Abstract
In the present study, a numerical model is developed to analyse equation of motion of the plate which is elastic in nature and has a shallow draft L/d ≤ 1/20 (small thickness). The platform may be of any shape (geometry) subjected to monochromatic waves. The developed numerical model is capable of investigating the VFLS of any geometry (arbitrary shape) at finite (0.05 ≤ h/λ ≤ 0.5) depth. A hybrid numerical model is developed and used to solve fluid–structure interaction between the elastic thin plate and water wave. A Higher Order Boundary Element Method (HOBEM) has been adopted in order to maintain the same order, basis function and contains the same nodes between BEM and FEM. Two equations have been determined to build the connection between plate displacement and velocity potential. Displacement of the floating platform has been obtained by solving the plate equation of motion. To solve the plate equation of motion, FEM has been adopted. The equation which relates the plate displacement and water is solved by Boundary Integral Equation (BIE). A modified Green’s function which differs from the bygone Green’s function has been developed by using the Bessel, Hankel and Struve functions of order zero. Both the equations are solved simultaneously to get the displacement of floating elastic plate and velocity potential. The results obtained are validated with Wang (J. Fluids Struct. 19:557–572, 2004 [22]).
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References
Watanabe E, Utsunomiya T, Wang CM (2004) Hydroelastic analysis of pontoon-type VLFS: a literature survey. Eng Struct 26(2):245–256. https://doi.org/10.1016/j.engstruct.2003.10.001
Kashiwagi M (1998) A B-spline Galerkin scheme for calculating the hydroelastic response of a very large floating structure in waves. J Mar Sci Technol 3(1):37–49. https://doi.org/10.1007/BF01239805
Wu C, Watanabe E, Utsunomiya T (1995) An eigenfunction expansion-matching method for analyzing the wave-induced responses of an elastic floating plate. Appl Ocean Res 17(5):301–310. https://doi.org/10.1016/0141-1187(95)00023-2
Kim JG, Cho SP, Kim KT, Lee PS (2014) Hydroelastic design contour for the preliminary design of very large floating structures. Ocean Eng 78:112–123. https://doi.org/10.1016/j.oceaneng.2013.11.006
Kim KT, Lee PS, Park KC (2013) A direct coupling method for 3D hydroelastic analysis of floating structures. Int J Numer Meth Eng 96(13):842–866. https://doi.org/10.1002/nme.4564
Taylor RE (2007) Hydroelastic analysis of plates and some approximations. J Eng Math 58(1):267–278. https://doi.org/10.1007/s10665-006-9121-7
Shirkol AI, Nasar T, Karmakar D (2016) Wave interaction with Very Large Floating Structure (VLFS) using BEM approach–revisited. Perspect Sci 8:533–535. https://doi.org/10.1016/j.pisc.2016.06.012
Lee CH, Newman JN (2000) An assessment of hydroelasticity for very large hinged vessels. J Fluids Struct 14(7):957–970. https://doi.org/10.1006/jfls.2000.0305
Newman JN (2005) Efficient hydrodynamic analysis of very large floating structures. Mar Struct 18(2):169–180. https://doi.org/10.1016/j.marstruc.2005.07.003
Khabakhpasheva TI, Korobkin AA (2002) Hydroelastic behaviour of compound floating plate in waves. J Eng Math 44(1):21–40. https://doi.org/10.1023/A:1020592414338
Wang CM, Tay ZY, Takagi K, Utsunomiya T (2010) Literature review of methods for mitigating hydroelastic response of VLFS under wave action. Appl Mech Rev 63(3):030802. https://doi.org/10.1115/1.4001690
Riyansyah M, Wang CM, Choo YS (2010) Connection design for two-floating beam system for minimum hydroelastic response. Mar Struct 23(1):67–87. https://doi.org/10.1016/j.marstruc.2010.01.001
Fu S, Moan T, Chen X, Cui W (2007) Hydroelastic analysis of flexible floating interconnected structures. Ocean Eng 34(11):1516–1531. https://doi.org/10.1016/j.oceaneng.2007.01.003
Gao RP, Tay ZY, Wang CM, Koh CG (2011) Hydroelastic response of very large floating structure with a flexible line connection. Ocean Eng 38(17):1957–1966. https://doi.org/10.1016/j.oceaneng.2011.09.021
Kim BW, Kyoung JH, Hong SY, Cho SK (2005) Investigation of the effect of stiffness distribution and structure shape on hydroelastic responses of very large floating structures. In: The fifteenth international offshore and polar engineering conference, International Society of Offshore and Polar Engineers
Kim BW, Hong SY, Kyoung JH, Cho SK (2007) Evaluation of bending moments and shear forces at unit connections of very large floating structures using hydroelastic and rigid body analyses. Ocean Eng 34(11):1668–1679. https://doi.org/10.1016/j.oceaneng.2006.10.018
Kashiwagi M. (2000) Research on hydroelastic responses of VLFS: recent progress and future work. Int J Offshore Polar Eng 10(02). doi: ISOPE-00-10-2-081
Squire VA, Dugan JP, Wadhams P, Rottier PJ, Liu AK (1995) Of ocean waves and sea ice. Annu Rev Fluid Mech 27(1):115–168. https://doi.org/10.1146/annurev.fl.27.010195.000555
Loukogeorgaki E, Michailides C, Angelides DC (2012) Hydroelastic analysis of a flexible mat-shaped floating breakwater under oblique wave action. J Fluids Struct 31:103–124. https://doi.org/10.1016/j.jfluidstructs.2012.02.011
Michailides C, Angelides DC (2012) Modeling of energy extraction and behavior of a Flexible Floating Breakwater. Appl Ocean Res 35:77–94. https://doi.org/10.1016/j.apor.2011.11.004
Bathe KJ (1996) Finite element procedure. Prentice Hall, New York
Wang CD, Meylan MH (2004) A higher-order-coupled boundary element and finite element method for the wave forcing of a floating elastic plate. J Fluids Struct 19(4):557–572. https://doi.org/10.1016/j.jfluidstructs.2004.02.006
Meylan MH, Squire VA (1996) Response of a circular ice floe to ocean waves. J Geophys Res-All Ser 101:8869–8884. https://doi.org/10.1029/95JC03706
Meylan MH (2002) Wave response of an ice floe of arbitrary geometry. J Geophys Res: Oceans 107(C1). https://doi.org/10.1029/2000jc000713
Sun Y, Lu D, Xu J, Zhang X (2017) A study of hydroelastic behavior of hinged VLFS. Int J Naval Archit Ocean Eng. https://doi.org/10.1016/j.ijnaoe.2017.05.002
Meylan M, Squire VA (1994) The response of ice floes to ocean waves. J Geophys Res-All Ser 99:891–900. https://doi.org/10.1029/93JC02695
Hermans AJ (2000) A boundary element method for the interaction of free-surface waves with a very large floating flexible platform. J Fluids Struct 14(7):943–956. https://doi.org/10.1006/jfls.2000.0313
Yago K, Endo H (1996) Model experiment and numerical calculation of the hydroelastic behavior of matlike VLFS. VLFS 96:209–214
Pan Y, Sahoo PK, Lu L (2016) Numerical study of hydrodynamic response of mooring lines for large floating structure in South China Sea. Ships Offshore Struct 11(7):774–781. https://doi.org/10.1080/17445302.2015.1066986
Yoon JS, Cho SP, Jiwinangun RG, Lee PS (2014) Hydroelastic analysis of floating plates with multiple hinge connections in regular waves. Mar Struct 36:65–87. https://doi.org/10.1016/j.marstruc.2014.02.002
Yiew LJ, Bennetts LG, Meylan MH, French BJ, Thomas GA (2016) Hydrodynamic responses of a thin floating disk to regular waves. Ocean Model 97:52–64. https://doi.org/10.1016/j.ocemod.2015.11.008
Skene DM, Bennetts LG, Meylan MH, Toffoli A (2015) Modelling water wave overwash of a thin floating plate. J Fluid Mech 777. https://doi.org/10.1017/jfm.2015.378
John F (1949) On the motion of floating bodies I. Commun Pure Appl Math 2(1):13–57. https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.3160020102
Hamamoto T, Suzuki A, Fujita KI (1997) Hybrid dynamic analysis of large tension leg floating structures using plate elements. In: The seventh international offshore and polar engineering conference, International Society of Offshore and Polar Engineers
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Shirkol, A.I., Nasar, T. (2019). Coupled Boundary Element Method (BEM) and Finite Element Method (FEM) for Hydroelastic Analysis of Floating Plate. In: Murali, K., Sriram, V., Samad, A., Saha, N. (eds) Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018). Lecture Notes in Civil Engineering, vol 22. Springer, Singapore. https://doi.org/10.1007/978-981-13-3119-0_6
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