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Fiber Trajectories Design of Ellipsoid Component Based on Topological Mapping Methodology

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Abstract

This paper presents a topological mapping algorithm for ellipsoid component winding trajectory. The sphere with double opposite holes was used as initial winding trajectory design model. The double opposite holes ellipsoid winding trajectory was obtained form that of the double-holes-sphere based on topological mapping algorithm. The basic equation of equilibrium for ellipsoidal mapping trajectory was given and its slippage coefficients were calculated using the non-geodesic law and differential geometry. The variation of slippage coefficients with holes-radius and ellipsoid rate were analyzed. The results show that, when ellipsoidal rate get close to 1 gradually, the better stability of fiber trajectories was obtained by topological mapping function. The ellipsoid component with lager holes-radius requires lower coefficient of friction between the fiber bundle and the ellipsoid surface. This fiber trajectory mapping function in the paper presents a useful tool for designing the double opposite holes ellipsoid filament-wound component trajectory.

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  1. Research Institute of 365, Northwestern Polytechnical University, Xi’an, Shaanxi, People’s Republic of China, 710072

    Rong Min & Bin Liu

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  1. Rong Min
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  2. Bin Liu
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Correspondence to Rong Min.

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Min, R., Liu, B. Fiber Trajectories Design of Ellipsoid Component Based on Topological Mapping Methodology. Appl Compos Mater 24, 661–674 (2017). https://doi.org/10.1007/s10443-016-9533-0

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  • DOI: https://doi.org/10.1007/s10443-016-9533-0

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