A Derivation of Bending Free Toroidal Shell Shapes for Tokamak Fusion Reactors

[+] Author and Article Information
W. H. Gray, W. C. T. Stoddart

Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830

J. E. Akin

University of Tennessee, Knoxville, Tenn. 37916

J. Appl. Mech 46(1), 120-124 (Mar 01, 1979) (5 pages) doi:10.1115/1.3424482 History: Received January 01, 1978; Revised July 01, 1978; Online July 12, 2010


This paper describes an extension of mathematical solutions to bending free shapes of toroidal pressure vessels. Previous work on this subject [1] derived a pure tension shape of a toroidal membrane which was subjected to a uniform internal pressure. This research was directed toward the finding of a pure tension shape of a toroidal membrane which is subjected to a pressure inversely proportional to the square of the toroidal radius. Such a relationship is possible when electromechanical forces are considered. This family of shapes, which are nearly circular for aspect ratios greater than 2.5, is derived by solving the equilibrium, constitutive, and kinematic relationships for a uniform toroidal shell using the linear membrane theory. Serious consideration should be given to these toroidal shapes, as they provide alternative methods of design for Tokamak fusion reactors.

Copyright © 1979 by ASME
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