A Novel Power Series Method for the Analysis of an Offshore Mooring Line

The mechanics of offshore mooring lines are described by a set of nonlinear equations of motion which have typically been solved through a numerical finite element or finite difference method (FEM or FDM), and through the lumped mass method (LMM). The mooring line nonlinearities are associated with the distributed drag forces depending on the relative velocities of the environmental flow and the structure, as well as the axial dynamic strain-displacement relationship given by the geometric compatibility condition of the flexible mooring line. In this study, a semi analytical-numerical novel approach based on the power series method (PSM) is presented and applied to the analysis of offshore mooring lines for renewable energy and oil and gas applications. This PSM enables the construction of analytical solutions for ordinary and partial differential equations (ODEs and PDEs) by using series of polynomials whose coefficients are determined, depending on initial and boundary conditions. We introduce the mooring spatial response as a vector in the Lagrangian coordinate, whose components are infinite bivariate polynomials. For case studies, a two-dimensional mooring line with fixed-fixed ends and subject to nonlinear drag, buoyancy and gravity forces is considered. The introduced boundary and initial conditions enable the analysis of an equilibrium or steady-state of a catenary-like mooring line configuration with variable slenderness and flexibility. Polynomials’ coefficients computation is performed with the aid of a MATLAB package. Numerical results of mooring line configurations and resultant tensions are presented for deep-water applications, and compared with those obtained from a semi-analytical and finite element model. The PSM applied to the mooring line in the present study is efficient and more computationally robust than traditional numerical methods. The PSM can be directly applied to the dynamic analysis of mooring lines.