Shear-induced buckling of a thin elastic disk undergoing spin-up

Abstract

The stability of a spinning thin elastic disk has been widely studied due to its central importance in engineering. While the plastic deformation and failure of an annular disk mounted on a rigid and accelerating circular shaft are well understood, shear-induced elastic buckling of the disk due to this ‘spin-up’ is yet to be reported. Here, we calculate this buckling behavior within the framework of the Föppl–von Kármán equations and give numerical results as a function of the disk’s aspect ratio (inner-to-outer radius) and Poisson’s ratio. This shows that shear-induced elastic buckling can dominate plastic failure in many cases of practical interest. When combined with existing theory for plastic failure, the results of the present study provide foundation results for a multitude of applications including the characterization of accelerating compact disks and deployment of space sails by centrifugal forces.