Earthquakes and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A substructure formulation for the earthquake -induced nonlinear structural pounding problem

  • Shi, Jianye (Institute of General Mechanics, RWTH Aachen University) ;
  • Bamer, Franz (Institute of General Mechanics, RWTH Aachen University) ;
  • Markert, Bernd (Institute of General Mechanics, RWTH Aachen University)
  • Received : 2018.06.12
  • Accepted : 2019.06.15
  • Published : 2019.07.25
⟨ Previous Next ⟩

Abstract

Earthquake-induced pounding is one of the major reasons for structural failure in earthquake prone cities. An accurate description of the pounding phenomenon of two buildings requires the consideration of systems with a large number of degrees of freedom including adequate contact impact formulations. In this paper, firstly, a node to surface formulation for the realization of state-of-the-art pounding models for structural beam elements is presented. Secondly, a hierarchical substructure technique is introduced, which is adapted to the structural pounding problem. The numerical accuracy and efficiency of the method, especially for the contact forces, are verified on an academic example, applying four different impact elements. Error estimations are carried out and compared with the classical modal truncation method. It is demonstrated that the hierarchical substructure method is indeed able to significantly speed up the numeric integration procedure by preserving a required level of accuracy.

Keywords

References

  1. Abdel Raheem, S.E. (2014), "Mitigation measures for earthquake induced pounding effects on seismic performance of adjacent buildings", Bull. Earthq. Eng., 12, 1705-1724. https://doi.org/10.1007/s10518-014-9592-2.
  2. Aldaikh, H., Alexander, N.A., Ibraim, E. and Oddbjornsson, O. (2015), "Two dimensional numerical and experimental models for the study of structure-soil-structure interaction involving three buildings", Comput. Struct., 150, 79-91. https://doi.org/10.1016/j.compstruc.2015.01.003.
  3. Anagnostopoulos, S.A. (1992), "Equivalent viscous damping for modeling inelastic impacts in earthquake pounding problems", Earthq. Eng. Struct. Dyn., 33,897-902. https://doi.org/10.1002/eqe.377.
  4. Anagnostopoulos, S.A. and Spiliopoulos, K.V. (1992), "An investigation of earthquake induced pounding between adjacent buildings", Earthq. Eng. Struct. Dyn., 21, 289-302. https://doi.org/10.1002/eqe.4290210402.
  5. Bamer, F. (2018), "A Hertz-pounding formulation with a nonlinear damping and a dry friction element", Acta Mechanica, https://10.1007/s00707-018-2233-0.
  6. Bamer, F. and Bucher, C. (2012), "Application of the proper orthogonal decomposition for linear and nonlinear structures under transient excitation", Acta Mechanica, 223(12), 2549-2563. https://doi.org/10.1007/s00707-012-0726-9.
  7. Bamer, F. and Markert B. (2018), "A nonlinear visco-elastoplastic model for structural pounding", Earthq. Eng. Struct. Dyn., 229(11), 4485-4494. https://doi:10.1002/eqe.3095.
  8. Bamer, F. and Markert, B. (2017), "An efficient response identification strategy for nonlinear structures subject to nonstationary generated seismic excitations", Mech. Bas. Des. Struct. Mach., 45(3), 313-330. https://doi:10.1080/15397734.2017.131726.
  9. Bamer, F., Kazhemi, A.A. and Bucher, C. (2017), "A new model order reduction strategy adapted to nonlinear problems in earthquake engineering", Earthq. Eng. Struct. Dyn., 46(4), 537-559. https://doi.org/10.1002/eqe.2802.
  10. Bamer, F., Shi, J. and Markert, B. (2017), "Efficient solution of the multiple seismic pounding problem using hierarchical substructure techniques", Comput. Mech., 62(4), 761-782. https://doi: 10.1007/s00466-017-1525-x.
  11. Barbato, M. and Tubaldi, E. (2013), "A probabilistic performancebased approach for mitigating the seismic pounding risk between adjacent buildings", Earthq. Eng. Struct. Dyn., 42, 1203-1219. https://doi.org/10.1002/eqe.2267.
  12. Bathe, K.J. (2006), Finite Element Procedures, Prentice Hall, Pearson Education, Inc.
  13. Bi, K., Hao, H. and Sun, Z. (2018), "3D FEM analysis of earthquake induced pounding responses between asymmetric buildings", Earthq. Struct., 13(4), 377-386. https://doi.org/10.12989/eas.2018.13.4.377.
  14. Boo, S.H., Kim, J.H. and Lee, P.S. (2018), "Towards improving the enhanced Craig-Bampton method", Comput. Struct., 196, 63-75. https://doi.org/10.1016/j.compstruc.2017.10.017.
  15. Chase, G.C., Boyer, F., Rodgers, G.W., Labrosse, G. and MacRae, A. (2014), "Probabilistic risk analysis of structural impact in seismic events for linear and nonlinear systems", Earthq. Eng. Struct. Dyn., 43, 1565-1580. https://doi.org/10.1002/eqe.2414.
  16. Chau, K.T. and Wei, X.X. (2001), "Pounding of structures modelled as non-linear impacts of two oscillators", Earthq. Eng. Struct. Dyn., 30, 633-651. https://doi.org/10.1002/eqe.27.
  17. Chau, K.T., Wei, X.X., Guo, X. and Shen, C.Y. (2003), "Experimental and theoretical simulations of seismic poundings between two adjacent structures", Earthq. Eng. Struct. Dyn., 32, 537-554. https://doi.org/10.1002/eqe.231.
  18. Choi, C.K. and Lee, T.Y. (2003), "Efficient remedy for membrane locking of 4-node flat shell elements by non-conforming modes", Comput. Meth. Appl. Mech. Eng., 192, 1961-1971. https://doi.org/10.1016/S0045-7825(03)00203-2.
  19. Chopra, A.K. (2007), Dynamics of Structures, Theory and Applications to Earthquake Engineering, Third Edition, Prentice Hall, New Jersey.
  20. Craig, R.R. and Bampton, M.C. (1968), "Coupling of substructures for dynamic analyses", AIAA J., 6, 1313-1319. https://doi.org/10.2514/3.4741.
  21. Davis, R.O. (1992), "Pounding of buildings modelled by an impact oscillator", Earthq. Eng. Struct. Dyn., 16, 253-274. https://doi.org/10.1002/eqe.4290210305.
  22. Efraimiadou, S., Hatzigeorgiou, G.D. and Beskos, D.E. (2013), "Structural pounding between adjacent buildings subjected to strong ground motions. Part I: The effect of different structures arrangement", Earthq. Eng. Struct. Dyn., 42(10), 1509-1528. https://doi:10.1002/eqe.2285.
  23. Efraimiadou, S., Hatzigeorgiou, G.D. and Beskos, D.E. (2013), "Structural pounding between adjacent buildings subjected to strong ground motions. Part II: The effect of multiple earthquakes", Earthq. Eng. Struct. Dyn., 42(10), 1529-1545. https://doi:10.1002/eqe.2284.
  24. Ghandil, M. and Aldaikh, H. (2017), "Damage-based seismic planar pounding analysis of adjacent symmetric buildings considering inelastic structure-soil-structure interaction", Earthq. Eng. Struct. Dyn., 46, 1141-1159. https://doi.org/10.1002/eqe.2848.
  25. Jankowski, R. (2005), "Non-linear viscoelastic modeling of earthquake-induced structural pounding", Earthq. Eng. Struct. Dyn., 34, 595-611. https://doi.org/10.1002/eqe.434.
  26. Jankowski, R. (2006), "Analytical expression between the impact damping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding", Earthq. Eng. Struct. Dyn., 35, 517-524. https://doi.org/10.1002/eqe.537.
  27. Jankowski, R. (2009), "Experimental study on earthquake-induced pounding between structural elements made of different building materials", Earthq. Eng. Struct. Dyn., 39, 343-354. https://doi.org/10.1002/eqe.941.
  28. Jankowski, R. and Mahmoud, S. (2016), "Linking of adjacent three-story buildings for mitigation of structural pounding during earthquakes", Bull. Earthq. Eng., 14, 3075-3097. https://doi.org/10.1007/s10518-016-9946-z.
  29. Kasai, K. and Maison, B.F. (1997), "Building pounding damage during the 1989 Loma Prieta earthquake", Eng. Struct., 19, 195-207. https://doi.org/10.1016/S0141-0296(96)00082-X.
  30. Kheyroddin, A., Kioumarsi, M., Kioumarsi, B. and Faraei, A. (2018), "Effect of lateral structural systems of adjacent buildings on pounding force", Earthq. Struct., 14(3), 229-239. https://doi.org/10.12989/eas.2018.14.3.229.
  31. Kim, J.H., Kim, J. and Lee, P.S. (2017), "Improving the accuracy of the dual Craig-Bampton method", Comput. Struct., 191, 22-32. https://doi.org/10.1016/j.compstruc.2017.05.010.
  32. Komodromos, P. (2007), "Simulation of the earthquake-induced pounding of seismically isolated buildings", Comput. Struct., 86, 618-626. https://doi.org/10.1016/j.compstruc.2007.08.001.
  33. Kun, C., Yang, Z. and Chouw, N. (2018), "Seismic response of skewed bridges including pounding effects", Earthq. Struct., 14(5), 467-476. https://doi.org/10.12989/eas.2018.14.5.467.
  34. Laursen, T.A. (2003), Computational Contact and Impact Mechanics, Springer-Verlag Berlin Heidelberg.
  35. Mavronicola, E. and Komodromos, P. (2011), "Assessing the suitability of equivalent linear elastic analysis of seismically isolated multi-storey buildings", Comput. Struct., 89, 1920-1931. https://doi.org/10.1016/j.compstruc.2011.05.010.
  36. Muthukumar, S. and DesRoches, R. (2006), "A Hertz contact model with non-linear damping for pounding simulation", Earthq. Eng. Struct. Dyn., 35, 811-828. https://doi.org/10.1002/eqe.557.
  37. Pantelides, C.P. and Ma, X. (1998), "Linear and nonlinear pounding of structural systems", Comput. Struct., 66, 79-92. https://doi.org/10.1016/S0045-7949(97)00045-X.
  38. Rixen, D.J. (2004), "A dual Craig-Bampton method for dynamic substructuring", J. Comput. Appl. Math., 168, 383-391. https://doi.org/10.1016/j.cam.2003.12.014.
  39. Shi J., Bamer F. and Markert B. (2018), "A structural pounding formulation using systematic modal truncation", Shock Vib., 2018, Article ID 6378085, 15. https://doi:10.1155/2018/6378085.
  40. Tubaldi, E., Freddi, F. and Barbato, M. (2016), "Probabilistic seismic demand model for pounding risk assessment", Earthq. Eng. Struct. Dyn., 45, 1743-1758. https://doi.org/10.1002/eqe.2725.
  41. Wriggers, P. (2006), Computational Contact Mechanics, Second Edition, Springer-Verlag Berlin Heidelberg.
  42. Ye, K., Li, L. and Zhu, H. (2009), "A note on the Hertz contact model with nonlinear damping for pounding simulation", Earthq. Eng. Struct. Dyn., 38, 1135-1142. https://doi.org/10.1002/eqe.883.
  43. Zargar, H., Ryan, K.L., Rawlinson, T.A. and Marshall, J.D. (2017), "Evaluation of a passive gap damper to control displacements in a shaking test of a seismically isolated three-story frame", Earthq. Eng. Struct. Dyn., 46, 51-71. https://doi.org/10.1002/eqe.2771.
  44. Zhang, D., Jia, H., Zheng, S., Xie, W. and Pandey, M.D. (2014), "A highly efficient and accurate stochastic seismic analysis approach for structures under tridirectional nonstationary multiple excitations", Comput. Struct., 145, 23-35. https://doi.org/10.1016/j.compstruc.2014.07.017.
  45. Zucca, S. and Epureanu, B.I. (2017), "Reduced order models for nonlinear dynamic analysis of structures with intermittent contacts", J. Vib. Control, 24(12), 2591-2604. https://doi:10.1177/1077546316689214.