Writhing Dynamics of Cables with Self-contact
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Marine cables under low tension and torsion on the sea floor can form highly contorted three-dimensional geometries that include loops (e.g. hockles) and tangles. These geometries arise from the conversion of torsional strain energy to bending strain energy or, kinematically, a conversion of twist to writhe. A dynamic form of Kirchhoff rod theory is reviewed herein that captures these nonlinear dynamic processes. The resulting theory is discretized using the generalized-alpha method for finite differencing in both space and time. Numerical solutions are presented for an example system of a cable subjected to increasing twist at one end. The solutions show the dynamic evolution of the cable from an initially straight element, through a buckled element in the approximate form of a helix, through the dynamic collapse of this helix into a loop, and subsequent intertwining of the loop with multiple sites of self-contact.
10 pages, 8 figures, 2 tables, in Proceedings of Fifth International Symposium on Cable Dynamics, Santa Margherita Ligure, Italy, pp. 27-36, Sept 15-18, 2003
10 pages, 8 figures, 2 tables, in Proceedings of Fifth International Symposium on Cable Dynamics, Santa Margherita Ligure, Italy, pp. 27-36, Sept 15-18, 2003