Non-geodesic filament winding on generic shells of revolution

Abstract

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.

Design of winding pattern of filament-wound composite pressure vessel with unequal openings based on non-geodesics

“…C f represents the cover degree of filament band after a layer of finished winding. Combining equation 21, cover factor C f is expressed as Combining equation (22), the overlap factor of filament band is obtained as…”

Manufacturing and Processing of Polymer Composites

“…The winding trajectories and pattern architecture can be numerically simulated which also facilitates non-geodesic winding [33][34][35]. However, the geometry of the filament wound part limits the choice of the winding angle.…”

Stability of filament-wound hyperbolic flexible pipes under internal pressure based on non-geodesic winding

“…Filament winding on doubly-curved shells of revolution has gained increasing attention in recent years. Koussios et al 15 established first-order differential equations describing non-geodesic trajectories on an ellipsoid, cone, and sphere mathematically, but the external load was not considered in the model. Min et al 16 proposed a topological mapping algorithm for optimal winding trajectory on an elliptical shell.…”

“…With Eq. (1), the parametric equation of the hyperboloid of one sheet at the curvilinear coordinate system is easily written as where r = R θ sinϕ.The parametric equation of the hyperboloid of one sheet at the cylindrical coordinate system is easily written as where The differential equation of non-geodesic trajectories is written as15…”