DOI QR코드

DOI QR Code

Efficient and accurate domain-truncation techniques for seismic soil-structure interaction

  • Guddati, Murthy (Department of Civil, Construction and Environmental Engineering, North Carolina State University) ;
  • Savadatti, Siddharth (Faculty of Engineering, University of Georgia)
  • Received : 2011.12.09
  • Accepted : 2012.04.10
  • Published : 2012.06.25

Abstract

We modify the formulation of a recently developed absorbing boundary condition (ABC), the perfectly matched discrete layers (PMDL), to incorporate the excitation coming from the exterior such as earthquake waves. The modified formulation indicates that the effect of the exterior excitation can be incorporated into PMDL ABCs (traditionally designed to treat only interior excitation) simply by applying appropriate forces on the nodes connected to the first PMDL layer. Numerical results are presented to clearly illustrate the effectiveness of the proposed method.

Keywords

References

  1. Asvadurov, S., Druskin, V., Guddati, M.N. and Knizhnerman, L. (2003), "On optimal finite-difference approximation of PML", Siam J. Numer. Anal., 41(1), 287-305. https://doi.org/10.1137/S0036142901391451
  2. 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
  3. Bielak, J., Loukakis, K., Hisada, Y. and Yoshimura, C. (2003), "Domain reduction method for three-dimensional earthquake modeling in localized regions, part I: theory", B. Seismol. Soc. Am., 93(2), 817-824. https://doi.org/10.1785/0120010251
  4. Chew, W.C. and Weedon, W.H. (1994), "A 3d perfectly matched medium from modified maxwells equations with stretched coordinates", Microw. Opt. Techn. Let., 7(13), 599-604. https://doi.org/10.1002/mop.4650071304
  5. Chew, W.C., Jin, J.M. and Michielssen, E. (1997), "Complex coordinate stretching as a generalized absorbing boundary condition", Microw. Opt. Techn. Let., 15(6), 363-369. https://doi.org/10.1002/(SICI)1098-2760(19970820)15:6<363::AID-MOP8>3.0.CO;2-C
  6. Engquist, B. and Majda, A. (1977), "Absorbing boundary-conditions for numerical-simulation of waves", Math. Comput., 31(139), 629-651. https://doi.org/10.1090/S0025-5718-1977-0436612-4
  7. Engquist, B. and Majda, A. (1979), "Radiation boundary-conditions for acoustic and elastic wave calculations", Commun. Pur. Appl. Math., 32(3), 313-357. https://doi.org/10.1002/cpa.3160320303
  8. Givoli, D. (2004), "High-order local non-reflecting boundary conditions: a review", Wave Motion, 39(4), 319-326. https://doi.org/10.1016/j.wavemoti.2003.12.004
  9. Guddati, M.N. (2006), "Arbitrarily wide-angle wave equations for complex media", Comput. Method. Appl. M., 195(1-3), 65-93. https://doi.org/10.1016/j.cma.2005.01.006
  10. Guddati, M.N. and Lim, K.W. (2006), "Continued fraction absorbing boundary conditions for convex polygonal domains", Int. J. Numer. Meth. Eng., 66(6), 949-977. https://doi.org/10.1002/nme.1574
  11. Guddati, M.N., Lim, K.W. and Zahid, M.A. (2008), "Perfectly matched discrete layers for unbounded domain modeling", Comput. Meth. Acoust. Probl., doi: 10.4203, 69-98.
  12. 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
  13. Higdon, R.L. (1987), "Numerical absorbing boundary-conditions for the wave-equation", Math. Comput., 49(179), 65-90. https://doi.org/10.1090/S0025-5718-1987-0890254-1
  14. Higdon, R.L. (1990), "Radiation boundary-conditions for elastic wave-propagation", Siam J. Numer. Anal., 27(4), 831-869. https://doi.org/10.1137/0727049
  15. Kausel, E. and Tassoulas, J.L. (1981), "Transmitting boundaries - a closed-form comparison", B. Seismol. Soc. Am., 71(1), 143-159.
  16. Kausel, E., Whitman, R.V., Morray, J.P. and Elsabee, F. (1978), "The spring method for embedded foundations", Nucl. Eng. Des., 48(2-3), 377-392. https://doi.org/10.1016/0029-5493(78)90085-7
  17. Lindman, E.L. (1975), "Free-space boundary-conditions for time-dependent wave-equation", J. Comput. Phys., 18(1), 66-78. https://doi.org/10.1016/0021-9991(75)90102-3
  18. Lysmer, J. and Waas, G. (1974), "Shear-waves in plane infinite structures", J. Eng. Mech.-ASCE, 98(1), 85-105.
  19. M., Nuray A. (1993), "Consistent formulation of direct and substructure methods in nonlinear soil-structure interaction", Soil Dyn. Earthq. Eng., 12(7), 403-410. https://doi.org/10.1016/0267-7261(93)90003-A
  20. Savadatti, S. and Guddati, M.N. (2010a), "Absorbing boundary conditions for scalar waves in anisotropic media. Part 1: Time harmonic modeling", J. Comput. Phys., 229(19), 6696-6714. https://doi.org/10.1016/j.jcp.2010.05.018
  21. Savadatti, S. and Guddati, M.N. (2010b), "Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling", J. Comput. Phys., 229(18), 6644-6662. https://doi.org/10.1016/j.jcp.2010.05.017
  22. Savadatti, S. and Guddati, M.N. (2011a), "Accurate absorbing boundary conditions for anisotropic elastic media. Part 1: Elliptic anisotropy", J. Comput. Phys., (under review).
  23. Savadatti, S. and Guddati, M.N. (2011b), "Accurate absorbing boundary conditions for anisotropic elastic media. Part 2: Untilted non-elliptic anisotropy", J. Comput. Phys., (under review).
  24. Trifunac, M.D. (1971), "Surface motion of a semi-cylindrical alluvial valley for incident plane Sh waves", B. Seismol. Soc. Am., 61(6), 1755-1770.
  25. Yoshimura, C., Bielak, J., Hisada, Y. and Fernandez, A. (2003), "Domain reduction method for three-dimensional earthquake modeling in localized regions, part II: Verification and applications", B. Seismol. Soc. Am., 93(2), 825-840. https://doi.org/10.1785/0120010252
  26. Zahid, M.A. and Guddati, M.N. (2006), "Padded continued fraction absorbing boundary conditions for dispersive waves", Comput. Method. Appl. M., 195(29-32), 3797-3819. https://doi.org/10.1016/j.cma.2005.01.023

Cited by

  1. Nonlinear analysis of soil–structure interaction using perfectly matched discrete layers vol.142, 2014, https://doi.org/10.1016/j.compstruc.2014.06.002
  2. Perfectly matched discrete layers for three-dimensional nonlinear soil–structure interaction analysis vol.165, 2016, https://doi.org/10.1016/j.compstruc.2015.12.004
  3. Perfectly Matched Discrete Layers with Analytical Wavelengths for Soil–Structure Interaction Analysis 2018, https://doi.org/10.1142/S0219455418501031
  4. Practical Numerical Model for Nonlinear Analyses of Wave Propagation and Soil-Structure Interaction in Infinite Poroelastic Media vol.22, pp.7, 2018, https://doi.org/10.5000/EESK.2018.22.7.379
  5. Smoothed response spectra including soil-structure interaction effects vol.19, pp.1, 2012, https://doi.org/10.1007/s11803-020-0546-1
  6. Structure-soil-structure interaction in a group of buildings using 3D nonlinear analyses vol.18, pp.6, 2012, https://doi.org/10.12989/eas.2020.18.6.667