Local water slamming of curved rigid hulls


  • J Xiao
  • R Batra




We use the boundary element method (BEM) to study transient plane strain deformations of water induced by a rigid hull impacting at normal incidence initially stationary water occupying a half space with the goal of finding the hydrodynamic pressure acting on the hull. Water is assumed to be incompressible and inviscid, and its deformations to have zero vorticity. Thus deformations of water are governed by the Laplace equation. Challenging issues addressed are finding the free surface of water whose evolution is governed by a nonlinear partial differential equation, determining the a priori unknown wetted length, and ensuring that water maintains contact with the hull without penetrating into it. The solution of the problem using the commercial software, LSDYNA, resulted in water penetrating into a rigid hull. The developed BEM code has been verified by using the method of manufactured solutions. Computed results for the hydrostatic pressure on straight hulls and ship bow section are found to compare well with the corresponding experimental findings. It is found that the peak pressure acting near the terminus of the wetted length decreases with an increase in the radius of the circular hull.


Faltinsen, O. M., Sea loads on ships and offshore structures. Vol. 1. 1993: Cambridge Univ Pr.

Von Karman, T., The impact on seaplane floats during landing. NASA, 1929(TN-321).

Wagner, H., Über Stoβ - und Gleitvorgänge an der Oberfläche von Flüssigkeiten. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 1932. 12(4): p. 193-215. https://doi.org/10.1002/zamm.19320120402

Dobrovol'Skaya, Z., On some problems of similarity flow of fluid with a free surface. Journal of Fluid Mechanics, 1969. 36(04): p. 805-829. https://doi.org/10.1017/s0022112069001996

Zhao, R. and O. Faltinsen, Water entry of two-dimensional bodies. Journal of Fluid Mechanics, 1993. 246(1): p. 593-612. https://doi.org/10.1017/s002211209300028x

Zhao, R., O. Faltinsen, and J. Aarsnes. Water entry of arbitrary two-dimensional sections with and without flow separation. in Twenty-first Symposium on NAVAL HYDRODYNAMICS. 1996.

Mei, X., Y. Liu, and D. K. P. Yue, On the water impact of general two-dimensional sections. Applied Ocean Research, 1999. 21(1): p. 1-15. https://doi.org/10.1016/s0141-1187(98)00034-0

Yettou, E. M., A. Desrochers, and Y. Champoux, A new analytical model for pressure estimation of symmetrical water impact of a rigid wedge at variable velocities. Journal of fluids and structures, 2007. 23(3): p. 501-522. https://doi.org/10.1016/j.jfluidstructs.2006.10.001

Donguy, B., B. Peseux, L. Gornet, and E. Fontaine. Three-dimensional hydroelastic water entry: preliminary results. in International Offshore and Polar Engineering Conference. 2001. Stavanger, Norway.

Stenius, I., A. Rosén, and J. Kuttenkeuler, Explicit FE-modelling of fluid-structure interaction in hull-water impacts. International Shipbuilding Progress, 2006. 53(2): p. 103-121.

Oger, G., M. Doring, B. Alessandrini, and P. Ferrant, Two-dimensional SPH simulations of wedge water entries. Journal of Computational Physics, 2006. 213(2): p. 803-822. https://doi.org/10.1016/j.jcp.2005.09.004

Lin, M. and T. Ho, Water-entry for a wedge in arbitrary water depth. Engineering analysis with boundary elements, 1994. 14(2): p. 179-185. https://doi.org/10.1016/0955-7997(94)90094-9

Battistin, D. and A. Iafrati, Hydrodynamic loads during water entry of two-dimensional and axisymmetric bodies. Journal of fluids and structures, 2003. 17(5): p. 643-664. https://doi.org/10.1016/s0889-9746(03)00010-0

Sun, H., A Boundary Element Method applied to strongly nonlinear wave-body interaction problems, 2007, Trondheim: Norwegian University of Science and Technology.

Sun, H. and O. M. Faltinsen, Water impact of horizontal circular cylinders and cylindrical shells. Applied Ocean Research, 2006. 28(5): p. 299-311. https://doi.org/10.1016/j.apor.2007.02.002

Sun, H. and O. M. Faltinsen, Water entry of a bow-flare ship section with roll angle. Journal of Marine Science and Technology, 2009. 14(1): p. 69-79. https://doi.org/10.1007/s00773-008-0026-1

Qin, Z. and R. Batra, Local slamming impact of sandwich composite hulls. International Journal of Solids and Structures, 2009. 46(10): p. 2011-2035. https://doi.org/10.1016/j.ijsolstr.2008.04.019

Das, K. and R. C. Batra, Local water slamming impact on sandwich composite hulls. Journal of fluids and structures, 2011. 27(4): p. 523-551. https://doi.org/10.1016/j.jfluidstructs.2012.11.001

Stenius, I., A. Rosén, and J. Kuttenkeuler, Hydroelastic interaction in panel-water impacts of high-speed craft. Ocean Engineering, 2010. 38(2-3): p. 371-381. https://doi.org/10.1016/j.oceaneng.2010.11.010

Lu, C., Y. He, and G. Wu, Coupled analysis of nonlinear interaction between fluid and structure during impact. Journal of fluids and structures, 2000. 14(1): p. 127-146. https://doi.org/10.1006/jfls.1999.0257

Panciroli, R., S. Abrate, G. Minak, and A. Zucchelli, Hydroelasticity in water-entry problems: Comparison between experimental and SPH results. Composite Structures, 2011. https://doi.org/10.1016/j.compstruct.2011.08.016

Charca, S., B. Shafiq, and F. Just, Repeated slamming of sandwich composite panels on water. Journal of Sandwich Structures and Materials, 2009. 11: p. 409-424. https://doi.org/10.1177/1099636209103169

Charca, S. and B. Shafiq, Damage assessment due to single slamming of foam core sandwich composites. Journal of Sandwich Structures and Materials, 2010. 12: p. 97-112. https://doi.org/10.1177/1099636209105402

Hu, Z. H., X. D. He, J. Shi, R. G. Wang, and H. J. Liu, Study on Delamination Problems of Composite Hull Structures under Slamming Loads. Polymers & Polymer Composites, 2011. 19(4-5): p. 433-437. https://doi.org/10.1177/0967391111019004-528

Van Paepegem, W., C. Blommaert, I. De Baere, J. Degrieck, G. De Backer, J. De Rouck, J. Degroote, J. Vierendeels, S. Matthys, and L. Taerwe, Slamming wave impact of a composite buoy for wave energy applications: Design and large - scale testing. Polymer Composites, 2011. 32(5): p. 700-713. https://doi.org/10.1002/pc.21089

Aureli, M., C. Prince, M. Porfiri, and S. D. Peterson, Energy harvesting from base excitation of ionic polymer metal composites in fluid environments. Smart Materials and Structures, 2010. 19: p. 015003. https://doi.org/10.1088/0964-1726/19/1/015003

París, F. and J. Cañas Boundary element method: fundamentals and applications 1997: Oxford University Press New York.

Greco, M., A two-dimensional study of green-water loading, 2001, Norwegian University of Science and Technology.

Longuet-Higgins, M. S. and E. Cokelet, The deformation of steep surface waves on water. I. A numerical method of computation. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1976. 350(1660): p. 1-26. https://doi.org/10.1098/rspa.1976.0092

Pozrikidis, C., Numerical computation in science and engineering 1998: Oxford University Press London.

Young, Y., Time-dependent hydroelastic analysis of cavitating propulsors. Journal of fluids and structures, 2007. 23(2): p. 269-295. https://doi.org/10.1016/j.jfluidstructs.2006.09.003

Batra, R. and X. Liang, Finite dynamic deformations of smart structures. Computational mechanics, 1997. 20(5): p. 427-438. https://doi.org/10.1007/s004660050263

Das, K., Analysis of instabilities in microelectromechanical systems, and of local water slamming, 2009, Ph.D. dissertation, Virginia Polytechnic Institute and State University.

Aarsnes, J., Drop test with ship sections-effect of roll angle. Marintek report, 1996. 603834(01).

Arai, M. and K. Matsunaga, A numerical and experimental study of bow flare slamming. Journal of the Society of Naval Architects of Japan, 1989. 166: p. 343-353. https://doi.org/10.2534/jjasnaoe1968.1989.166_343



How to Cite

Xiao, J. and Batra, R. (2012) “Local water slamming of curved rigid hulls”, The International Journal of Multiphysics, 6(3), pp. 305-340. doi: 10.1260/1750-9548.6.3.305.