Model of toroidal magnet systems as orthotropic shells of finite thickness

A method for analyzing the stresses in toroidal shells of revolution, acted upon by arbitrary force fields, is described. The equations of Reisnner for orthotropic, axisymmetric shells of revolution are derived and solved for finite-thickness toroidal shells. As a design tool for the shape optimization of fusion magnets, such as the in-plane load support systems of toakamaks or bumpy tori, the analytical technique is a major extension of the work of W.H. Gray et al, which solved the stress equation for bending free toroidal shell shapes, subjected to a Lorentz force. The work described below is simultaneously an extension of the theory of shells and an alteration of the perceived 'optimal' shape for tokamak toroidal field magnets