Topology Optimization of a Transition Piece for an Offshore Wind Turbine Foundation by Varying the Structural Design Domain

Abstract

Topology optimization (TO) is widely used in offshore wind foundation design, but the optimized topology depends strongly on the predefined design domain. For transition pieces, defining a suitable design domain remains difficult at the conceptual design stage. This study proposes a TO framework for jacket-foundation transition pieces in which the design domain is systematically varied using four geometric factors: width (w), height (h), tower-connection diameter (d), and the distance between the bottom legs and the outer edge (l). A design of experiments scheme is used to generate candidate domains. Under the ultimate limit state load case, TO is performed for all candidates by minimizing structural compliance subject to a prescribed volume fraction. Then, the resulting structural responses are used to build a surrogate model for multi-objective optimization of the design-domain parameters. Finally, the optimized topology is geometrically reconstructed and incorporated into the full foundation model. Its modal characteristics, stress level, and fatigue performance are evaluated. The results show that systematic variation of the transition piece design domain improves the applicability of TO to offshore wind foundation design and leads to a lighter, mechanically feasible transition piece configuration.

Keywords

Offshore wind turbines / Jacket foundation / Transition pieces / Topology optimization / Structural design domain

References

[1] AlHamaydeh M, Barakat S, Nasif O (2017) Optimization of support structures for offshore wind turbines using genetic algorithm with domain-trimming. Mathematical Problems in Engineering 5978375. https://doi.org/10.1155/2017/5978375

[2] Arany L, Bhattacharya S, Macdonald J, Hogan SJ. Design of monopiles for offshore wind turbines in 10 steps. Soil Dynamics and Earthquake Engineering, 2017, 92: 126-152.

[3] American Clean PowerASCE/AWEA Recommended practice for compliance of large land-based wind turbine support structures 2011, 2011(2011-01-28)[2025-12-24]

[4] Bendsøe MP. Optimal shape design as a material distribution problem. Structural Optimization, 1989, 1: 193-202.

[5] Bendsøe MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 712197224.

[6] Bhattacharya S. Design of foundations for offshore wind turbines, 2019, Hoboken: John Wiley & Sons Ltd

[7] Ciampoli M, Petrini F. Performance-based design of offshore wind turbines. Earth and Space 2010: Engineering, Science, Construction, and Operations in Challenging Environments, 2010, Reston: ASCE, 2063-2078.

[8] Colherinhas GB, de Morais MVG, Petrini F. Global vibration control of offshore wind turbines with a flexible monopile foundation using a pendulum-tuned mass damper: risk mitigation and performance incrementation. Ocean Engineering, 2024, 297: 117168.

[9] Couceiro I, París J, Navarrina F, Guizán R, Colominas I. Optimization of offshore steel jackets: review and proposal of a new formulation for time-dependent constraints. Archives of Computational Methods in Engineering, 2020, 27410491069.

[10] Damiani R, Dykes K, Scott G. A comparison study of offshore wind support structures with monopiles and jackets for U. S. waters. Journal of Physics: Conference Series, 2016, 7539092003

[11] Damiani R, Song H. A jacket sizing tool for offshore wind turbines within the systems engineering initiative. Offshore Technology Conference, 2013Houston: Offshore Technology Conference OTC-24140-MS

[12] Deb K, Jain H. An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I: solving problems with box constraints. IEEE Transactions on Evolutionary Computation, 2014, 184577601.

[13] Díaz H, Guedes Soares C. Review of the current status, technology and future trends of offshore wind farms. Ocean Engineering, 2020, 209: 107381.

[14] DNVDNV-OS-J101 Design of offshore wind turbine structures, 2014, Høvik: Det Norske Veritas AS(2010-10)[2025-12-24]

[15] DNVDNV-RP-C205 Environmental conditions and environmental loads, 2014, Høvik: DNV GL AS[2025-12-24]

[16] DNVDNV-RP-C203 Fatigue design of offshore steel structures, 2025, Høvik: DNV[2025-12-24]

[17] Fischer T, de Vries WE, Schmidt B. Upwind design basis (WP4: offshore foundations and support structures), 2011

[18] Gaidai O, Yakimov V, Wang F, Sun J, Wang K. Bivariate reliability analysis for floating wind turbines. International Journal of Low-Carbon Technologies, 2024, 19: 63-72.

[19] Gentils T, Wang L, Kolios A. Integrated structural optimisation of offshore wind turbine support structures based on finite element analysis and genetic algorithm. Applied Energy, 2017, 199: 187-204.

[20] Ghaemifard S, Ghannadiasl A. Design and analysis of offshore wind turbines: problem formulation and optimization techniques. Journal of Marine Science and Application, 2024, 23: 707-722.

[21] Girão de Morais MV, Mendes MV, Pedroso LJ. Rahimpour MR. Foundation and support structures of wind turbines and optimization. Encyclopedia of renewable energy, sustainability and the environment, 20241st ednOxfordElsevier377392.

[22] Ibhadode O, Zhang Z, Sixt J, Nsiempba KM, Orakwe J, Martinez-Marchese A, Ero O, Shahabad SI, Bonakdar A, Toyserkani E. Topology optimization for metal additive manufacturing: current trends, challenges, and future outlook. Virtual and Physical Prototyping, 2023, 181e2181192.

[23] IECIEC 61400-3 Wind turbines-Part 3: Design requirements for offshore wind turbines, 2009, Geneva: International Electrotechnical Commission(2009-02-01) [2025-12-24]

[24] Iyke BN. Climate change, energy security risk, and clean energy investment. Energy Economics, 2024, 129: 107225.

[25] Jiang Z, Hu W, Dong W, Gao Z, Ren Z. Structural reliability analysis of wind turbines: a review. Energies, 2017, 10122099.

[26] Jonkman J, Butterfield S, Musial W, Scott G. Definition of a 5 MW reference wind turbine for offshore system development, 2009, Golden: National Renewable Energy Laboratory

[27] Lan R, Long K, Saeed A, Geng R, Chen Y, Zhang J, Tao T, Liu J. Fail-safe topology optimization for a four-leg jacket structure of offshore wind turbines. Structures, 2024, 62: 106183.

[28] Lee YS, González JA, Lee JH, Kim YI, Park KC, Han S. Structural topology optimization of the transition piece for an offshore wind turbine with jacket foundation. Renewable Energy, 2016, 85: 1214-1225.

[29] Liu F, Chen Y, Qin W, Li J. Optimal design of liquid cooling structure with bionic leaf vein branch channel for power battery. Applied Thermal Engineering, 2023, 218: 119283.

[30] Liu Z, Wei L, Wang J, Hu B, Song Y, Zhang Z. Research on optimization design of wind turbine steel tower foundation based on machine learning. Structures, 2025, 80: 109840.

[31] Long K, Du X, Xu S, Xie YM. Maximizing the effective Young’s modulus of a composite material by exploiting the Poisson effect. Composite Structures, 2016, 153: 593-600.

[32] Lozano Minguez E. Fatigue and fracture mechanics of offshore wind turbine support structures, 2015, Bedford: Cranfield University

[33] Ma C, Zi G. Comparative study on the structural behavior of a transition piece for offshore wind turbine with jacket support. Steel and Composite Structures, 2022, 433363373

[34] Marjan A, Huang L. Topology optimisation of offshore wind turbine jacket foundation for fatigue life and mass reduction. Ocean Engineering, 2023, 289: 116228.

[35] Mendoza JMF, Ibarra D. Technology-enabled circular business models for the hybridisation of wind farms: Integrated wind and solar energy, power-to-gas and power-to-liquid systems. Sustainable Production and Consumption, 2023, 36: 308-327.

[36] Niu H, Shan Z, Tang L, Wang Z. Effect of the transition piece on the natural frequencies of monopile-supported offshore wind turbines. Soil Dynamics and Earthquake Engineering, 2024, 187: 108982.

[37] Pan C, Tang Q, He Z, Wang L, Chen L. Structure optimization of battery module with a parallel multi-channel liquid cooling plate based on orthogonal test. Journal of Electrochemical Energy Conversion and Storage, 2020, 172021104.

[38] Quan H, Guo Y, Li R, Su Q, Chai Y. Optimization design and experimental study of vortex pump based on orthogonal test. Science Progress, 2020, 10310036850419881883.

[39] Rong Y, Zhao ZL, Feng XQ, Xie YM. Structural topology optimization with an adaptive design domain. Computer Methods in Applied Mechanics and Engineering, 2022, 389: 114382.

[40] Schaffer W, Seo J, Choi E, Lee J. Optimized retrofit design of in-service monopile foundation offshore wind turbine transition zone. Engineering Structures, 2020, 220: 111001.

[41] Shi W, Park H, Chung C, Baek J, Kim Y, Kim C. Load analysis and comparison of different jacket foundations. Renewable Energy, 2013, 54: 201-210.

[42] Shittu AA, Mehmanparast A, Wang L, Salonitis K, Kolios A. Comparative study of structural reliability assessment methods for offshore wind turbine jacket support structures. Applied Sciences, 2020, 103860.

[43] Sui Z, Sui Y, Wu W. Multi-objective optimization of a microchannel membrane-based absorber with inclined grooves based on CFD and machine learning. Energy, 2022, 240: 122809.

[44] Sunday K, Brennan F. A review of offshore wind monopiles structural design achievements and challenges. Ocean Engineering, 2021, 235: 109409.

[45] Svanberg K. The method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987, 242359373.

[46] Tian X, Wang Q, Liu G, Liu Y, Xie Y, Deng W. Topology optimization design for offshore platform jacket structure. Applied Ocean Research, 2019, 84: 38-50.

[47] van Dijk NP, Maute K, Langelaar M, van Keulen F. Level-set methods for structural topology optimization: a review. Structural and Multidisciplinary Optimization, 2013, 483437472.

[48] Wang Z, Mantey SK, Zhang X. A numerical tool for efficient analysis and optimization of offshore wind turbine jacket substructure considering realistic boundary and loading conditions. Marine Structures, 2024, 95: 103605.

[49] Wei K, Arwade SR, Myers AT, Hallowell S, Hajjar JF, Hines EM, Pang W. Toward performance-based evaluation for offshore wind turbine jacket support structures. Renewable Energy, 2016, 97: 709-721.

[50] Wei X, Wang T, Wang Y, Liu Y, Jiang M, Zhang P. Horizontal Bearing Performance of the Four-Bucket Jacket Foundation. Journal of Marine Science and Application, 2025, 243542551.

[51] World Forum Offshore WindWFO global offshore wind report 2024, 2025, Hamburg: World Forum Offshore Wind e.V.

[52] Wu X, Hu Y, Li Y, Yang J, Duan L, Wang T, Adcock T, Jiang Z, Gao Z, Lin Z, Borthwick A, Liao S. Foundations of offshore wind turbines: a review. Renewable and Sustainable Energy Reviews, 2019, 104: 379-393.

[53] Xie YM, Steven GP. A simple evolutionary procedure for structural optimization. Computers & Structures, 1993, 495885896.

[54] Yu Y, Wei M, Yu J, Cui Y, Gao R, Dong Z, Wang X. Reliability-based design method for marine structures combining topology, shape, and size optimization. Ocean Engineering, 2023, 286: 115490.

[55] Zhai J, Yin Q, Ji C. Performance-based design of environmental parameters for offshore wind turbine foundations. Ocean Engineering, 2024, 309: 118520.

[56] Zhang C, Long K, Zhang J, Lu F, Bai X, Jia J. A topology optimization methodology for the offshore wind turbine jacket structure in the concept phase. Ocean Engineering, 2022, 266: 112974.

[57] Zhang P, Ma Y, Le C, Ding H. Experimental Study on Tilt Adjustment Technique of Tripod Bucket Jacket Foundation for Offshore Wind Turbine in Sand. Journal of Marine Science and Application, 2022, 214192204.

[58] Zhang XL, Zhang BJ, Wang D, Xu CS. Fatigue damage analysis method of offshore wind turbine foundation. Ocean Engineering, 2024, 302: 117618.

[59] Zhang X, Wu Y, Mantey SK, Gao Y, He B, Wang Z. Optimized design of offshore wind turbine transition pieces through an information modelling approach and a hybrid optimization framework. Ocean Engineering, 2025, 325: 120819.

[60] Zheng C, Jin H, Shi F, Liu J, Jiao H, Xu L, Ma Z (2026) Fatigue reliability analysis of cast steel nodes of offshore wind turbine jacket structure. Journal of Marine Science and Application. https://doi.org/10.1007/s11804-026-00851-4

[61] Zhou M, Rozvany GIN. The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering, 1991, 891–3309336.

[62] Zhou Y, Zhang J, Long K, Saeed A, Chen Y, Geng R, Tao T, Guo X. Concurrent design on three-legged jacket structure and transition piece of offshore wind turbine by exploiting topology optimization. CMES-Computer Modeling in Engineering & Sciences, 2025, 143217431761.

[63] Zhou Y, Zhang J, Long K, Saeed A, Tao T, Chen J. Topology optimization on a jacket structure for offshore wind turbines by altering structural design domain. Applied Ocean Research, 2025, 154: 104421.

[64] Zhu JH, Zhang WH, Xia L. Topology optimization in aircraft and aerospace structures design. Archives of Computational Methods in Engineering, 2016, 234595622.

[65] Zuo W, Saitou K. Multi-material topology optimization using ordered SIMP interpolation. Structural and Multidisciplinary Optimization, 2017, 552477491.

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