Optimal Design of Rotating Disks in Creep

Minimum-weight design of axially-symmetric rotating disks in a state of stationary creep is determined for a prescribed value of the creep velocity at the outer edge of the disk. The constitutive equations used for stationary creep are Norton's law generalized to multiaxial states of stress based on von Mises' criterion and associated flow rule. The resulting nonlinear optimization problem is solved iteratively using a series expansion to approximate the thickness variation of the disk, In each iteration step the nonlinear creep equations are solved for the stresses and a linearized perturbation problem is solved for the stress gradients. The optimization procedure is used to determine the optimal shape of a solid rotating disk carrying a uniform traction at the outer edge, and this result is compared with the corresponding disk of uniform strength. Variations in the optimal shape due to a central hole and due to temperature distributions are illustrated by some examples.