Polyester mooring line is gradually becoming popular in deepwater engineering because of its lightweight property. In catenary mooring system, the horizontal restoring force comes from the gravity effect of the catenary mooring line which occupies the payload of the platform. Thus, the synthetic mooring line overcomes the drawback together with the taut mooring system which utilizes the axial elasticity to offer restoring force. The synthetic mooring line may only be one seventh weight of the steel mooring line and has low tensile stiffness which leads to a large stretch, and nonlinear material characteristics such as visco-elasticity. These two terms need to improve the slender rod theory which is proposed by Garrett for no stretched lines and improved by Paulling and Webster for small stretched lines. In this topic, a method for large stretched slender rod theory is introduced with the finite element method to deal with the problems of the large rotation and the large deformation. And then a linear visco-elastic model in the stretch-tension relation is utilized to simulate the properties of polyester line such as creep, strain-stress hysteresis and excitation period-dependent stiffness. Finally, an implementation method for integrating the visco-elastic model into slender rod theory is proposed with the numerical method and corroborated by a specified case which has the analytical results.

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