Non-geodesic filament winding on generic shells of revolution

The application of non-geodesic filament winding significantly enlarges the design space for composite structures. The formulation and evaluation of these trajectories however, is a rather complicated problem. In this paper, under the limitation of exclusively considering generic shells of revolution, we present the basic equations supporting such a path description. These equations are already known but the emphasis of the derivation presented here is mainly oriented towards the relation between basic geometric quantities (metrics and curvatures) and the resulting fibre path orientation (winding angle distribution). In addition, we propose here the idea of formulating the friction distribution along the tow in such a way that the resulting path can be analytically described. Furthermore, we provide analytical results for some basic shapes.