Stochastic analysis of fluid-structure interaction systems by Lagrangian approach

  • Bayraktar, Alemdar (Karadeniz Technical University, Department of Civil Engineering) ;
  • Hancer, Ebru (Karadeniz Technical University, Department of Civil Engineering)
  • Received : 2003.05.09
  • Accepted : 2005.04.11
  • Published : 2005.07.10


In the present paper it is aimed to perform the stochastic dynamic analysis of fluid and fluidstructure systems by using the Lagrangian approach. For that reason, variable-number-nodes twodimensional isoparametric fluid finite elements are programmed in Fortran language by the authors and incorporated into a general-purpose computer program for stochastic dynamic analysis of structure systems, STOCAL. Formulation of the fluid elements includes the effects of compressible wave propagation and surface sloshing motion. For numerical example a rigid fluid tank and a dam-reservoir interaction system are selected and modeled by finite element method. Results obtained from the modal analysis are compared with the results of the analytical and numerical solutions. The Pacoima Dam record S16E component recorded during the San Fernando Earthquake in 1971 is used as a ground motion. The mean of maximum values of displacements and hydrodynamic pressures are compared with the deterministic analysis results.


  1. Akkas, N., Akay, H.U. and Yilmaz, C. (1979), 'Applicability of general-purpose finite element programs in solid-fluid interaction problems', Comput. Struct., 10, 773-783
  2. Araujo, J.M. and Awruch, A.M. (1998), 'Probabilistic finite element analysis of concrete gravity dams', Advances in Engineering Software, 29,97-104
  3. Bathe, K-J. (1982), Finite Element Procedures in Engineering Analysis, Prentice-Hall Inc., Englewood Cliffs, New Jersey
  4. Bathe, K-J. and Harm, W.F. (1979), 'On transient analysis of fluid-structure system', Comput. Struct., 10, 383-391
  5. Bayraktar, A (1995), 'Dynamic response of dam-reservoir-foundation systems subjected to asynchronous ground motion', Ph.D. Thesis, Department of Civil Engineering, Karadeniz Technical University (in Turkish)
  6. Bayraktar, A., Dumanoglu, A.A and Calayir, Y. (1996), 'Asynchronous dynamic analysis of dam-reservoir-foundation systems by the Lagrangian approach', Comput. Struct., 58,925-935
  7. Button, MR, Der Kiureghian, A and Wilson, E.L. (1981), 'STOCAL-User Information Manual', Report No. UCB-SESM/81-2, Department of Civil Engineering, University of California, Berkeley, CA
  8. Calayir, Y. (1994), 'Dynamic analysis of concrete gravity dams using the Eulerian and the Lagrangian approaches', Ph.D. Thesis, Department of Civil Engineering, Karadeniz Technical University (in Turkish)
  9. Calayir, Y. and Dumanoglu, A.A. (1993), 'Static and dynamic analysis of fluid and fluid-structure systems by Lagrangian method', Comput. Struct., 49(4), 625-632
  10. Clough, R.W. and Penzien, J. (1975), Dynamics of Structures, McGraw Hill Book Company, Singapore
  11. Der Kiureghian, A. (1980), 'Structural response to stationary excitation', J Eng. Mech. Div., EM6, 106, 1195-1213
  12. Deshpande, S.S., Belkune, R.M. and Ramesh, C.K. (1981), 'Dynamic analysis of coupled fluid-structure interaction problems', Numerical Methods for Coupled Problems, Editors: E. Hinton, P. Bettess, R.W. Lewis, Pineridge Press, Swansea, UK, 367-378
  13. Di Paola, M. and Zingales, M. (2003), 'Stochastic seismic analysis of hydrodynamic pressure in dam reservoir systems', Earthq. Eng. Struct. Dyn., 32, 165-172
  14. Fenves, G and Chopra, A.K. (1984), 'EAGD-84: A computer program for earthquake analysis of concrete gravity dams', Report No. EERC 84-11, Earthquake Engineering Research Center, University of California, Berkeley, CA
  15. Greeves, EJ. (1990), 'The investigation of calibration of a novel Lagrangian fluid finite element with particular reference to dynamic fluid-structure interaction', Report No. UBCE/EE 90-05, Department of Civil Engineering, University of Bristol, Bristol
  16. Greeves, EJ. and Dumanoglu, A.A. (1989), 'The implementation of an efficient computer analysis for fluidstructure interaction using the Eulerian approach within SAP-IV', Report No. UCB/EE 89-10, Department of Civil Engineering, University of Bristol, Bristol
  17. Hamdi, M.A., Ousset, Y. and Verchery, G.A. (1978), 'Displacement method for the analysis of vibrations of coupled fluid-structure interaction systems', Int. J Numer. Meth. Eng., 13, 139-150
  18. Lamb, H. (1932), Hydrodynamics, 6th Ed., Cambridge University Press, London
  19. Lin, Y.K. (1967), Probabilistic Theory of Structural Dynamics, 1st Ed., McGraw Hill Book Company, New York
  20. Mackerle, J. (1999), 'Fluid-structure interaction problems, finite element and boundary element approaches', Finite Elements in Analysis and Design, 31, 231-240
  21. Malkus, D.S. (1976), 'A finite element displacement model valid for any value of the compressibility', Int. J Solids Struct., 12, 731-738
  22. Manolis, G.D. and Koliopoulos, P.K. (2001), Stochastic Structural Dynamics in Earthquake Engineering, WIT Press, Southampton
  23. 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 Engineering and Design, 76, 137-151
  24. Vanmarcke, E.H. (1975), 'On the distribution of the first-passage time for normal stationary random process', J Appl. Mech., 42, 215-220
  25. Wilson, E.L. and Khalvati, M. (1983), 'Finite elements for the dynamic analysis of fluid-solid systems', Int. J Numer. Meth. Eng., 19, 1657-1668
  26. Yang, C.Y. (1986), Random Vibration of Structures, John Wiley and Sons Inc., New York
  27. Zienkewics, O.C. and Bettess, P. (1978), 'Fluid-structure dynamic interaction and wave forces. An introduction to numerical treatment', Int. J Numer. Meth. Eng., 13, 1-16

Cited by

  1. The Effect of the Spatially Varying Earthquake Ground Motion on Random Hydrodynamic Pressures vol.13, pp.6, 2010,
  2. Seismic risk assessment of storage tanks in Turkish industrial facilities vol.24, pp.4, 2011,
  3. Stochastic dynamic response of dam–reservoir–foundation systems to spatially varying earthquake ground motions vol.29, pp.3, 2009,
  4. The effects of ice cover on stochastic response of concrete gravity dams to multi-support seismic excitation vol.55, pp.3, 2009,
  5. Comparison of uniform and spatially varying ground motion effects on the stochastic response of fluid-structure interaction systems vol.33, pp.4, 2009,