An Approximate Solution for the Compression of a Bonded Thin Annular Disk

Abstract

An approximate solution for the compression of a bonded thin annular disk is presented based on the so-called Perturbation-Ritz Method. The solution is essentially the outer expansion of the problem, with the unknown constants determined by the Ritz Method minimizing the potential energy. It is valid throughout the thin disk except in the boundary layers, which are confined to very narrow regions near the lateral surfaces. The solution asymptotically approaches the exact one as the disk thickness reduces towards zero. Both the incompressible and compressible cases are discussed. The relationships of the stiffness and stress distributions with the key parameters such as the shape factor, the radius ratio, and Poisson’s ratio are investigated. A better understanding of the compression of a bonded thin annular disk is achieved.