Impact onto an Ice Floe

  • Khabakhpasheva, Tatyana (School of Mathematics, University of East Anglia) ;
  • Chen, Yang (Department of Naval Architecture and Marine Engineering, University of Michigan) ;
  • Korobkin, Alexander (School of Mathematics, University of East Anglia) ;
  • Maki, Kevin (Department of Naval Architecture and Marine Engineering, University of Michigan)
  • 투고 : 2018.09.30
  • 심사 : 2018.11.18
  • 발행 : 2018.12.31


The unsteady problem of a rigid body impact onto a floating plate is studied. Both the plate and the water are at rest before impact. The plate motion is caused by the impact force transmitted to the plate through an elastic layer with viscous damping on the top of the plate. The hydrodynamic force is calculated by using the second-order model of plate impact by Iafrati and Korobkin (2011). The present study is concerned with the deceleration experienced by a rigid body during its collision with a floating object. The problem is studied also by a fully-nonlinear computational-fluid-dynamics method. The elastic layer is treated with a moving body-fitted grid, the impacting body with an immersed boundary method, and a discrete-element method is used for the contact-force model. The presence of the elastic layer between the impacting bod- ies may lead to multiple bouncing of them, if the bodies are relatively light, before their interaction is settled and they continue to penetrate together into the water. The present study is motivated by ship slamming in icy waters, and by the effect of ice conditions on conventional free-fall lifeboats.


E1GPC1_2018_v4n4_146_f0001.png 이미지

Fig. 1. Two-dimensional slamming for open water (a), with ice floe (b), which is attaced to the body surface later on (c), with an ice floe near the impact region (d), several floes under and near the body surface (e) and floes on the body surface (f).

E1GPC1_2018_v4n4_146_f0002.png 이미지

Fig. 2. Impact on a floating elastic plate of large length.

E1GPC1_2018_v4n4_146_f0003.png 이미지

Fig. 3. Impact of two spheres studied by Joukowski (1884).

E1GPC1_2018_v4n4_146_f0004.png 이미지

Fig. 4. Impact on a floating plate with an elastic layer on the top of it before the interaction (a) and during the interaction (b).

E1GPC1_2018_v4n4_146_f0005.png 이미지

Fig. 5. Comparison of the theoretical and numerical results for the plate indentation h, dis- placements hp and hb, speeds $h_{p}^{'}$ and $h_{b}^{'}$ and the accelerations $h_{p}^{''}$ and $h_{b}^{''}$ of the plate and the body, respectively, as functions of time t.

E1GPC1_2018_v4n4_146_f0006.png 이미지

Fig. 6: Impact of a large body onto a floating plate with pile-up effect.

E1GPC1_2018_v4n4_146_f0007.png 이미지

Fig. 7. Non-dimensional penetration depth of the body (a) and the non-dimensional hydrody- namic force (b) as functions of the scaled length, c/l, of the wetted part of the body surface.


연구 과제번호 : Vertical Penetration of an Object Through Broken Ice and Floating Ice Plate, Numerical Analysis of Slamming Models for the Design of Advanced Naval Vessels

연구 과제 주관 기관 : NICOP


  1. Ermanyuk, E. V. and Ohkusu, M., "Impact of a disk on shallow water," Journal of Fluids and Structures, Vol. 20(3), pp.345-357, 2005.
  2. Fryba, L.," History of Winkler foundation," In Proceedings of the 3rd Herbertov Workshop Inter- action of Railway Vehicles with the Track and its Substructure, Knothe, K., Grassie, S.L., Elkins, J.A. (eds.), Herbertov, Czech Republic, September 1994. Vehicle System Dynamics Supplement, vol. 24, pp. 7-12, 1995.
  3. Hertz, H., "Ueber die Beruhrung fester elastischer Korper," J Reine Angew Math., Vol. 92, pp.156-171, 1882.
  4. Iafrati, A. and Korobkin, A.A., "Hydrodynamic loads during early stage of flat plate impact onto water surface," Physics of Fluids, Vol. 20(8), p.082104, 2008.
  5. Iafrati, A. and Korobkin, A.A., "Asymptotic estimates of hydrodynamic loads in the early stage of water entry of a circular disk," Journal of Engineering Mathematics, Vol. 69(2-3), pp.199-224, 2011.
  6. Johnson, K. L., Contact mechanics, Cambridge University Press, London, 1987.
  7. Jordaan, I.J., and Timco, G.W, "Dynamics of the ice-crushing process," Journal of Glaciology, Vol. 34(118), pp.318-326, 1988.
  8. Joukowski, N. E., "On impact of two spheres, one of which floats in liquid," Zap. Mat. Otd. Novorossiiskogo Obshchestva Estestvoispytatelej, Vol. 5, pp.43-48, 1884.
  9. Khabakhpasheva, T. I. and A. A. Korobkin, A.A., "Oblique impact of a smooth body on a thin layer of inviscid liquid," Proc. R. Soc. A, Vol. 469, no. 2151, 20120615, pp.1-14, 2013.
  10. Khabakhpasheva, T.I., Chen Y., Korobkin A.A., and Maki K., "Water impact near the edge of a floating ice sheet," In Proc. 33rd International Workshop Water Waves Floating Bodies, Guidel-Plages, France, 4-7 April, 4pp, 2018.
  11. Korobkin, A., "Unsteady hydroelasticity of floating plates," Journal of Fluids and Structures, Vol. 14, no. 7, pp.971-991, 2000.
  12. Korobkin, A., "Water impact problems in ship hydrodynamics," In: Ohkusu M (ed) Advances in marine hydrodynamics, chap 7. Computational Mechanics Publications, Southampton, Boston, pp.323-371, 1996.
  13. Korobkin, A., Khabakhpasheva, T., Malenica, S., Kim, Y., "A comparison study of water impact and water exit models," International Journal of Naval Architecture and Ocean Engineering, Vol. 6(4), pp.1182-1196, 2014.
  14. Korobkin, A. A. and Ohkusu, M., "Impact of two circular plates one of which is floating on a thin layer of liquid," Journal of Engineering Mathematics, Vol. 50(4), pp.343-358, 2004.
  15. Kurdyumov, V. A., and Kheisin, D.E., "Hydrodynamic Model of the Impact of a Solid on Ice," Soviet Applied Mechanics, Vol. 12(10), pp.1063-1068, 1976.
  16. Lloyd's report "Arctic opening: Opportunity and Risk in the High North", 2012.
  17. Lubbad, R. and Loset, S., "A numerical model for real-time simulation of ship-ice interaction," Cold Regions Science and Technology, Vol. 65(2), pp.111-127, 2011.
  18. Mahrenholtz, O.H., "Beam on viscoelastic foundation: an extension of Winkler's model," Archive of Applied Mechanics, Vol. 80(1), pp.93-102, 2010.
  19. Piro, D.J., A Hydroelastic Method for the Analysis of Global Ship Response Due to Slamming Events, Doctoral dissertation, University of Michigan, 2013.
  20. Re, S. and Veitch, B., "Performance limits of evacuation systems in ice," In: Proceeding of 17th International Conference on Port and Ocean Engineering under Arctic Conditions, Trondheim, Norway, pp.807-817, 2003.
  21. Timoshenko, S. and Young, D.H., Vibration Problems in Engineering, D. van Nostrand Company, 1955.
  22. Wagner, H., "Uber Stoss- und Gleitvorgange an der Oberache von Flussigkeiten," ZAMM, Journal of Applied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 12(4), pp.193-215, 1932.
  23. Winkler, E., Die Lehre von der Elasticitaet und Festigkeit: mit besonderer R ucksicht auf ihre Anwendung in der Technik fur polytechnische Schulen, Bauakademien, Ingenieue, Maschinenbauer, Architecten, etc. Dominicus, 1867.
  24. Ye, H., Chen, Y., and Maki, K.J., \A Direct-Forcing Immersed Boundary Method for Moving Bodies on Unstructured Grids", 2018. (in preparation).