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

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Fig. 3. Comparison of the original and calculated tension-extension relation using 8 polynomials for Polyamide 3&8 Strand rope.

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Fig. 4. Comparison of the original and calculated tension-extension relation using 8 polynomials for Polyamide Double Braided rope.

Table 1. Summary of the relative errors of the calculated compared to the original values of the tension-extension curve. Rope type/Number of polynomials Minimum value, % Maximum value, % Polyamide 3&8 Strand/4 polynomials -2.0 12.8 Polyamide 3&8 Strand/8 polynomials -1.5 0.3 Polyamide Double Braided/8 polynomials -0.5 0.6

4. Conclusion This study introduces an advanced finite element formulation for synthetic mooring lines, enhancing previous models by explicitly including the non-linear tension-extension behaviour of synthetic ropes, as specified by OCIMF (2008). Unlike conventional formulations, this method directly embeds the non-linear rope characteristics into the geometric stiffness matrix, removing the need for iterative procedures to compute tensions for axial deformations. Additionally, the stiffness matrix's purely analytical structure simplifies implementation, avoiding the requirement for numerical integration along the element length. This was achieved by modelling the non-linear properties of synthetic ropes with a second-order polynomial, whose coefficients were calculated using Newton interpolation. The formulated method’s efficiency is demonstrated via a single rope, focusing on the tension-extension relationship for Polyamide 3&8 Strand and Polyamide Double Braided ropes. For the former, 4 or 8 polynomials