Lumped, constrained cable modeling with explicit state-space formulation using an elastic version of Baumgarte stabilization

Abstract

This paper presents a modeling approach for efficient simulation of slender structures, such as wires, cables and ropes. Lumped structural elements are connected using constraints. These are solved explicitly, using an elastic version of Baumgarte stabilization. This avoids singularities in the matrix inversions. The resulting explicit state-space formulation filters the higher order dynamics and can be solved using simple numerical integration methods. Constraints are demonstrated for modeling different aspects: Internal cable forces, one cable sliding along another cable and contact between cable and seabed. Also, a cable initialization routine is presented for rapid building of different interconnected cable geometries, ranging from cases in offshore crane operations to in-sea equipment such as seismic cables. Two case studies are presented to illustrate the effectiveness and the robustness of the proposed modeling approach; the first one being a test of two connected, sinking cables, and the last one being a larger case demonstrating the use of the cable library in an offshore seismic survey case.