Inverse problem of fracture mechanics for a disk fitted onto a rotating shaft

A plane problem of fracture mechanics for a circular disk fitted onto a rotating shaft is considered. The disk is assumed to be fitted tightly onto the shaft, and there are $N$ randomly located straight-line cracks of length $2l_k$ ($k=1,2,\dots,N$) near the inner surface of the disk. The interference between the disk and the rotating shaft, providing minimization of fracture parameters (stress intensity factor) of the disk, is theoretically studied on the basis of the minimax criterion. A closed system of algebraic equations is constructed, which allows the problem of optimal design to be solved. A simplified method of minimization of disk fracture parameters is considered.