Abstract: The mathematical model of filament-wound composite elbows is presented based on geodesic trajectories. The cylindrical sections are used for transiting the torus part in the middle and the both end parts. The torus part is overwound using geodesics, and the both cylindrical parts are produced using non-geodesics to ensure a smooth transition of fiber trajectories at the both ends. The stability-ensuring conditions of composite elbows are derived with the aid of differential geometry. The equations for determining the winding patterns and the minimum-required winding angles are formulated. The influence of various relative bending radii and tube radii on the resulting winding angles is evaluated. The obtained winding patterns are simulated and validated using MATLAB codes. The results show that the winding patterns obtained using the present method satisfy the windability of the elbow and meet the basic requirements for filament winding technology.

Key words: filament winding, composite materials, elbow, geodesic, non-geodesic