Study Of Numerical Methods For Mooring Line Static And Dynamic Analysis Based On Rod Theory

The research about mooring lines has been paid greatly attention, and there are mainlythree kinds of numerical models which have widely recognition over the offshore industry:the Catenary model which is mainly used for the static analysis, and other two for thedynamics of slender rods–lumped mass model and slender rod theory model. In this paper,we carry the mooring line’s static and dynamic analysis by the slender rod theory model,which is based on the Non-Linear Finite Element Method. Compared with other models, thegreatest superiority of slender rod model is that the derivation of motion equations of mooringline are in a3-D Cartesian coordinate system, and this makes the analysis effectively.Different with the Catenary model, the slender rod model can handle the dynamic stiffnessand geometric nonlinearity easily. And compared with the lumped mass method, the slenderrod model has a big improvement on the calculation efficiency and numerical precision.In this paper, a3D finite element formulation was adopted to realize the static anddynamic analysis of mooring lines. The Galerkin method was used to discretize the dynamicequations in space, resulting into a set of nonlinear2nd-order ordinary differential equationsin the time domain. About the boundary condition numerical treatment, the writer also gave adetail present. By assuming that the ocean bottom is flat and elastic, we use a spring mat torepresent the ocean bottom. As for the top boundary condition, a spring-damping implementwas used to model the connection between mooring lines and the structure. We use theNewton iterative schemes to solve the static problem; and for the dynamic analysis, Adams-Moulton method and Newmark-βmethod were both employed for time-domain integrationof the discretized equations. Besides these, because dynamic system is sensitive to start-uptransients, the imposed motion is "ramped" to provide a smooth start.Based on these, the author wrote a FORTRAN program to carry on the mooring linestatic and dynamic analysis, and did some works to prove the accuracy and effective of theprogram. For the static analysis, we used simply supported beam、a fixed end cantileverbeam and catenary method to test and verify the program; A pendulum with large amplitudeand a beam which is forces with a sinusoidal motion at one side were employed for thedynamic analysis program proving. At last, we chose a real mooring line to do some analysisabout the influence of time step and vibration frequency. Through the comparison with theoretical results, it has been proved that the program based on slender rod theory appears tobe working correctly and predictably.