Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 709178, 9 pages
Research Article

Design of an Annular Disc Subject to Thermomechanical Loading

1A.Yu. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Prospect Vernadskogo, Moscow 119526, Russia
2Department of Mechanical Engineering and Advanced Institute for Manufacturing with High-tech Innovations, National Chung Cheng University, 168 University Road, Chia-Yi 62102, Taiwan

Received 27 July 2012; Accepted 3 September 2012

Academic Editor: Valery Yakhno

Copyright © 2012 Sergei Alexandrov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two solutions to design a thin annular disc of variable thickness subject to thermomechanical loading are proposed. It is assumed that the thickness of the disc is everywhere sufficiently small for the stresses to be averaged through the thickness. The state of stress is plane. The initiation of plastic yielding is controlled by Mises yield criterion. The design criterion for one of the solutions proposed requires that the distribution of stresses is uniform over the entire disc. In this case there is a relation between optimal values of the loading parameters at the final stage. The specific shape of the disc corresponds to each pair of such parameters. The other solution is obtained under the additional requirement that the distribution of strains is uniform. This solution exists for the disc of constant thickness at specific values of the loading parameters.