A power series method for static and dynamic analysis of offshore mooring lines

Abstract

The mooring line response is described by the nonlinear partial differential equations (PDEs). The nonlinearity arises from the cable geometry through the drag force and the geometric compatibility condition. This paper develops a power series method (PSM) and applies this semi-analytical approach to solve the PDEs of moorling line motion, which often have been dealt with fully numerically. This technique permits solutions for some differential equations through approximation with polynomial series. Besides being less computationally intensive, PSM-based analyses are straightforward to implement. For the present model, vector components are approximated with infinite polynomial series being functions of spatial and temporal variables. The paper addresses a two-dimensional mooring line model with a fixed bottom end and subject to hydrodynamic and hydrostatic forces. A harmonic excitation at the top end is approximated by a local polynomial approximation enabling the inference of wave parameters. The analysis highlights the effects of pretension, mass per unit length, and offset on the mooring line response. The dynamic analysis enables the evaluation of dynamic tensions for various polynomial orders of temporal and spatial coordinates. It is noticed that the numerical convergence occurs when increasing the degree of polynomials to be up to at least the seventh degree.