Nonlinear Hydroelastic Waves in Deep Water: Propagation and Profile Inversion Captured by Strong CFD-FEA Coupling

Abstract

This paper investigates the hydroelastic interaction between nonlinear regular waves and a thin elastic plate floating on deep water. A two-way fluid-structure interaction (FSI) framework, previously developed by the authors by coupling computational fluid dynamics (CFD) and finite element analysis (FEA), is employed to reproduce nonlinear hydroelastic wave responses. To account for the high structural flexibility and to improve computational efficiency, a Laplace matrix scheme is newly incorporated into the framework. The numerical results are validated against experimental data and analytical solutions reported in earlier studies by some of the present authors. The simulations reveal nonlinear wave profiles characterized by a steepened crest and a flattened trough, as well as their inverted counterparts, across different incident-wave frequency regimes. In the inverted-wave regime, a transition in wave profile is observed during propagation: the response shifts from an elevated form on the weatherside to a depressed form near the mid-plate region.

Keywords

Computational fluid dynamics-finite element analysis / Two-way coupling / Hydroelasticity / Very large floating structure / Non-linear waves

References

[1] Aquelet N, Souli M, Olovsson L. Euler-Lagrange coupling with damping effects: Application to slamming problems. Computer Methods in Applied Mechanics and Engineering, 2006, 195: 110-132

[2] Badia S, Quaini A, Quarteroni A. Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect. Computer Methods in Applied Mechanics and Engineering, 2008, 197: 4216-4232

[3] Bathe KJ. Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme. Computers & Structures, 2007, 85: 437-445

[4] Belibassakis KA, Athanassoulis GA. A coupled-mode technique for weakly nonlinear wave interaction with large floating structures lying over variable bathymetry regions. Applied Ocean Research, 2006, 28: 59-76

[5] Brown DL, Cortez R, Minion ML. Accurate projection methods for the incompressible Navier-Stokes equations. Journal of Computational Physics, 2001, 168: 464-499

[6] Causin P, Gerbeau JF, Nobile F. Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Computer Methods in Applied Mechanics and Engineering, 2005, 194: 4506-4527

[7] Choi J, Yoon SB. Numerical simulations using momentum source wave-maker applied to RANS equation model. Coastal Engineering, 2009, 56: 1043-1060

[8] He G, Xie B, Wang W, Liu S, Jing P. Ship loading influence on the slamming impact of typical sections of an S-175 container ship. J. Mar. Sci. Eng., 2020, 8(3): 163

[9] Huang S, Hu Z, Chen C. Application of CFD-FEA coupling to predict hydroelastic responses of a single module VLFS in extreme wave conditions. Ocean Engineering, 2023, 280: 114754

[10] Idelsohn S, Del Pin F, Rossi RSouli M, Benson DJ. Avoiding instabilities caused by added mass effects in fluid-structure interaction problems. Arbitrary Lagrangian - Eulerian and Fluid-Structure Interaction, 2013, Hoboken. John Wiley & Sons, Inc.: 165-220

[11] Iijima K, Fujikubo M. Hydro-elastoplastic behaviour of VLFS under extreme vertical bending moment by segmented beam approach. Marine Structures, 2018, 57: 1-17

[12] Iijima K, Kyaw SS, Maeda T, Akira T. Cnoidal wave on a long elastic floating plate at shallow water depth. Proceedings of the ASME 2024 43rd International Conference on Ocean, Offshore and Arctic Engineering, Singapore, Singapore, 2024, V004T05A003

[13] Iijima K, Ma C. Second order wave propagating along VLFS. Proceedings of the ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering, Glasgow, UK, 2019, V009T13A001

[14] Iijima K, Ma C, Pambela AR, Maeda T. DIC measurement of deflection waves travelling along a thin flexural plate floating at water surface. Ocean Engineering, 2022, 266: 113079

[15] ITTC. Recommended procedures and guidelines: Practical guidelines for ship CFD applications. International Towing Tank Conference, Rio de Janeiro, 2011, 1-18

[16] Jiang C, Li Q, Hu P, Zhang G, Jiang S, El Moctar O. Experimental analysis of wave-structure interaction for very large modular floating structures. Ocean Engineering, 2025, 315: 119763

[17] Kashiwagi M. A B-spline Galerkin scheme for calculating the hydroelastic response of a very large floating structure in waves. J. Mar. Sci. Technol., 1998, 3: 37-49

[18] Liang S, Gou Y, Teng B. A three-dimensional nonlinear hydroelastic model for rectangular floating elastic plates and the examination on the peak frequency with maximum nonlinear response. Journal of Fluids and Structures, 2024, 131: 104217

[19] Loukogeorgaki E, Lentsiou EN, Aksel M, Yagci O. Experimental investigation of the hydroelastic and the structural response of a moored pontoon-type modular floating breakwater with flexible connectors. Coastal Engineering, 2017, 121: 240-254

[20] Loukogeorgaki E, Yagci O, Sedat Kabdasli M. 3D experimental investigation of the structural response and the effectiveness of a moored floating breakwater with flexibly connected modules. Coastal Engineering, 2014, 91: 164-180

[21] Ma C, Iijima K, Oka M. Nonlinear waves in a floating thin elastic plate, predicted by a coupled SPH and FEM simulation and by an analytical solution. Ocean Engineering, 2020, 204: 107243

[22] Mehl M, Uekermann B, Bijl H, Blom D, Gatzhammer B, Van Zuijlen A. Parallel coupling numerics for partitioned fluid-structure interaction simulations. Computers & Mathematics with Applications, 2016, 71: 869-891

[23] Mohapatra SC, Guedes Soares C. Hydroelastic behaviour of a submerged horizontal flexible porous structure in three-dimensions. J. Fluids Struct., 2021, 104: 103319

[24] Mohapatra SC, Guedes Soares C. 3D hydroelastic modelling of fluid-structure interactions of porous flexible structures. J. Fluids Struct., 2022, 112: 103588

[25] Newmark NM. A method of computation for structural dynamics. J. Engrg. Mech. Div., 1959, 85: 67-94

[26] Ohmatsu S. Numerical calculation of hydroelastic responses of pontoon type VLFS. Journal of the Society of Naval Architects of Japan, 1997, 1997(182): 329-340

[27] Pambela AR, Ma C, Maeda T, Iijima K. Stokes wave traveling along a thin elastic plate floating at water surface. Journal of Fluids and Structures, 2023, 120: 103919

[28] Riggs HR, Suzuki H, Ertekin RC, Kim JW, Iijima K. Comparison of hydroelastic computer codes based on the ISSC VLFS benchmark. Ocean Engineering, 2008, 35: 589-597

[29] Suzuki H, Yoshida K, Iijima K. A consideration of the structural design of a large-scale floating structure. J. Mar. Sci. Technol., 1996, 1: 255-267

[30] Vanden-Broeck JM, Părău EI. Two-dimensional generalized solitary waves and periodic waves under an ice sheet. Phil. Trans. R. Soc. A, 2011, 369: 2957-2972

[31] Walker HF, Ni P. Anderson acceleration for fixed-point iterations. SIAM J. Numer. Anal., 2011, 49: 1715-1735

[32] Wei Y, Yu S, Jin P, Huang L, Elsherbiny K, Tezdogan T. Coupled analysis between catenary mooring and VLFS with structural hydroelasticity in waves. Marine Structures, 2024, 93: 103516

[33] Xia X, Shen HT. Nonlinear interaction of ice cover with shallow water waves in channels. J. Fluid Mech., 2002, 467: 259-268

[34] Xie B, He G, Zhao C, Jing P, Kumar Pal S, Iijima K, Jin R, Chen B, Ghassemi H. Experimental and numerical investigation on the hydroelastic response of barge and KVLCC2 ship. Ocean Engineering, 2024, 307: 118081

[35] Xie B, Pal SK, Iijima K, Tatsumi A, Badalotti T. Investigation of higher-order springing of a ship in regular waves by experimental analysis and two-way CFD-FEA coupled method. Marine Structures, 2025, 99: 103712

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