PSI - Issue 82

Ivan Ćatipović et al. / Procedia Structural Integrity 82 (2026) 302 – 308 Ivan Ćatipović et al. / Structural Integrity Procedia 00 (2026) 000–000

303

2

1. Introduction Synthetic mooring lines have been effective alternatives to steel wire ropes or chains for decades, offering cost savings, easier handling, and better strength-to-weight ratios (Wang et al., 2019). These ropes are used in mooring systems (Xu et al., 2019) for wave energy converters (WEC), offshore wind farms (Weller et al., 2015), and fish cages (Gutiérrez-Romero et al., 2020). Designing offshore mooring systems per standards like DNVGL-OS-E301 (2015) involves coupled dynamic analysis of mooring lines and vessels, considering stiffness, damping, and inertial forces. Stiffness includes non-linear elasticity and geometric stiffness (Tahar and Kim, 2008, 2003). A quadratic drag model based on the Morison equation (Vendhan, 2019) is used for damping. Inertial forces are evaluated via this model using fluid accelerations. These models are applied in offshore renewable energy (Wang, 2020; Wiegard et al., 2019) and fish cages (Hou et al., 2022). Validation exists for wave energy converters (Ringsberg et al., 2020). Similar techniques are expected for floating photovoltaics (FPV) as presented by Kanotra and Shankar (2022). The importance of mooring systems for FPVs is highlighted in DNVGL-RP-0584 (2021), emphasising their role in structural integrity.

Nomenclature A

cross-sectional area of a mooring line shape functions for modelling the displacements coefficients of Newton interpolation polynomial

A k

b 0 , b 1 , b 2

function for calculating the axial deformation based on the real tension

f

finite element length stiffness matrix

L

! !"#$% &

distributed mass of a mooring line

m

MBL

minimum break loading

shape functions for modelling the effective tension force position vector of the deformed shape of a mooring line acceleration vector of a mooring line

P n

r

! !!

arc length of an extended mooring line

s

real tension

T

effective tension force

T E

a 0 , a 1 , a 2

coefficients for calculating the axial deformation based on the real tension

axial deformation nodal effective tensions density of seawater

e

λ n

ρ

Previous research by Ćatipović et al. (2011, 2012, 2021a, 2021b) focused on synthetic ropes, which experience significant deformations during use, notably axial elongation that can reach 30% to 40%, depending on the type. In these studies, a finite element (FE) formulation was proposed to account for the influence of mooring line elongation on stiffness. In Ćatipović et al. (2021b), the formulation was improved by incorporating the effects of line elongation on inertial and damping forces. An extended approach was developed to model axial deformations up to 40% in Ćatipović et al. (2021a). All these models assume linear material properties related to line stiffness. Recent studies show that non-linear properties of mooring ropes are included in FEM models, but specific non linear rope stiffness models are not directly embedded, necessitating iterative methods such as Newton-Raphson to maintain tension-extension consistency. Ćatipović et al. (2025) proposed a new FE formulation with direct non linear rope stiffness formulation based on the Syrope model. Following Ćatipović et al. (2025), this study aims to expand its application. It incorporates non-linear properties from OCIMF (2018, 2008) into the FE formulation using Newton interpolating polynomials. A case study with a single finite element illustrates this approach for polyamide ropes.