Euler–Lagrange coupling with damping effects: application to slamming problems. (English) Zbl 1137.74430

Summary: During a high velocity impact of a structure on a nearly incompressible fluid, impulse loads with high-pressure peaks occur. This physical phenomenon called ‘slamming’ is a concern in shipbuilding industry because of the possibility of hull damage. Shipbuilding companies have carried out several studies on slamming modeling using FEM software with added mass techniques to represent fluid effects. In the added mass method inertia effects of the fluid are not taken into account and are only valid when the deadrise angle is small. This paper presents the prediction of the local high pressure load on a rigid wedge impacting a free surface, where the fluid is represented by solving Navier-Stokes equations with an Eulerian or ALE formulation. The fluid–structure interaction is simulated using a coupling algorithm; the fluid is treated on a fixed or moving mesh using an ALE formulation and the structure on a deformable mesh using a Lagrangian formulation. A new coupling algorithm is developed in the paper. The coupling algorithm computes the coupling forces at the fluid-structure interface. These forces are added to the fluid and structure nodal forces, where fluid and structure are solved using an explicit finite element formulation. Predicting the local pressure peak on the structure requires an accurate fluid-structure interaction algorithm. The Euler-Lagrange coupling algorithm presented in this paper uses a penalty based formulation similar to penalty contact in Lagrangian analyses. Both penalty coupling and penalty contact can generate high frequency oscillations due to the nearly incompressible nature of the fluid. In this paper, a damping force based on the relative velocity of the fluid and the structure is introduced to smooth out non-physical high frequency oscillations induced by the penalty springs in the coupling algorithm.


74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)


Full Text: DOI


[1] Von Kármán, T., The Impact on Seaplane Floats during Landing (1929), NACA TN321: NACA TN321 Washington
[2] Wagner, H., Über Stoß- und Gleitvogänge an der Oberfläche von Flüssigkeiten, Zeitsch. f. Angew. Math. Mech., 12, 4, 193-235 (1932) · Zbl 0005.12601
[3] Watanabe, I., Analytical expression of hydrodynamic impact pressure by matched asymptotic expansion technique, T. West-Jpn. Soc. Nav. Arch., 71 (1986)
[4] Zhao, R.; Faltinsen, O. M., Water entry of two-dimensional bodies, J. Fluid Mech., 246, 593-612 (1993) · Zbl 0766.76008
[5] Benson, D. J., Computational methods in Lagrangian and Eulerian hydrocodes, Comput. Methods Appl. Mech. Engrg., 99, 2, 235-394 (1992) · Zbl 0763.73052
[6] Souli, M.; Ouahsine, A.; Lewin, L., ALE and fluid-structure interaction problems, Comput. Methods Appl. Mech. Engrg., 190, 659-675 (2000) · Zbl 1012.76051
[7] Belytschko, T.; Liu, W. K.; Moran, B., Nonlinear Finite Elements for Continua and Structures (2000), John Wiley & Sons, Ltd. · Zbl 0959.74001
[8] Van Leer, B., Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection, J. Comput. Phys., 167, 276-299 (1977) · Zbl 0339.76056
[9] Zhong, Z. H., Finite Element Procedures for Contact-impact Problems (1993), Oxford University Press: Oxford University Press Oxford
[10] Souli, M.; Zolesio, J. P., Arbitrary Lagrangian-Eulerian and free surface methods in fluid mechanics, Comput. Methods Appl. Mech. Engrg., 191, 451-466 (2001) · Zbl 0999.76084
[11] Rabier, S.; Medale, M., Computation of free surface flows with a projection FEM in a moving mesh framework, Comput. Methods Appl. Mech. Engrg., 192, 41-42, 4703-4721 (2003) · Zbl 1054.76052
[12] Benson, D. J., An efficient, accurate, simple ALE method for nonlinear finite element programs, Comput. Methods Appl. Mech. Engrg., 72, 305-350 (1989) · Zbl 0675.73037
[13] Belytschko, T.; Lin, J.; Tsay, C. S., Explicit algorithms for nonlinear dynamics of shells, Comput. Methods Appl. Mech. Engrg., 42, 225-251 (1984) · Zbl 0512.73073
[16] Aquelet, N.; Souli, M.; Gabrys, J.; Olovsson, L., A new ALE formulation for sloshing analysis, Struct. Engrg. Mech., 16, 4, 423-440 (2003)
[17] Cho, J. R.; Lee, H. W., Numerical study on liquid sloshing in baffled tank by nonlinear finite element method, Comput. Methods Appl. Mech. Engrg., 19, 23-26, 2581-2598 (2004) · Zbl 1067.76564
[18] Belytschko, T.; Neal, M. O., Contact-impact by the pinball algorithm with penalty, projection, and Lagrangian methods, (Proceedings of the Symposium on Computational Techniques for Impact, Penetration, and Performation of Solids. Proceedings of the Symposium on Computational Techniques for Impact, Penetration, and Performation of Solids, AMD, vol. 103 (1989), ASME: ASME New York, NY), 97-140
[19] Piperno, S.; Larrouturou, B.; Lesoinne, M., Analysis and compensation of numerical damping in one-dimensional acoustic piston simulations, Int. J. Comput. Fluid Dyn., 6, 157-174 (1996)
[20] Hilber, H. M.; Hughes, T. J.R.; Taylor, R. L., Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engrg. Struct. Dynam., 5, 283-292 (1977)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.