An Exact Solution of the Differential Equation For flow-Loaded Ropes

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Author(s) Mathias Paschen
Pages 562-566
Volume 5
Issue 11
Date November, 2016
Keywords Ideal Thread, flow-Loaded Cable, Differential Equation, Explicit Solution, Validation of Numerical Models

Flow loaded threads, ropes, cables, etc. are usually computed as discretised tension systems. The application of methods of continuum mechanics often fails due to the nonlinearity of the differential equations describing the system. The catenary curve is the only exact solution known until now. This mathematical model requires significant physical assumptions: The thread is ideal. That means it is flexible but non-elastic; its mass is continuously distributed along its length. Flow induced loads do not occur, or they are negligible. In a majority of ocean engineering applications the effects of hydrodynamic loads on threads, cables, etc. are not negligible. Therefore, the hydrodynamic loads have to be considered. Considering a rope whose weight is compensated by its hydrostatic buoyancy, a further solution of the differential equations can be specified. This exact solution can be used for the validation of results from various numerical models.
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