Analytical Model of Non-Linear Load Reduction Devices for Catenary Moorings

Abstract

Abstract Load reduction devices are extensible components installed along mooring lines to provide peak and mean mooring load reduction, and are of articular interest for floating offshore wind. Various concepts exist, including ballasted pendulums, thermoplastic springs and hydraulic dampers, all of which provide compliance to environmental loads. This enables lighter mooring lines, smaller anchors and increased fatigue life of mooring lines — contributing to higher reliability and lower cost. Load reduction devices are designed to exhibit a non-linear load-extension behaviour: lower stiffness in the operational strain range to reduce loads, and higher stiffness at high strain. These devices are becoming an increasingly common consideration for FOWTs, and are pushing traditional analysis/design to readily incorporate nonlinearity. Well-established static catenary equations, used to define mooring tension-offset profiles, only account for linear elasticity such that capturing non-linear response typically requires finite element modelling. This paper presents an alternative through parameterising equations for three different non-linear load-extension curves and incorporating them into the existing catenary equations. For a given non-linear load-extension curve and length of load reduction device, the resulting analytical model can be solved quasi-instantaneously using Newton-Raphson or Newton-Krylov iterations to give vertical and horizontal mooring line tensions and thus strain of the device. Results from the new analytical model are compared with finite element predictions showing agreement to within 1%. The analytical model can be solved for any two unknowns, such that optimal load reduction device length and stiffness can be determined instantaneously given maximum environmental load and allowable surge. The new analytical equations are implemented into a graphical app, which allows the user to input any load reduction device parameters and visualise the resulting mooring system’s geometry and tension-offset profile.