PSI - Issue 82

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2026) 000–000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2026) 000–000

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ScienceDirect

Procedia Structural Integrity 82 (2026) 302–308

© 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers Abstract Current practice in positioning offshore objects at specific sea locations often involves the use of mooring lines made from various synthetic ropes, such as aramid, polyester, and polyamide ropes. These ropes exhibit pronounced nonlinear tension extension properties, which originate from their construction and material characteristics. The most widely used method for assessing the response of mooring lines subjected to environmental loads transmitted from the offshore object is the finite element method (FEM). In current FEM formulations, the non-linear relations of a rope are incorporated but included indirectly in the element formulation. Consequently, to evaluate the tension in a mooring line associated with a specific extension of the rope, an additional iterative numerical procedure is necessary, which increases the calculation time. The approach presented here eliminates the need for these additional iterative procedures, as the nonlinear tension-extension relation, which can be considered in a general form, is incorporated directly into the FEM formulation. This was achieved by describing the tension-extension relation using appropriate fitting functions that are compatible with the formulations of the stiffness matrix of the finite element (FE), allowing for a fully analytical derivation of the matrix and eliminating the need for numerical integrations over an element's length. Therefore, this study further improves the current FEM by implementing the non-linear properties of synthetic ropes directly into the element formulation. The efficiency and accuracy of the newly developed formulation proved adequate in case studies of different types of synthetic ropes. © 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers Keywords: Synthetic mooring lines; Finite element formulation; Non-linear rope stiffness 8th International Conference on Structural Integrity and Durability (ICSID2025) Development of a finite element for mooring lines with nonlinear tension-extension properties Ivan Ćatipović*, Tomislav Prosinečki, Antonio Mikulić, Neven Alujević University of Zagreb, Faculty of Mech. Eng. And Nav. Arch., I. Lučića 5, 10000 Zagreb, Croatia Abstract Current practice in positioning offshore objects at specific sea locations often involves the use of mooring lines made from various synthetic ropes, such as aramid, polyester, and polyamide ropes. These ropes exhibit pronounced nonlinear tension extension properties, which originate from their construction and material characteristics. The most widely used method for assessing the response of mooring lines subjected to environmental loads transmitted from the offshore object is the finite element method (FEM). In current FEM formulations, the non-linear relations of a rope are incorporated but included indirectly in the element formulation. Consequently, to evaluate the tension in a mooring line associated with a specific extension of the rope, an additional iterative numerical procedure is necessary, which increases the calculation time. The approach presented here eliminates the need for these additional iterative procedures, as the nonlinear tension-extension relation, which can be considered in a general form, is incorporated directly into the FEM formulation. This was achieved by describing the tension-extension relation using appropriate fitting functions that are compatible with the formulations of the stiffness matrix of the finite element (FE), allowing for a fully analytical derivation of the matrix and eliminating the need for numerical integrations over an element's length. Therefore, this study further improves the current FEM by implementing the non-linear properties of synthetic ropes directly into the element formulation. The efficiency and accuracy of the newly developed formulation proved adequate in case studies of different types of synthetic ropes. © 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers Keywords: Synthetic mooring lines; Finite element formulation; Non-linear rope stiffness 8th International Conference on Structural Integrity and Durability (ICSID2025) Development of a finite element for mooring lines with nonlinear tension-extension properties Ivan Ćatipović*, Tomislav Prosinečki, Antonio Mikulić, Neven Alujević University of Zagreb, Faculty of Mech. Eng. And Nav. Arch., I. Lučića 5, 10000 Zagreb, Croatia

* Corresponding author. Tel.: +385 1 6168 508; fax: +385 1 6156 940. E-mail address: ivan.catipovic@fsb.unizg.hr * Corresponding author. Tel.: +385 1 6168 508; fax: +385 1 6156 940. E-mail address: ivan.catipovic@fsb.unizg.hr

2452-3216 © 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers 2452-3216 © 2026 The Authors. Copy from the contract: Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers

2452-3216 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSID organizers 10.1016/j.prostr.2026.04.046