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Year 2025, Volume: 9 Issue: 1, 134 - 153, 17.06.2025

Ali Ete

https://doi.org/10.38088/jise.1614320

Abstract

References

  • [1] Chakrabarti, S. (2005). Handbook of offshore engineering. 1st ed.1-2, Oxford: El-Sevier Applied Science.
  • [2] API RP 2A-WSD. (2007) Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Working Stress Design - Twenty-First Edition, Errata and Supplement 3.
  • [3] Abdel Raheem Sh, E., Abdel Aal E, M. A., Abdel Shafy A. G. A. and Abdel Seed, F. K. (2012). Nonlinear analysis of offshore structures under wave loadings, Proceedings of the 15th World Conference on Earthquake Engineering-15WCEE, 24–28.
  • [4] Raheem, A. E. S. (2013). Nonlinear response of fixed jacket offshore platform under structural and wave loads, Coupled Systems Mechanics, 2: 111–126. DOI: 10.12989/csm.2013.2.1.111
  • [5] A storm at sea from the view of an oil rig, URL: https://www.reddit.com/r/pics/comments/13q5u9/a_storm_at_sea_from_the_view_of_an_oil_rig/
  • [6] Witz, J. Lyons, G. Patel, M.H. and Brown, D. (1994). Advanced Offshore Engineering, Offshore Engineering Handbook Series. Bentham Press, London, UK.
  • [7] Karadeniz, H. (2013). Stochastic Analysis of Offshore Steel Structures. An Analytical Appraisal, Springer Series in Reliability Engineering. DOI:10.1007/978-1-84996-190-5
  • [8] Boccotti, P. (2015). Wave mechanics and wave loads on marine structures, in: Butterworth-Heinemann publication, Waltham, MA 02451, USA, ISBN: 978-0-12-800343-5, 978–978.
  • [9] Linton, C.M. and Evans, D.V. (1990). The interaction of waves with arrays of vertical circular cylinders, J. Fluid Mech, 215: 549-569. DOI: https://doi.org/10.1017/S0022112090002750
  • [10] Kriebel, D.L. (1990). Nonlinear wave interaction with a vertical circular cylinder. Part I: Diffraction Theory, Ocean Engineering, 17(4): 345–377. https://doi.org/10.1016/0029-8018(90)90029-6
  • [11] Kriebel, D.L. (1992). Nonlinear wave interaction with a vertical circular cylinder. part II: Wave Run-Up, Ocean Engineering, 19(1):75-99. https://doi.org/10.1016/0029-8018(92)90048-9
  • [12] Zhu, S. (1993). Diffraction of short-crested waves around a circular cylinder, Ocean Engineering, 20: 389–407, https://doi.org/10.1016/0029-8018(93)90003-Z
  • [13] Vugts, J.H. Tempel, J.V.D. and Schrama, E.A. (2001). Hydro-dynamic loading on Monotower support structures for preliminary design. Interfaculty Offshore Technology, Faculty of Civil Engineering and Geosciences, Delft University of Technology.
  • [14] Wilson, J.F. (2003). Dynamics of Offshore Structures, John Wiley & Sons, Inc, United States of America. ISBN: 978-0-471-26467-5.
  • [15] Harish, N. Sukomal, M. Shanthala, B. and Subba, R. (2010). Analysis of offshore jacket platform, Natl. Conf. on Sustainable Water Resources Management - SWARM, 7–9.
  • [16] Karadeniz, H. Togan, V. and Vrouwenvelder, T. (2008a). Optimization of steel monopod offshore-towers under probabilistic constraints, Proceedings of the International Mechanical Engineering Congress and Exposition, Boston, USA.
  • [17] Karadeniz, H. Togan, V. and Vrouwenvelder, T. (2008b). Reliability based optimization of steel monopod offshore towers, Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal.
  • [18] Slåke, T. (2016). Analysis of Jacket type fixed platforms- Effect of various mass modelling approaches for Topsides on structural response, MASTER Thesis, University of Stavanger, Stavanger, Stavanger, Norway.
  • [19] Morison, J.R. Brien, M.P. WJohnson, J. and Schaaf, S.A. (1950). The force exerted by surface wave on piles, Petroleum Transactions, American Institute of Mining Engineers, 189:149-154. DOI:10.2118/950149-G
  • [20] Mendes, A.C. Kolodziej, J.A. and Correia, H.J.D. (2004). Numerical modelling of wave-current loading on offshore jacket structures, Transactions on the Built Environment, 71. DOI: 10.2495/FSI030091
  • [21] Lipsett, A.W. (1986). A perturbation solution for nonlinear structural response to oscillatory flow, Applied Ocean Research, 8(4):183-189. https://doi.org/10.1016/S0141-1187(86)80035-9
  • [22] Gudmestad, O.T. and Moe, G. (1996). Hydrodynamic Coefficients for Calculation of Hydrodynamic Loads on Offshore Truss Structures, Marine Structures, 9:23. 0951-8339(95)00023-23-2
  • [23] Sunder, S. and Connor, J. (1981). Sensitivity analyses for steel jacket offshore platforms, Applied Ocean Research, 3(1):19-28. DOI:10.1016/0141-1187(81)90081-X
  • [24] Chandrasekaran, S. Jain, A.K. and Chandak, N.R. (2004). Technical note: Influence of hydrodynamic coefficients in the response behavior of triangular TLPs in regular waves, Ocean Engineering, 31:2319-2342. https://doi.org/10.1016/j.oceaneng.2004.06.005
  • [25] Gücüyen, E. Erdem, R.T. and Gökkuş, Ü. (2012). Irregular wave effects on dynamic behavior of piles, Arabian J. Sci. Eng. King Fahd University of Petroleum and Minerals. DOI 10.1007/s13369-012-0428-6.
  • [26] Edvardsen, K. (2015). Forces on simplified offshore structures according to different wave models, Norway.
  • [27] Karadeniz, H. (1989). Advanced stochastic analysis program for offshore structures - Theoretical outline and the user’s manual of SAPOS, Report, Dept. of Civil Engineering, Delft University of Technology, Delft, Netherland.
  • [28] CSI Analysis Reference Manual. (2014). CSI analysis reference manual for SAP2000 Version 16; Computers & Structures Inc. (CSI): Walnut Creek, CA, USA.
  • [29] SACS (2009). Version 12, EDI, Soft-ware Manual Version 7.
  • [30] Abaqus theory manual. (2004). Version 6.14-1 Hibbitt. Karlsson and Sorensen, Inc. Pawtucket, RI.
  • [31] ANSYS (2016). AQWA user’s manual release 17.0. ANSYS Inc.: Canonsburg, PA, USA.
  • [32] Cermelli, C. Aubault, A. Roddier, D. and Mccoy, T. (2010). Qualification of a Semi-Submersible Floating Foundation for Multi-Megawatt Wind Turbines, Offshore Technology Conference, Offshore Technology Conference, 1–15.
  • [33] Computers, Structures, Inc, (2011). Automatic Wave Loads Technical Note Wave Load Overview. Computers and Structures, Inc, Berkeley, CA.
  • [34] Doman, A.C. (2014). Three-Dimensional equivalent static analysis and design methodology of a reinforced concrete floating offshore wind turbine platform, California State University, Sacramento.
  • [35] Lai, W.J. Lin, Ch.Y. Huang, Ch.Ch. and Lee, R.M. (2016). Dynamic Analysis of Jacket Substructure for Offshore Wind Turbine Generators under Extreme Environmental Conditions, Appl. Sci, 6:307. doi:10.3390/app6100307
  • [36] Kazemi Daliri, A. (2017). Evaluation of using new materials in offshore jacket structures and risers, PhD. Dissertation, İstanbul Aydin University, Istanbul, Turkey.
  • [37] Noorzaei, J. Bahrom, S. I. Jaafar, M.S. Abdul, W. Thanoon, M. and Mohammad, Sh. (2005). Simulation of Wave and Current Forces on Template Offshore Structures, Suranaree J. Sci. Technol, 12(3):193-210.
  • [38] Ishwarya, S. (2016). Nonlinear static and dynamic analyses of jacket-type offshore platform, Anna University, Chennai.
  • [39] Karadeniz, H. (1996). Spectral Analysis Program for Offshore Structures (SAPOS), Response calculation and fatigue damage estimates, Proc. of the 2nd Int. Conference in Civil Engineering on Computer Applications, Research and Practice, ICCE-96, 1:339-349.
  • [40] Yaylacı, M. (2007). Applications of offshore Structure and Explicated of Design Parameters, Karadeniz Technical University, Trabzon, Turkey.
  • [41] Mc Namara, J.F. Gilroy, J.P. Sorensen, E.P. and Hibbitt, H.D. (1985). ABAQUS/AQUA application to offshore risers and pipelines, Maritime Simulation, Proceedings of the First Intercontinental Symposium, Springer.
  • [42] Kuntiyawichai, K. and Chucheepsakul, S. (2004). Analysis of offshore structures subjected to various types of sea wave, Proceedings of OMAE04, 23rd International Conference on Offshore Mechanics and Arctic Engineering, Vancouver, Canada.
  • [43] Huizer, C.O. (2017). Modelling loads of steady current and waves with Abaqus, Aqua. URL: Url-2<https://info.simuleon.com/blog/modelling-loads-of-steady-current-and-waves-with-abaqus-aqua
  • [44] Das, B. and Janardhan, P. (2017). Model Development and Load Analysis of Offshore Jacket Structure using SAP2000, International Journal for Research in Applied Science and Engineering Technology (IJRASET), 5:1482-1493. doi:10.22214/ijraset.2017.4263
  • [45] Dağlı, B. Y. Yiğit, M.E. and Gökkuş, U. (2017). Behaviour of large cylindrical offshore structures subjected to wave loads, TEM Journal, 6(3):550-557. DOI:10.18421/TEM63-16
  • [46] Lamb H. (1993) Hydrodynamics. Cambridge University Press, Cambridge.
  • [47] Maccamy, R.C. and Fuchs, R.A. (1954). Wave Forces on Piles: A Diffraction Theory, Army Corps of Engineers, Beach Erosion Board. U.S. Beach Erosion Board, ech. Memo No. 69.
  • [48] Sarpkaya, T. and Isaacson, M. (1981). Diffraction theory is reviewed in Mechanics of Wave Forces on Offshore Structures, Van Nostrand Reinhold Co.
  • [49] Det Norske Veritas - DNV (1977). Result for the Design, Construction and Inspection of Offshore Structures, Oslo, (Reprint with correction 1981). http://www.dnv.com
  • [50] Sawaragi, T. (1995). Coastal engineering- waves, beaches, wave-structure interaction. Elsevier, Amsterdam.
  • [51] Butterfield, S. Musial, W. Jonkman, J. Sclavounos, P. and Wayman, L. (2007). Engineering Challenges for Floating Offshore Wind Turbines, Golden, Colorado: National Renewable Energy Laboratory

Wave Actions and Responses for Large-Diameter Monopod Platform Structures

Year 2025, Volume: 9 Issue: 1, 134 - 153, 17.06.2025

Ali Ete

https://doi.org/10.38088/jise.1614320

Abstract

The sea-wave loads acting on the fixed offshore structures are estimated by using Airy's linear wave theory and Morison's equation, dissociating the total force into an inertia force component and a drag force component. The contribution of each component of the total force on tubular members can vary significantly based on size specification, from standard pipe members of fixed jacket structures to wide-ranging cylindrical Monopod towers. Inconclusive results can be seen in some published articles in estimating static wave loads using the hydrodynamic module of offshore platforms, indicating that this is still a subject of investigation. A demonstration of an example steel Monopod under Airy's type wave loading is presented. Several finite element offshore structure simulation packages use this simple monopod model for computationally efficient static wave load case simulations. The displacement pattern and the base shear force and bending moment of the Monopod model are calculated. The analytical solution is checked with numerical results of standard commercial FE software packages for verification and comparison purposes. The results show that the wave load calculation module of the finite element-based design programs considered in this study is underestimated, mainly when the contribution of the inertia coefficient to total instantaneous wave force is dominant, like in the monopod case with a large diameter. It can be thought that the differences here are due to the inertia coefficient weighting of the Morrison equation used in wave force calculations.

Keywords

Offshore Structure Monopod Platform Morison Equation Linear Airy Sea-wave loads Hydrodynamic module Commercial offshore software

References

  • [1] Chakrabarti, S. (2005). Handbook of offshore engineering. 1st ed.1-2, Oxford: El-Sevier Applied Science.
  • [2] API RP 2A-WSD. (2007) Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Working Stress Design - Twenty-First Edition, Errata and Supplement 3.
  • [3] Abdel Raheem Sh, E., Abdel Aal E, M. A., Abdel Shafy A. G. A. and Abdel Seed, F. K. (2012). Nonlinear analysis of offshore structures under wave loadings, Proceedings of the 15th World Conference on Earthquake Engineering-15WCEE, 24–28.
  • [4] Raheem, A. E. S. (2013). Nonlinear response of fixed jacket offshore platform under structural and wave loads, Coupled Systems Mechanics, 2: 111–126. DOI: 10.12989/csm.2013.2.1.111
  • [5] A storm at sea from the view of an oil rig, URL: https://www.reddit.com/r/pics/comments/13q5u9/a_storm_at_sea_from_the_view_of_an_oil_rig/
  • [6] Witz, J. Lyons, G. Patel, M.H. and Brown, D. (1994). Advanced Offshore Engineering, Offshore Engineering Handbook Series. Bentham Press, London, UK.
  • [7] Karadeniz, H. (2013). Stochastic Analysis of Offshore Steel Structures. An Analytical Appraisal, Springer Series in Reliability Engineering. DOI:10.1007/978-1-84996-190-5
  • [8] Boccotti, P. (2015). Wave mechanics and wave loads on marine structures, in: Butterworth-Heinemann publication, Waltham, MA 02451, USA, ISBN: 978-0-12-800343-5, 978–978.
  • [9] Linton, C.M. and Evans, D.V. (1990). The interaction of waves with arrays of vertical circular cylinders, J. Fluid Mech, 215: 549-569. DOI: https://doi.org/10.1017/S0022112090002750
  • [10] Kriebel, D.L. (1990). Nonlinear wave interaction with a vertical circular cylinder. Part I: Diffraction Theory, Ocean Engineering, 17(4): 345–377. https://doi.org/10.1016/0029-8018(90)90029-6
  • [11] Kriebel, D.L. (1992). Nonlinear wave interaction with a vertical circular cylinder. part II: Wave Run-Up, Ocean Engineering, 19(1):75-99. https://doi.org/10.1016/0029-8018(92)90048-9
  • [12] Zhu, S. (1993). Diffraction of short-crested waves around a circular cylinder, Ocean Engineering, 20: 389–407, https://doi.org/10.1016/0029-8018(93)90003-Z
  • [13] Vugts, J.H. Tempel, J.V.D. and Schrama, E.A. (2001). Hydro-dynamic loading on Monotower support structures for preliminary design. Interfaculty Offshore Technology, Faculty of Civil Engineering and Geosciences, Delft University of Technology.
  • [14] Wilson, J.F. (2003). Dynamics of Offshore Structures, John Wiley & Sons, Inc, United States of America. ISBN: 978-0-471-26467-5.
  • [15] Harish, N. Sukomal, M. Shanthala, B. and Subba, R. (2010). Analysis of offshore jacket platform, Natl. Conf. on Sustainable Water Resources Management - SWARM, 7–9.
  • [16] Karadeniz, H. Togan, V. and Vrouwenvelder, T. (2008a). Optimization of steel monopod offshore-towers under probabilistic constraints, Proceedings of the International Mechanical Engineering Congress and Exposition, Boston, USA.
  • [17] Karadeniz, H. Togan, V. and Vrouwenvelder, T. (2008b). Reliability based optimization of steel monopod offshore towers, Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal.
  • [18] Slåke, T. (2016). Analysis of Jacket type fixed platforms- Effect of various mass modelling approaches for Topsides on structural response, MASTER Thesis, University of Stavanger, Stavanger, Stavanger, Norway.
  • [19] Morison, J.R. Brien, M.P. WJohnson, J. and Schaaf, S.A. (1950). The force exerted by surface wave on piles, Petroleum Transactions, American Institute of Mining Engineers, 189:149-154. DOI:10.2118/950149-G
  • [20] Mendes, A.C. Kolodziej, J.A. and Correia, H.J.D. (2004). Numerical modelling of wave-current loading on offshore jacket structures, Transactions on the Built Environment, 71. DOI: 10.2495/FSI030091
  • [21] Lipsett, A.W. (1986). A perturbation solution for nonlinear structural response to oscillatory flow, Applied Ocean Research, 8(4):183-189. https://doi.org/10.1016/S0141-1187(86)80035-9
  • [22] Gudmestad, O.T. and Moe, G. (1996). Hydrodynamic Coefficients for Calculation of Hydrodynamic Loads on Offshore Truss Structures, Marine Structures, 9:23. 0951-8339(95)00023-23-2
  • [23] Sunder, S. and Connor, J. (1981). Sensitivity analyses for steel jacket offshore platforms, Applied Ocean Research, 3(1):19-28. DOI:10.1016/0141-1187(81)90081-X
  • [24] Chandrasekaran, S. Jain, A.K. and Chandak, N.R. (2004). Technical note: Influence of hydrodynamic coefficients in the response behavior of triangular TLPs in regular waves, Ocean Engineering, 31:2319-2342. https://doi.org/10.1016/j.oceaneng.2004.06.005
  • [25] Gücüyen, E. Erdem, R.T. and Gökkuş, Ü. (2012). Irregular wave effects on dynamic behavior of piles, Arabian J. Sci. Eng. King Fahd University of Petroleum and Minerals. DOI 10.1007/s13369-012-0428-6.
  • [26] Edvardsen, K. (2015). Forces on simplified offshore structures according to different wave models, Norway.
  • [27] Karadeniz, H. (1989). Advanced stochastic analysis program for offshore structures - Theoretical outline and the user’s manual of SAPOS, Report, Dept. of Civil Engineering, Delft University of Technology, Delft, Netherland.
  • [28] CSI Analysis Reference Manual. (2014). CSI analysis reference manual for SAP2000 Version 16; Computers & Structures Inc. (CSI): Walnut Creek, CA, USA.
  • [29] SACS (2009). Version 12, EDI, Soft-ware Manual Version 7.
  • [30] Abaqus theory manual. (2004). Version 6.14-1 Hibbitt. Karlsson and Sorensen, Inc. Pawtucket, RI.
  • [31] ANSYS (2016). AQWA user’s manual release 17.0. ANSYS Inc.: Canonsburg, PA, USA.
  • [32] Cermelli, C. Aubault, A. Roddier, D. and Mccoy, T. (2010). Qualification of a Semi-Submersible Floating Foundation for Multi-Megawatt Wind Turbines, Offshore Technology Conference, Offshore Technology Conference, 1–15.
  • [33] Computers, Structures, Inc, (2011). Automatic Wave Loads Technical Note Wave Load Overview. Computers and Structures, Inc, Berkeley, CA.
  • [34] Doman, A.C. (2014). Three-Dimensional equivalent static analysis and design methodology of a reinforced concrete floating offshore wind turbine platform, California State University, Sacramento.
  • [35] Lai, W.J. Lin, Ch.Y. Huang, Ch.Ch. and Lee, R.M. (2016). Dynamic Analysis of Jacket Substructure for Offshore Wind Turbine Generators under Extreme Environmental Conditions, Appl. Sci, 6:307. doi:10.3390/app6100307
  • [36] Kazemi Daliri, A. (2017). Evaluation of using new materials in offshore jacket structures and risers, PhD. Dissertation, İstanbul Aydin University, Istanbul, Turkey.
  • [37] Noorzaei, J. Bahrom, S. I. Jaafar, M.S. Abdul, W. Thanoon, M. and Mohammad, Sh. (2005). Simulation of Wave and Current Forces on Template Offshore Structures, Suranaree J. Sci. Technol, 12(3):193-210.
  • [38] Ishwarya, S. (2016). Nonlinear static and dynamic analyses of jacket-type offshore platform, Anna University, Chennai.
  • [39] Karadeniz, H. (1996). Spectral Analysis Program for Offshore Structures (SAPOS), Response calculation and fatigue damage estimates, Proc. of the 2nd Int. Conference in Civil Engineering on Computer Applications, Research and Practice, ICCE-96, 1:339-349.
  • [40] Yaylacı, M. (2007). Applications of offshore Structure and Explicated of Design Parameters, Karadeniz Technical University, Trabzon, Turkey.
  • [41] Mc Namara, J.F. Gilroy, J.P. Sorensen, E.P. and Hibbitt, H.D. (1985). ABAQUS/AQUA application to offshore risers and pipelines, Maritime Simulation, Proceedings of the First Intercontinental Symposium, Springer.
  • [42] Kuntiyawichai, K. and Chucheepsakul, S. (2004). Analysis of offshore structures subjected to various types of sea wave, Proceedings of OMAE04, 23rd International Conference on Offshore Mechanics and Arctic Engineering, Vancouver, Canada.
  • [43] Huizer, C.O. (2017). Modelling loads of steady current and waves with Abaqus, Aqua. URL: Url-2<https://info.simuleon.com/blog/modelling-loads-of-steady-current-and-waves-with-abaqus-aqua
  • [44] Das, B. and Janardhan, P. (2017). Model Development and Load Analysis of Offshore Jacket Structure using SAP2000, International Journal for Research in Applied Science and Engineering Technology (IJRASET), 5:1482-1493. doi:10.22214/ijraset.2017.4263
  • [45] Dağlı, B. Y. Yiğit, M.E. and Gökkuş, U. (2017). Behaviour of large cylindrical offshore structures subjected to wave loads, TEM Journal, 6(3):550-557. DOI:10.18421/TEM63-16
  • [46] Lamb H. (1993) Hydrodynamics. Cambridge University Press, Cambridge.
  • [47] Maccamy, R.C. and Fuchs, R.A. (1954). Wave Forces on Piles: A Diffraction Theory, Army Corps of Engineers, Beach Erosion Board. U.S. Beach Erosion Board, ech. Memo No. 69.
  • [48] Sarpkaya, T. and Isaacson, M. (1981). Diffraction theory is reviewed in Mechanics of Wave Forces on Offshore Structures, Van Nostrand Reinhold Co.
  • [49] Det Norske Veritas - DNV (1977). Result for the Design, Construction and Inspection of Offshore Structures, Oslo, (Reprint with correction 1981). http://www.dnv.com
  • [50] Sawaragi, T. (1995). Coastal engineering- waves, beaches, wave-structure interaction. Elsevier, Amsterdam.
  • [51] Butterfield, S. Musial, W. Jonkman, J. Sclavounos, P. and Wayman, L. (2007). Engineering Challenges for Floating Offshore Wind Turbines, Golden, Colorado: National Renewable Energy Laboratory
There are 51 citations in total.

Details

Primary Language English
Subjects Numerical Modelization in Civil Engineering
Journal Section Research Articles
Authors

Ali Ete 0000-0002-4874-1567

Early Pub Date June 13, 2025
Publication Date June 17, 2025
Submission Date January 6, 2025
Acceptance Date April 16, 2025
Published in Issue Year 2025 Volume: 9 Issue: 1

Cite

APA Ete, A. (2025). Wave Actions and Responses for Large-Diameter Monopod Platform Structures. Journal of Innovative Science and Engineering, 9(1), 134-153. https://doi.org/10.38088/jise.1614320
AMA Ete A. Wave Actions and Responses for Large-Diameter Monopod Platform Structures. JISE. June 2025;9(1):134-153. doi:10.38088/jise.1614320
Chicago Ete, Ali. “Wave Actions and Responses for Large-Diameter Monopod Platform Structures”. Journal of Innovative Science and Engineering 9, no. 1 (June 2025): 134-53. https://doi.org/10.38088/jise.1614320.
EndNote Ete A (June 1, 2025) Wave Actions and Responses for Large-Diameter Monopod Platform Structures. Journal of Innovative Science and Engineering 9 1 134–153.
IEEE A. Ete, “Wave Actions and Responses for Large-Diameter Monopod Platform Structures”, JISE, vol. 9, no. 1, pp. 134–153, 2025, doi: 10.38088/jise.1614320.
ISNAD Ete, Ali. “Wave Actions and Responses for Large-Diameter Monopod Platform Structures”. Journal of Innovative Science and Engineering 9/1 (June2025), 134-153. https://doi.org/10.38088/jise.1614320.
JAMA Ete A. Wave Actions and Responses for Large-Diameter Monopod Platform Structures. JISE. 2025;9:134–153.
MLA Ete, Ali. “Wave Actions and Responses for Large-Diameter Monopod Platform Structures”. Journal of Innovative Science and Engineering, vol. 9, no. 1, 2025, pp. 134-53, doi:10.38088/jise.1614320.
Vancouver Ete A. Wave Actions and Responses for Large-Diameter Monopod Platform Structures. JISE. 2025;9(1):134-53.
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