The Karush–Kuhn–Tucker optimality conditions in minimum weight design of elastic rotating disks with variable thickness and density

Rotating discs work mostly at high angular velocity. High speed results in large centrifugal forces in discs and induces large stresses and deformations. Minimizing weight of such disks yields various benefits such as low dead weights and lower costs. In order to attain a certain and reliable analysis, disk with variable thickness and density is considered. Semi-analytical solutions for the elastic stress distribution in rotating annular disks with uniform and variable thicknesses and densities are obtained under plane stress assumption by authors in previous works. The optimum disk profile for minimum weight design is achieved by the Karush–Kuhn–Tucker (KKT) optimality conditions. Inequality constrain equation is used in optimization to make sure that maximum von Mises stress is always less than yielding strength of the material of the disk.