Composite toroidal pressure vessels are recently gaining more attention because of their structural efficiency and new-fashioned configuration. However, there have been few investigations with respect to winding toroidal structures, mostly limited to geodesic winding patterns. One of the shortcomings of geodesic winding is that the strength of the fibers is not completely utilized, because its winding angle on a torus is fairly big in general. This paper outlines an efficient and simple optimal design method on laminated toroidal structures subject to internal pressure, winding pattern and layer thickness distributions. First an optimality relation for the helically winding angle and laminated thickness ratio is derived based on the minimum strain energy criterion. With the aid of the netting theory, the helical and hoop winding patterns considering the variation of the layer thickness are presented using the optimality condition mentioned above. The general criteria for fiber bridging and slippage on a torus are formulated with the aid of differential geometry. The relation between slippage coefficient and helically winding angle is obtained to meet stable winding requirements. The helical winding angle and layer thickness at the equator of the torus are considered as design variables, while the minimum structural weight acts as the objective function. An optimal design example with a toroidal pressure vessel is here outlined to demonstrate the favorable performance and robustness of the proposed method. The results show that the optimization algorithm is efficient and convergent to stable solutions while the optimum winding path obtained does satisfy the winding principles. The recommended design-oriented method can be applied both during preliminary dimensioning and optimization of filament wound toroidal pressure vessels.
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