`Mathematical Problems in EngineeringVolume 2011 (2011), Article ID 210624, 23 pageshttp://dx.doi.org/10.1155/2011/210624`
Research Article

## Finite Element Analysis of Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary

1State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
2Changjiang Institute of Survey, Planning, Design, and Research, Wuhan 430010, China

Received 30 May 2011; Accepted 23 August 2011

Copyright © 2011 Yichao Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. A. K. Chopra and P. Chakrabarti, “Earthquake analysis of concrete gravity dams including dam water foundation rock interaction,” Earthquake Engineering and Structural Dynamics, vol. 9, no. 4, pp. 363–383, 1981.
2. J. F. Hall and A. K. Chopra, “Two-dimensional dynamic analysis of concrete gravity and embankment dams including hydrodynamic effects,” Earthquake Engineering and Structural Dynamics, vol. 10, no. 2, pp. 305–332, 1982.
3. O. C. Zienkiewicz and P. Bettess, “Fluid-structure dynamic interaction and wave forces. An introduction to numerical treatment,” International Journal for Numerical Methods in Engineering, vol. 13, no. 1, pp. 1–16, 1978.
4. S. Küçükarslan, S. B. Coşkun, and B. Taşkin, “Transient analysis of dam-reservoir interaction including the reservoir bottom effects,” Journal of Fluids and Structures, vol. 20, no. 8, pp. 1073–1084, 2005.
5. A. Sommerfeld, Partial Differential Equations in Physics, Academic Press, New York, NY, USA, 1949.
6. C. S. Tsai, G. C. Lee, and R. L. Ketter, “Semi-analytical method for time-domain analyses of dam-reservoir interactions,” International Journal for Numerical Methods in Engineering, vol. 29, no. 5, pp. 913–933, 1990.
7. C. S. Tsai and G. C. Lee, “Time-domain analyses of dam-reservoir system. II: substructure method,” Journal of Engineering Mechanics, vol. 117, no. 9, pp. 2007–2026, 1991.
8. R. Yang, C. S. Tsai, and G. C. Lee, “Explicit time-domain transmitting boundary for dam-reservoir interaction analysis,” International Journal for Numerical Methods in Engineering, vol. 36, no. 11, pp. 1789–1804, 1993.
9. T. Touhei and T. Ohmachi, “A FE-BE method for dynamic analysis of dam-foundation-reservoir systems in the time domain,” Earthquake Engineering and Structural Dynamics, vol. 22, no. 3, pp. 195–209, 1993.
10. R. J. Câmara, “A method for coupled arch dam-foundation-reservoir seismic behaviour analysis,” Earthquake Engineering and Structural Dynamics, vol. 29, no. 4, pp. 441–460, 2000.
11. O. Czygan and O. von Estorff, “Fluid-structure interaction by coupling BEM and nonlinear FEM,” Engineering Analysis with Boundary Elements, vol. 26, no. 9, pp. 773–779, 2002.
12. D. Soares Jr., O. von Estorff, and W. J. Mansur, “Efficient non-linear solid-fluid interaction analysis by an iterative BEM/FEM coupling,” International Journal for Numerical Methods in Engineering, vol. 64, no. 11, pp. 1416–1431, 2005.
13. A. Seghir, A. Tahakourt, and G. Bonnet, “Coupling FEM and symmetric BEM for dynamic interaction of dam-reservoir systems,” Engineering Analysis with Boundary Elements, vol. 33, no. 10, pp. 1201–1210, 2009.
14. S. M. Li, H. Liang, and A. M. Li, “A semi-analytical solution for characteristics of a dam-reservoir system with absorptive reservoir bottom,” Journal of Hydrodynamics, vol. 20, no. 6, pp. 727–734, 2008.
15. G. Lin, J. Du, and Z. Hu, “Dynamic dam-reservoir interaction analysis including effect of reservoir boundary absorption,” Science in China Series E: Technological Sciences, vol. 50, no. 1, pp. 1–10, 2007.
16. S. V. Tsynkov, “Numerical solution of problems on unbounded domains. A review,” Applied Numerical Mathematics, vol. 27, no. 4, pp. 465–532, 1998.
17. D. Givoli, “High-order local non-reflecting boundary conditions: a review,” Wave Motion, vol. 39, no. 4, pp. 319–326, 2004, New computational methods for wave propagatio.
18. S. Prempramote, C. Song, F. Tin-Loi, and G. Lin, “High-order doubly asymptotic open boundaries for scalar wave equation,” International Journal for Numerical Methods in Engineering, vol. 79, no. 3, pp. 340–374, 2009.
19. T. Geers, “Singly and doubly asymptotic computational boundaries,” in Proceedings of the IUTAM Symposium on Computational Methods for Unbounded Domains, pp. 135–141, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998.
20. T. L. Geers, “Doubly asymptotic approximations for transient motions of submerged structures,” Journal of the Acoustical Society of America, vol. 64, no. 5, pp. 1500–1508, 1978.
21. P. Underwood and T. L. Geers, “Doubly asymptotic, boundary-element analysis of dynamic soil-structure interaction,” International Journal of Solids and Structures, vol. 17, no. 7, pp. 687–697, 1981.
22. T. L. Geers and B. A. Lewis, “Doubly asymptotic approximations for transient elastodynamics,” International Journal of Solids and Structures, vol. 34, no. 11, pp. 1293–1305, 1997.
23. T. L. Geers and B. J. Toothaker, “Third-order doubly asymptotic approximations for computational acoustics,” Journal of Computational Acoustics, vol. 8, no. 1, pp. 101–120, 2000.
24. M. H. Bazyar and C. Song, “A continued-fraction-based high-order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry,” International Journal for Numerical Methods in Engineering, vol. 74, no. 2, pp. 209–237, 2008.
25. X. Wang, F. Jin, S. Prempramote, and C. Song, “Time-domain analysis of gravity dam-reservoir interaction using high-order doubly asymptotic open boundary,” Computers and Structures, vol. 89, no. 7-8, pp. 668–680, 2011.
26. D. Givoli, B. Neta, and I. Patlashenko, “Finite element analysis of time-dependent semi-infinite wave-guides with high-order boundary treatment,” International Journal for Numerical Methods in Engineering, vol. 58, no. 13, pp. 1955–1983, 2003.
27. C. Song and J. P. Wolf, “The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics,” Computer Methods in Applied Mechanics and Engineering, vol. 147, no. 3-4, pp. 329–355, 1997.
28. K.-C. Park, “Partitioned transient analysis procedures for coupled-field problems: stability analysis,” Journal of Applied Mechanics, vol. 47, no. 2, pp. 370–376, 1980.
29. K. C. Park and C. A. Felippa, “Partitioned transient analysis procedures for coupled-field problems: accuracy analysis,” Journal of Applied Mechanics, vol. 47, no. 4, pp. 919–926, 1980.