This paper is concerned with the membrane shell analysis of filament overwound toroidal pressure vessels and optimum design of such pressure vessels using the results of the analysis by means of mathematical nonlinear programming. The nature of the coupling between overwind and linear has been considered based on two extreme idealizations. In the first, the overwind is rigidly coupled with the liner, so that the two deform together in the meridional direction as the vessel dilates. In the second, the overwind is free to slide relative to the linear, but the overall elongations of the two around a meridian are identical. Optimized designs with the two idealizations show only minor differences, and it is concluded that either approximation is satisfactory for the purposes of vessel design. Aspects taken into account are the intrinsic overwind thickness variation arising from the winding process and the effects of fiber pre-tension. Pre-tension can be used not only to defer the onset of yielding, but also to achieve a favorable in-plane stress ratio which minimizes the von Mises equivalent stress in the metal liner. Aramid fibers are the most appropriate fibers to be used for the overwind in this type of application. The quantity of fiber required is determined by both its short-term strength and its long-term stress rupture characteristics. An optimization procedure for the design of such vessels, taking all these factors into account, has been established. The stress distributions in the vessels designed in this way have been examined and discussed through the examples. A design which gives due consideration of possible mechanical damage to the surface of the overwind has also been addressed.
