MPS-FEM Coupled Method for Study of Wave-Structure Interaction

Abstract

Nowadays, an increasing number of ships and marine structures are manufactured and inevitably operated in rough sea. As a result, some phenomena related to the violent fluid-elastic structure interactions (e.g., hydrodynamic slamming on marine vessels, tsunami impact on onshore structures, and sloshing in liquid containers) have aroused huge challenges to ocean engineering fields. In this paper, the moving particle semi-implicit (MPS) method and finite element method (FEM) coupled method is proposed for use in numerical investigations of the interaction between a regular wave and a horizontal suspended structure. The fluid domain calculated by the MPS method is dispersed into fluid particles, and the structure domain solved by the FEM method is dispersed into beam elements. The generation of the 2D regular wave is firstly conducted, and convergence verification is performed to determine appropriate particle spacing for the simulation. Next, the regular wave interacting with a rigid structure is initially performed and verified through the comparison with the laboratory experiments. By verification, the MPS-FEM coupled method can be applied to fluid-structure interaction (FSI) problems with waves. On this basis, taking the flexibility of structure into consideration, the elastic dynamic response of the structure subjected to the wave slamming is investigated, including the evolutions of the free surface, the variation of the wave impact pressures, the velocity distribution, and the structural deformation response. By comparison with the rigid case, the effects of the structural flexibility on wave-elastic structure interaction can be obtained.

Keywords

MPS-FEM coupled method / Fluid-structure interaction (FSI) / Regular wave / Wave impact pressure / Structure deformation response

References

[1] Antoci C, Gallati M, Sibilla S. Numerical simulation of fluid–structure interaction by SPH. Comput Struct, 2007, 85(11): 879-890

[2] Attaway SW, Heinstein MW, Swegle JW. Coupling of smooth particle hydrodynamics with the finite element method. Nucl Eng Des, 1994, 150(2–3): 199-205

[3] Canelas RB, Crespo AJC, Domínguez JM, Rui MLF, Gómez-Gesteira M. SPH–DCDEM model for arbitrary geometries in free surface solid–fluid flows. Comput Phys Commun, 2016, 202: 131-140

[4] Cuomo G, Tirindelli M, Allsop W. Wave-in-deck loads on exposed jetties. Coast Eng, 2007, 54(9): 657-679

[5] Fourey G, Hermange C, Le Touzé D, Oger G. An efficient FSI coupling strategy between smoothed particle hydrodynamics and finite element methods. Comput Phys Commun, 2017, 217: 66-81

[6] Gao R, Ren B, Wang GY, Wang YX. Numerical modelling of regular wave slamming on subface of open-piled structures with the corrected SPH method. Appl Ocean Res, 2012, 34: 173-186

[7] Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics-theory and application to non-spherical stars. Mon Not R Astron Soc, 1977, 181: 375-389

[8] Hashimoto H, Le Touzé D (2014) Coupled MPS-FEM model for violent flows-structures interaction. Proceedings of the 29th International Workshop on Water Waves and Floating Bodies, Osaka, Japan, pp 1–4

[9] He GH, Kashiwagi M. Nonlinear analysis on wave-plate interaction due to disturbed vertical elastic plate. J Hydrodynam Ser B, 2010, 22(5): 507-512

[10] Hsiao KM, Lin JY, Lin WY. A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams. Comput Methods Appl Mech Eng, 1999, 169(1–2): 1-18

[11] Hwang SC, Park JC, Gotoh H, Khayyer A, Kang KJ. Numerical simulations of sloshing flows with elastic baffles by using a particle-based fluid–structure interaction analysis method. Ocean Eng, 2016, 118: 227-241

[12] Idelsohn SR, Marti J, Limache A, Oñate E. Unified Lagrangian formulation for elastic solids and incompressible fluids: application to fluid–structure interaction problems via the PFEM. Comput Methods Appl Mech Eng, 2008, 197(19): 1762-1776

[13] Johnson GR. Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computations. Nucl Eng Des, 1994, 150(2–3): 265-274

[14] Khayyer A, Gotoh H, Falahaty H, Shimizu Y. An enhanced ISPH-SPH coupled method for simulation of incompressible fluid-elastic structure interactions. Comput Phys Commun, 2018, 232: 139-164

[15] Khayyer A, Gotoh H, Falahaty H, Shimizu Y. Towards development of enhanced fully-Lagrangian mesh-free computational methods for fluid-structure interaction. J Hydrodyn, 2018, 30(1): 49-61

[16] Koshizuka S, Oka Y. Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl Sci Eng, 1996, 123: 421-434

[17] Lee BH, Park JC, Kim MH, Hwang SC. Step-by-step improvement of MPS method in simulating violent free-surface motions and impact-loads. Comput Methods Appl Mech Eng, 2011, 200(9): 1113-1125

[18] Liao K, Hu C. A coupled FDM-FEM method for free surface flow interaction with thin elastic plate. J Mar Sci Technol, 2013, 18(1): 1-11

[19] Lo HY, Liu PL. Solitary waves incident on a submerged horizontal plate. J Waterw Port Coast Ocean Eng, 2014, 140(3): 04014009

[20] Lucy LB. A numerical approach to the testing of the fission hypothesis. Astron J, 1977, 82(12): 1013-1024

[21] Mitsume N, Yoshimura S, Murotani K, Yamada T. Improved MPS-FE fluid-structure interaction coupled method with MPS polygon wall boundary model. Comput Model Eng Sci, 2014, 101(4): 229-247

[22] Nelli F, Bennetts LG, Skene DM, Monty JP, Lee JH, Meylan MH, Toffoli A. Reflection and transmission of regular water waves by a thin, floating plate. Wave Motion, 2017, 70: 209-221

[23] Newmark NM. A method of computation for structural dynamics. J Eng Mech Div, 1959, 85(3): 67-94

[24] Rao CP, Zhang YL, Wan DC (2017a) FSI analysis of solitary wave interacting with horizontal flexible plate by MPSFEM method. Proceedings of the Twenty-seven. International Ocean and Polar Engineering Conference, San Francisco, 263–272

[25] Rao CP, Zhang YL, Wan DC. Numerical simulation of the solitary wave interacting with an elastic structure using MPS-FEM coupled method. J Mar Sci Appl, 2017, 16(4): 395-404

[26] Schumacher T, Higgins C, Bradner C, Cox D, Yim S (2008) Largescale wave flume experiments on highway bridge superstructures exposed to hurricane wave forces. The Sixth National Seismic Conference on Bridges and Highways, Charleston, pp 2A3–2A5

[27] Seiffert B, Hayatdavoodi M, Ertekin RC. Experiments and computations of solitary-wave forces on a coastal-bridge deck. Part I: Flat plate. Coast Eng, 2014, 88: 194-209

[28] Sun Z, Djidjeli K, Xing JT, Cheng F. Coupled MPS-modal superposition method for 2D nonlinear fluid-structure interaction problems with free surface. J Fluids Struct, 2016, 61: 295-323

[29] Tanaka M, Masunaga T. Stabilization and smoothing of pressure in MPS method by quasi-compressibility. J Comput Phys, 2010, 229(11): 4279-4290

[30] Tang ZY, Wan DC. Numerical simulation of impinging jet flows by modified MPS method. Eng Comput, 2015, 32(4): 1153-1171

[31] Tang ZY, Zhang YL, Wan DC. Numerical simulation of 3-D free surface flows by overlapping MPS. J Hydrodyn, 2016, 28(2): 306-312

[32] Wang YX, Ren B (2002) Experimental study of irregular wave slamming. Proceedings of The Twelfth International Offshore and Polar Engineering Conference, Kitakyushu, 492–495

[33] Zhang YX, Wan DC (2012) Apply MPS method to simulate liquid sloshing in LNG tank. Proceedings of 22nd International Offshore and Polar Engineering Conference, Rhodes, 381–391

[34] Zhang YL, Wan DC. Numerical study of interactions between waves and free rolling body by IMPS method. Comput Fluids, 2017, 155: 124-133

[35] Zhang YL, Wan DC. MPS-FEM coupled method for sloshing flows in an elastic tank. Ocean Eng, 2018, 152: 416-427

[36] Zhang YX, Wan DC, Hino T. Comparative study of MPS method and level-set method for sloshing flows. J Hydrodyn, 2014, 26(4): 577-585

[37] Zhang YL, Chen X, Wan DC. An MPS-FEM coupled method for the comparative study of liquid sloshing flows interacting with rigid and elastic baffles. Appl Math Mech, 2016, 37(12): 1359-1377

[38] Zhang YL, Tang ZY, Wan DC. MPS-FEM coupled method for interaction between sloshing flow and elastic structure in rolling tanks, 2016, Berkeley: Proceedings of the 7th International Conference on Computational Methods, , No. 1493-6106-1-PB