{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T19:37:32Z","timestamp":1774294652931,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,2,26]],"date-time":"2022-02-26T00:00:00Z","timestamp":1645833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["PTDC\/ECI-EGC\/31488\/2017"],"award-info":[{"award-number":["PTDC\/ECI-EGC\/31488\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BD\/147178\/2019"],"award-info":[{"award-number":["SFRH\/BD\/147178\/2019"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/UIDP\/00134\/2020"],"award-info":[{"award-number":["UIDB\/UIDP\/00134\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JMSE"],"abstract":"<jats:p>The mooring force in a fish cage array subjected to currents and waves is investigated using the finite element method. Firstly, the numerical model of a fish cage array with six gravity cages is built by Ansys\/APDL. Collars and bottom rings are simulated with pipe and beam elements while the rest structure is simulated with link elements, including the net and mooring cables. Thus, the weight and hydrodynamic load on the cables can be considered. The initial shape of the mooring ropes is calculated based on mooring dynamics. Since each component is a slender structure in the cage array, the Morison equation is used to calculate the hydrodynamic load. Secondly, the mooring forces are assessed for the system in different sea states. The locations of the maximum mooring force on different parts in the mooring system are found. The mean values and amplitudes of maximum mooring forces on different parts are calculated. The main ropes have the maximum mooring forces under all sea states. The mean values of the maximum mooring forces increase with the current velocity and wave height. When the attack angle is 0\u00b0 and 90\u00b0, the two adjacent bridle ropes do not play the role of pulling the cage together. One is pulled tight and the other one is slack.<\/jats:p>","DOI":"10.3390\/jmse10030331","type":"journal-article","created":{"date-parts":[[2022,2,27]],"date-time":"2022-02-27T20:47:17Z","timestamp":1645994837000},"page":"331","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Numerical Study on the Mooring Force in an Offshore Fish Cage Array"],"prefix":"10.3390","volume":"10","author":[{"given":"Zhongchi","family":"Liu","sequence":"first","affiliation":[{"name":"Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6990-8071","authenticated-orcid":false,"given":"Shan","family":"Wang","sequence":"additional","affiliation":[{"name":"Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8570-4263","authenticated-orcid":false,"given":"C.","family":"Guedes Soares","sequence":"additional","affiliation":[{"name":"Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,26]]},"reference":[{"key":"ref_1","unstructured":"FAO (2018). The State of World Fisheries and Aquaculture, Fisheries and Aquaculture Department, Food and Agriculture Organization of the United Nations. Publishing Policy and Support Branch, Office of Knowledge Exchange, Research and Extension."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"57","DOI":"10.3354\/aei00007","article-title":"Environmental issues of fish farming in offshore waters: Perspectives, concerns and research needs","volume":"1","author":"Holmer","year":"2010","journal-title":"Aquac. Environ. Interact."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"22","DOI":"10.4031\/MTSJ.44.3.11","article-title":"Site Selection Criteria for Open Ocean Aquaculture","volume":"44","author":"Benetti","year":"2010","journal-title":"Mar. Technol. Soc. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"107961","DOI":"10.1016\/j.oceaneng.2020.107961","article-title":"Fluid-structure interactions of cage based aquaculture: From structures to organisms","volume":"217","author":"Xu","year":"2020","journal-title":"Ocean Eng."},{"key":"ref_5","unstructured":"F\u00f8re, H.M., Endresen, P.C., and Bjelland, H.V. (2021, January 21\u201330). Load Coefficients and Dimensions of Raschel Knitted Netting Materials in Fish Farms. Proceedings of the ASME 2021 40th International Conference on Ocean, Offshore and Arctic Engineering, Online."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"108872","DOI":"10.1016\/j.oceaneng.2021.108872","article-title":"Experimental investigation on the fluid\u2013structure interaction of a flexible net cage used to farm Pacific bluefin tuna (Thunnus orientalis)","volume":"226","author":"Dong","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Hou, H.-M., Dong, G.-H., and Xu, T.-J. (2020). Analysis of probabilistic fatigue damage of mooring system for offshore fish cage considering long-term stochastic wave conditions. Ships Offshore Struct., 1\u201312.","DOI":"10.1080\/17445302.2020.1834752"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2124","DOI":"10.1016\/j.oceaneng.2007.04.007","article-title":"Development of structural modeling techniques for evaluating HDPE plastic net pens used in marine aquaculture","volume":"34","author":"Fredriksson","year":"2007","journal-title":"Ocean Eng."},{"key":"ref_9","unstructured":"Guedes Soares, C., Garbatov, Y., and Fonseca, N. (2005). New net cage de-signs to prevent tearing during handling. Maritime Transportation and Exploitation of Ocean and Coastal Resources, Taylor & Francis Group."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Endresen, P.C., F\u00f8re, M., Fredheim, A., Kristiansen, D., and Enerhaug, B. (2013, January 9\u201314). Numerical Modeling of Wake Effect on Aquaculture Nets. Proceedings of the ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering, Nantes, France. Ocean Space Utilization.","DOI":"10.1115\/OMAE2013-11446"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.aquaeng.2016.08.001","article-title":"Fatigue assessment for the floating collar of a fish cage using the deterministic method in waves","volume":"74","author":"Bai","year":"2016","journal-title":"Aquac. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.aquaeng.2015.05.005","article-title":"Experimental study on flow velocity and mooring loads for multiple net cages in steady current","volume":"67","author":"Zhao","year":"2015","journal-title":"Aquac. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.marstruc.2013.08.005","article-title":"Experimental investigation on hydrodynamics of floating cylinder in oscillatory and steady flows by forced oscillation test","volume":"34","author":"Fu","year":"2013","journal-title":"Mar. Struct."},{"key":"ref_14","unstructured":"Guedes Soares, C., Garbatov, Y., and Fonseca, N. (2005). Response from current and regular\/irregular waves on a typical polyethylene fish farm. Maritime Transportation and Exploitation of Ocean and Coastal Resources, Taylor & Francis Group."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Guedes Soares, C., Garbatov, Y., and Fonseca, N. (2005). Computation modeling of the moored flexible structures. Maritime Transportation and Exploitation of Ocean and Coastal Resources, Taylor & Francis Group.","DOI":"10.1201\/9781439833728"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.oceaneng.2013.07.004","article-title":"Dynamic responses of floating fish cage in waves and current","volume":"72","author":"Li","year":"2013","journal-title":"Ocean Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.marstruc.2013.08.002","article-title":"Nonlinear hydroelastic analysis of an aquaculture fish cage in irregular waves","volume":"34","author":"Li","year":"2013","journal-title":"Mar. Struct."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.aquaeng.2013.09.006","article-title":"Field measurements of cage deformation using acoustic sensors","volume":"57","author":"DeCew","year":"2013","journal-title":"Aquac. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.aquaeng.2018.02.001","article-title":"Drag forces and deformation of aquaculture cages\u2014Full-scale towing tests in the field","volume":"81","author":"Gansel","year":"2018","journal-title":"Aquac. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"107027","DOI":"10.1016\/j.oceaneng.2020.107027","article-title":"Review of developments in porous membranes and net-type structures for breakwaters and fish cages","volume":"200","author":"Guo","year":"2020","journal-title":"Ocean Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"108383","DOI":"10.1016\/j.oceaneng.2020.108383","article-title":"Model uncertainty in hydrodynamic characteristics by numerical models for aquaculture plant and mooring system","volume":"219","author":"Dong","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_22","first-page":"685","article-title":"Validation of tools for the analysis of offshore aquaculture installations","volume":"Volume 2","author":"Santos","year":"2021","journal-title":"Developments in Maritime Technology and Engineering"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"102591","DOI":"10.1016\/j.apor.2021.102591","article-title":"Dynamic wave induced loads on a moored flexible cylindrical net cage with analytical and numerical model simulations","volume":"110","author":"Mohapatra","year":"2021","journal-title":"Appl. Ocean Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"102172","DOI":"10.1016\/j.aquaeng.2021.102172","article-title":"Dynamic Analysis of an Array of Semi-rigid \u201cSea Station\u201d Fish Cages subjected to waves","volume":"94","author":"Zhang","year":"2021","journal-title":"Aquac. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1016\/j.rser.2019.05.027","article-title":"Review of mooring design for floating wave energy converters","volume":"111","author":"Xu","year":"2019","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1016\/j.renene.2015.03.058","article-title":"Synthetic mooring ropes for marine renewable energy applications","volume":"83","author":"Weller","year":"2015","journal-title":"Renew. Energy"},{"key":"ref_27","unstructured":"Thomsen, J.B., Kofoed, J.P., Delaney, M., and Banfield, S. (July, January 26). Initial Assessment of Mooring Solutions for Floating Wave Energy Converters. Proceedings of the Twenty-Sixth (2016) International Ocean and Polar Engineering Conference, Rhodes, Greece."},{"key":"ref_28","unstructured":"Guedes Soares, C. (2019). An overview of synthetic mooring cables in marine application. Advances in Renewable Energies Offshore, Taylor and Francis Group."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.oceaneng.2018.04.071","article-title":"An experimental investigation on the bedding-in behavior of synthetic fiber ropes","volume":"160","author":"Lian","year":"2018","journal-title":"Ocean Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.renene.2020.05.070","article-title":"Experimental investigation on hybrid mooring systems for wave energy converters","volume":"158","author":"Xu","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Guedes Soares, C. (2020). Experimental study of nonlinear behavior of a nylon mooring rope at different scales. Developments in Renewable Energies Offshore, Taylor and Francis.","DOI":"10.1201\/9781003134572"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Liu, Z., Mohapatra, S., and Guedes Soares, C. (2021). Finite Element Analysis of the Effect of Currents on the Dynamics of a Moored Flexible Cylindrical Net Cage. J. Mar. Sci. Eng., 9.","DOI":"10.3390\/jmse9020159"},{"key":"ref_33","first-page":"705","article-title":"Numerical modelling of full-scale aquaculture cages under uniform flow","volume":"Volume 2","author":"Santos","year":"2021","journal-title":"Developments in Maritime Technology and Engineering"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.jfluidstructs.2016.05.013","article-title":"Structural response of high solidity net cage models in uniform flow","volume":"65","author":"Lader","year":"2016","journal-title":"J. Fluids Struct."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.aquaeng.2008.01.003","article-title":"Effects of waves and currents on gravity-type cages in the open sea","volume":"38","author":"Huang","year":"2008","journal-title":"Aquac. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Endresen, P.C., Birkevold, J., F\u00f8re, M., Fredheim, A., Kristiansen, D., and Lader, P. (2014, January 8\u201313). Simulation and Validation of a Numerical Model of a Full Aquaculture Net-Cage System. Proceedings of the ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering, San Francisco, CA, USA. Professor Emeritus, J. Randolph Paulling Honoring Symposium on Ocean Technology.","DOI":"10.1115\/OMAE2014-23382"},{"key":"ref_37","unstructured":"Chakrabarti, S.K. (2005). Handbook of Offshore Engineering, Elsevier."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Faltinsen, O.M. (1990). Viscous Wave Loads and Damping. Sea Loads on Ships and Offshore Structures, Cambridge University Press.","DOI":"10.1146\/annurev.fluid.22.1.35"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Faltinsen, O.M. (1990). Stationkeeping. Sea Loads on Ships and Offshore Structures, Cambridge University Press.","DOI":"10.1146\/annurev.fluid.22.1.35"}],"container-title":["Journal of Marine Science and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2077-1312\/10\/3\/331\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:28:22Z","timestamp":1760135302000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2077-1312\/10\/3\/331"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,26]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["jmse10030331"],"URL":"https:\/\/doi.org\/10.3390\/jmse10030331","relation":{},"ISSN":["2077-1312"],"issn-type":[{"value":"2077-1312","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,26]]}}}