that the minimum weight obtained for all three methods is almost identical. The KKT method gives a profile with slightly less weight (6% less than SA and 1% less than PSO) while the implementation of PSO and SA methods are easier and provide more flexibility compared with those of the KKT method. The effectiveness of the proposed optimization methods is shown.