Coupled systems mechanics

  • 제7권3호
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  • Pages.353-371
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  • 2018
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  • 2234-2184(pISSN)
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  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
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Application of Wavenumber-TD approach for time harmonic analysis of concrete arch dam-reservoir systems

  • Lotfi, Vahid (Department of Civil and Environmental Engineering, Amirkabir University of Technology) ;
  • Zenz, Gerald (Institute of Hydraulic Engineering and Water Resources Management, Department of Civil Engineering, Graz University of Technology)
  • 투고 : 2017.09.20
  • 심사 : 2017.12.19
  • 발행 : 2018.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

The Wavenumber or more accurately Wavenumber-FD approach was initially introduced for two-dimensional dynamic analysis of concrete gravity dam-reservoir systems. The technique was formulated in the context of pure finite element programming in frequency domain. Later on, a variation of the method was proposed which was referred to as Wavenumber-TD approach suitable for time domain type of analysis. Recently, it is also shown that Wavenumber-FD approach may be applied for three-dimensional dynamic analysis of concrete arch dam-reservoir systems. In the present study, application of its variation (i.e., Wavenumber-TD approach) is investigated for three-dimensional problems. The method is initially described. Subsequently, the response of idealized Morrow Point arch dam-reservoir system is obtained by this method and its special cases (i.e., two other well-known absorbing conditions) for time harmonic excitation in stream direction. All results for various considered cases are compared against the exact response for models with different values of normalized reservoir length and reservoir base/sidewalls absorptive conditions.

키워드

참고문헌

  1. Amanabadi, J. and Lotfi, V. (2017), "Dynamic analysis of three-dimensional dam-reservoir systems by Wavenumber approach in the frequency domain", J. Hydrodyn., Under Review.
  2. Basu, U. and Chopra, A.K. (2003), "Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: Theory and finite-element implementation", Comput. Meth. Appl. Mech. Eng., 192(11-12), 1337-1375. https://doi.org/10.1016/S0045-7825(02)00642-4
  3. Berenger, J.P. (1994), "A perfectly matched layer for the absorption of electromagnetic waves", J. Comput. Phys., 114 (2), 185-200. https://doi.org/10.1006/jcph.1994.1159
  4. Chew, W.C. and Weedon, W.H. (1994), "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates", Microw. Opt. Techn. Let., 7(13), 599-604. https://doi.org/10.1002/mop.4650071304
  5. Chopra, A.K. (1967), "Hydrodynamic pressure on dams during earthquake", J. Eng. Mech.-ASCE, 93(6), 205-223.
  6. Chopra, A.K., Chakrabarti, P. and Gupta, S. (1980), Earthquake Response of Concrete Gravity Dams Including Hydrodynamic and Foundation Interaction Effects, Report No. EERC-80/01, Earthquake Engineering Research Center, University of California, Berkeley, U.S.A.
  7. Fenves, G. and Chopra, A.K. (1985), "Effects of reservoir bottom absorption and dam-water-foundation interaction on frequency response functions for concrete gravity dams", Earthq. Eng. Struct. D., 13(1), 13-31. https://doi.org/10.1002/eqe.4290130104
  8. Fok, K.-L. and Chopra, A.K. (1986), "Frequency response functions for arch dams: hydrodynamic and foundation flexibility effects", Earthquake Eng. Struct. Dyn., 14(5), 769-795. https://doi.org/10.1002/eqe.4290140507
  9. Givoli, D. and Neta, B. (2003), "High order non-reflecting boundary scheme for time-dependent waves", J. Comput. Phys., 186(1), 24-46. https://doi.org/10.1016/S0021-9991(03)00005-6
  10. Givoli, D., Hagstrom, T. and Patlashenko, I. (2006), "Finite-element formulation with high-order absorbing conditions for time-dependent waves", Comput. Meth. Appl. M., 195(29-32), 3666-3690. https://doi.org/10.1016/j.cma.2005.01.021
  11. Hagstrom, T. and Warburton, T. (2004), "A new auxiliary variable formulation of high order local radiation boundary condition: corner compatibility conditions and extensions to first-order systems", Wave Motion, 39(4), 327-338. https://doi.org/10.1016/j.wavemoti.2003.12.007
  12. Hagstrom, T., Mar-Or, A. and Givoli, D. (2008), "High-order local absorbing conditions for the wave equation: extensions and improvements", J. Comput. Phys., 227(6), 3322-3357. https://doi.org/10.1016/j.jcp.2007.11.040
  13. Hall, J.F. and Chopra, A.K. (1983), "Dynamic analysis of arch dams including hydrodynamic effects", J. Eng. Mech. Div., 109(1), 149-163. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:1(149)
  14. Higdon, R.L. (1986), "Absorbing boundary conditions for difference approximations to the multidimensional wave equation", Math. Comput., 47(176), 437-459. https://doi.org/10.1090/S0025-5718-1986-0856696-4
  15. Jafari, M. and Lotfi, V. (2017), "Dynamic analysis of concrete gravity dam-reservoir systems by Wavenumber approach for the general reservoir base condition", Submitted to the International Journal of Science and Technology (Scientia Iranica), Accepted.
  16. Jiong, L., Jian-wei, M. and Hui-zhu, Y (2009), "The study of perfectly matched layer absorbing boundaries for SH wave fields", Appl. Geophys., 6(3), 267-274. https://doi.org/10.1007/s11770-009-0023-0
  17. Khazaee, A. and Lotfi, V. (2014a), "Application of perfectly matched layers in the transient analysis of damreservoir systems", J. Soil Dynam. Earthq. Eng., 60(1), 51-68. https://doi.org/10.1016/j.soildyn.2014.01.005
  18. Khazaee, A. and Lotfi, V. (2014b), "Time harmonic analysis of dam-foundation systems by perfectly matched layers", J. Struct. Eng. Mech., 50(3), 349-364. https://doi.org/10.12989/sem.2014.50.3.349
  19. Kim, S. and Pasciak, J.E. (2012), "Analysis of cartesian PML approximation to acoustic scattering problems in R2", Wave Mot., 49, 238-257. https://doi.org/10.1016/j.wavemoti.2011.10.001
  20. Lotfi, V. (2004), "Direct frequency domain analysis of concrete arch dams based on FE-(FE-HE)-BE technique", J. Comp. Concrete, 1(3), 285-302. https://doi.org/10.12989/cac.2004.1.3.285
  21. Lotfi, V. and Samii, A. (2012), "Dynamic analysis of concrete gravity dam-reservoir systems by Wavenumber approach in the frequency domain", Earthq. Struct., 3(3-4), 533-548. https://doi.org/10.12989/eas.2012.3.3_4.533
  22. Lotfi, V. and Zenz, G. (2017), "Time harmonic analysis of concrete gravity dam-reservoir systems by Wavenumber-TD approach", J. Struct Eng Mech., Under Review.
  23. Rabinovich, D., Givoli, D., Bielak, J. and Hagstrom, T. (2011), "A finite element scheme with a high order absorbing boundary condition for elastodynamics", Comput. Meth. Appl. Mech., 200(23-24), 2048-2066. https://doi.org/10.1016/j.cma.2011.03.006
  24. Samii, A. and Lotfi, V. (2012), "High-order adjustable boundary condition for absorbing evanescent modes of waveguides and its application in coupled fluid-structure analysis", Wave Motion, 49(2), 238-257. https://doi.org/10.1016/j.wavemoti.2011.10.001
  25. Sharan, S.K. (1987), "Time domain analysis of infinite fluid vibration", Int. J. Numer. Meth. Eng., 24(5), 945-958. https://doi.org/10.1002/nme.1620240508
  26. Sommerfeld, A. (1949), Partial Differential Equations in Physics, Academic Press, New York, U.S.A.
  27. Tan, H. and Chopra, A.K. (1995), "Earthquake analysis of arch dam including dam-water-foundation rock interaction", Earthq. Eng. Struct. Dyn., 24(11), 1453-1474. https://doi.org/10.1002/eqe.4290241104
  28. Waas, G. (1972), "Linear two-dimensional analysis of soil dynamics problems in semi-infinite layered media", Ph.D. Dissertation, University of California, Berkeley, California, U.S.A.
  29. Zhen, Q., Minghui, L., Xiaodong, Z., Yao, Y., Cai, Z. and Jianyong, S. (2009), "The implementation of an improved NPML absorbing boundary condition in elastic wave modeling", Appl. Geophys., 6(2), 113-121. https://doi.org/10.1007/s11770-009-0012-3
  30. Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z. (2013), The Finite Element Method, Butterworth-Heinemann, Oxford, U.K.

피인용 문헌

  1. Application of Hagstrom-Warburton high-order truncation boundary condition on time harmonic analysis of concrete arch dam-reservoir systems vol.38, pp.7, 2018, https://doi.org/10.1108/ec-08-2020-0441