Dynamic Simulation of a Mooring Catenary Based on the Lumped-Mass Approach: OpenModelica and Python Implementations
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In this paper, the theoretical background behind the formulation and solution of a discretized lumped-mass mathematical-model of the physically continuous and inelastic mooring catenary is re-visited. The drag term of the Morison equation is used to determine the fluid loads, and the sea-bed interaction is prescribed as vertical spring loads on the interacting nodes. Numerical solution to the equation of motion is sought through a finite-difference method. The initial conditions are determined using the catenary theory, the instantaneous boundary conditions are prescribed, and the in-elasticity of the mooring segments is specified as the constraint equation. The solution procedure is then implemented as both Python and Modelica code. Results of the Modelica simulation are then compared with those generated using the popular ocean-engineering software, Orcaflex. Finally, conclusions are drawn based on the analysis of simulation results. The codes and results are made available for download.