2D Finite element analysis of rectangular water tank with separator wall using direct coupling

  • Received : 2015.05.26
  • Accepted : 2015.12.12
  • Published : 2015.12.25


The present paper deals with the analysis of water tank with elastic separator wall. Both fluid and structure are discretized and modeled by eight node-elements. In the governing equations, pressure for the fluid domain and displacement for the separator wall are considered as nodal variables. A method namely, direct coupled for the analysis of water tank has been carried out in this study. In direct coupled approach, the solution of the fluid-structure system is accomplished by considering these as a single system. The hydrodynamic pressure on tank wall is presented for different lengths of tank. The results show that the magnitude of hydrodynamic pressure is quite large when the distances between the separator wall and tank wall are relatively closer and this is due to higher rotating tendency of fluid and the higher sloshed displacement at free surface.


finite element;direct coupling;indirect coupling;sloshed displacement;elastic separator wall


  1. Akkose, M., Adanur, S., Bayraktar, A. and Dumanoglu, A.A. (2008), "Elasto-plastic earthquake response of arch dams including fluid-structure interaction by the Lagrangian approach", Appl. Math. Model., 32(11), 2396-2412.
  2. Antoniadis, I. and Kanarachos, A. (1998), "Decoupling procedures for fluid-structure interaction problems", Comput. Method. Appl. M., 70(1), 1-25.
  3. Barrios, H. H., Zavoni, E.H., Alvaro, A. and Rodriguez, A. (2007), "Nonlinear sloshing response of cylindrical tanks subjected to earthquake ground motion", Eng. Struct., 29(12), 3364-3376.
  4. Bermudez, A., Duran, R., Muschietti, M.A., Rodriguez, R. and Solomin, J. (1995), "Finite element vibration analysis of fluid-solid systems without spurious modes", SIAM J. Numer. Anal., 32(4), 1280-1295.
  5. Biswal, K.C., Bhattacharyya, S.K. and Sinha. P.K. (2006), "Non-linear sloshing in partially liquid filled containers with baffles", Int. J. Numer. Meth. Eng., 68(3), 317-337
  6. Bouaanani, N. and Lu. F.Y. (2009), "Assessment of potential-based fluid finite elements for seismic analysis of dam-reservoir systems", Comput. Struct., 87(3-4), 206-224.
  7. Chen, H.C. and Taylor, R.L. (1990), "Vibration analysis of fluid solid systems using a finite element displacement formulation", Int. J. Numer. Method. Eng., 29(4), 683-698.
  8. Chopra, A.K. (1967), "Hydrodynamic pressures on dams during earthquakes", J. Eng. Mech. - ASCE, 93(6), 205-223.
  9. Choun, Y.S. and Yun, C.B. (1996), "Sloshing characteristic in rectangular tanks with a submerged block", Comput. Struct., 61(3), 401-413.
  10. Chwang, A.T. (1978), "Hydrodynamic pressure on sloping dams during earthquakes. Part - 2.Exact theory", J. Fluid Mech., 87(2), 343-348.
  11. Gill, S. (1951), "A process for the step-by-step integration of differential equations in an automatic digital computing machine", Proceedings of the Cambridge Philosophical Society, 47(1), 96-108.
  12. Gogoi, I. and Maity, D. (2005), "Seismic safety of aged concrete gravity dams considering fluid-structure interaction", J. Earthq. Eng., 9(5), 1-20.
  13. Hua, C.W., Fuh, C.B. and Kan. H.T. (2013), "Hydrodynamic forces induced by transient sloshing in a 3D rectangular tank due to oblique horizontal excitation", J. Comput. Math. Appl., 65(8), 1163-1186.
  14. Kassiotis, C., Ibrahimbegovic, A. and Matthies, H. (2010), "Partitioned solution to fluid-structure interaction problem in application to free-surface flow", Eur. J. Mech. Part B: Fluids, 29(6), 510-521.
  15. Kassiotis, C., Ibrahimbegovic, A., Niekamp, R. and Matthies, H. (2011a), "Partitioned solution to nonlinear fluid-structure interaction problems. Part I: implicit coupling algorithms and stability proof", Comput. Mech., 47, 305-323.
  16. Kassiotis, C., Ibrahimbegovic, A., Niekamp, R. and Matthies, H. (2011b), "Partitioned solution to nonlinear fluid-structure interaction problems. Part II: CTL based software implementation with nested parallelization", Comput. Mech., 47, 335-357.
  17. Lotfi, V. (2004), "Frequency domain analysis of concrete gravity dams by decoupled modal approach", Dam Eng., 15(2), 141-165.
  18. Maity, D. and Bhattacharyya, S.K. (1997), "Finite element analysis of fluid-structure system for small fluid displacement", Int. J. Struct., 17, 1-18.
  19. Maity, D. and Bhattacharyya, S.K. (2003), "A parametric study on fluid-structure interaction problems", J. Sound Vib., 263(4), 917-935.
  20. Olson, L.G. and Bathe, K.J. (1983), "A study of displacement-based fluid finite elements for calculating frequencies of fluid and fluid-structure systems", Nuclear Eng. Des., 76(2), 137-151.
  21. Onate, E., Garcia, J., Idelsohn, R. and Delpin, S. (2006), "Finite calculus formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches", Comput. Method. Appl. M., 195(23-24), 3001-3037.
  22. Pal, P. and Bhattacharyya, S.K. (2013), "Slosh dynamics of liquid-filled composite containers: A two dimensional meshless local Petrov-Galerkin approach", J. Fluid. Struct., 39, 60-75.
  23. Pani, P.K. and Bhattacharyy, S.K. (2007), "Fluid-structure interaction effects on dynamic pressure of a rectangular lock-gate", J. Finite Elem. Anal. Des., 43(10), 739-748.
  24. Panigrahy, P.K., Saha, U.K. and Maity. D. (2009), "Experimental studies on sloshing behavior due to horizontal movement of liquids in baffled tanks", J. Ocean Eng., 36(3-4), 213-222.
  25. Ralston, A. andWilf, H.S. (1965), Mathematical Models for Digital Computers, Wiley1, New York.
  26. Sami, A. and Lotfi, V. (2007), "Comparison of coupled and decoupled modal approaches in seismic analysis of concrete gravity dams in time domain", Finite Elem. Anal. Des., 43(13), 1003- 1012.
  27. Singh, R.K., Kant, T. and Kakodkar, A. (1991), "Coupled shell-fluid interaction problems with degenerate shell and three-dimensional fluid elements", Comput. Struct., 38(5-6), 515-528.
  28. Tung, C.C. (1979), "Hydrodynamic forces on submerged vertical circular cylindrical tanks underground excitation", Appl. Ocean Res., 1(2), 75-78.
  29. Williams, A.N. and Moubayed, W.I. (1990), "Earthquake-induced hydrodynamic pressures on submerged cylindrical storage tanks", J. Ocean Eng., 17(3), 181-199.
  30. Zienkiewicz, O.C. and Newton, R.E. (1969), "Coupled vibration of a structure submerged in a compressible Fluid", Proceedings of the International Symposium on Finite Element Techniques, Stuttgart.