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Unconditional stability for explicit pseudodynamic testing

  • Chang, Shuenn-Yih (Department of Civil Engineering, National Taipei University of Technology)
  • Received : 2003.07.18
  • Accepted : 2004.04.27
  • Published : 2004.10.25

Abstract

In this study, a newly developed unconditionally stable explicit method is employed to solve momentum equations of motion in performing pseudodynamic tests. Due to the explicitness of each time step this pseudodynamic algorithm can be explicitly implemented, and thus its implementation is simple when compared to an implicit pseudodynamic algorithm. In addition, the unconditional stability might be the most promising property of this algorithm in performing pseudodynamic tests. Furthermore, it can have the improved properties if using momentum equations of motion instead of force equations of motion for the step-by-step integration. These characteristics are thoroughly verified analytically and/or numerically. In addition, actual pseudodynamic tests are performed to confirm the superiority of this pseudodynamic algorithm.

Keywords

References

  1. Bathe, K.J. and Wilson, E.L. (1973), "Stability and accuracy analysis of direct integration methods", Earthq. Eng. Struct. Dyn., 1, 283-291. https://doi.org/10.1002/eqe.4290010308
  2. Belytschko, T. and Hughes, T.J.R. (1983), Computational Methods for Transient Analysis, Elsevier Science Publishers B.V., North-Holland.
  3. Chang, S.Y. and Mahin, S.A. (1992), "Two new implicit algorithms of pseudodynamic test methods", M. Eng. Thesis, University of California, Berkeley.
  4. Chang, S.Y. (1997), "Improved numerical dissipation for explicit methods in pseudodynamic tests", Earthq. Eng. Struct. Dyn., 26, 917-929. https://doi.org/10.1002/(SICI)1096-9845(199709)26:9<917::AID-EQE685>3.0.CO;2-9
  5. Chang, S.Y. (2001a), "Application of the momentum equations of motion to pseudodynamic testing", Philosophical Transactions of the Royal Society.
  6. Chang, S.Y. (2001b), "Analytical study of the superiority of the momentum equations of motion for impulsive loads", Comput. Struct., 79(15), 1377-1394. https://doi.org/10.1016/S0045-7949(01)00044-X
  7. Chang, S.Y. (2002a), "Explicit pseudodynamic algorithm with unconditional stability", J. Eng. Mech., ASCE, 128(9), 935-947. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:9(935)
  8. Chang, S.Y. (2002b), "Integrated equations of motion for direct integration methods", Struct. Eng. Mech., An Int. J., 13(5), 569-589. https://doi.org/10.12989/sem.2002.13.5.569
  9. Chang, S.Y. (2003), "Accuracy of time history analysis of impulse", J. Struct. Eng., ASCE, 129(3), 357-372. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:3(357)
  10. Chang, S.Y., Tsai, K.C. and Chen, K.C. (1998), "Improved time integration for pseudodynamic tests", Earthq. Eng. Struct. Dyn., 27, 711-730. https://doi.org/10.1002/(SICI)1096-9845(199807)27:7<711::AID-EQE753>3.0.CO;2-6
  11. Clough, R.W. and Penzien, J. (1993), Dynamics of Structures, McGraw-Hill, Inc, International Editions.
  12. Hilber, H.M., Hughes, T.J.R. and Taylor, R.L. (1977), "Improved numerical dissipation for time integration algorithms in structural dynamics", Earthq. Eng. Struct. Dyn., 5, 283-292. https://doi.org/10.1002/eqe.4290050306
  13. Nakashima, M., Kaminosomo, T. and Ishida, M. (1990), "Integration techniques for substructure pseudodynamic test", Proc. of Fourth U.S. National Conf. on Earthq. Eng., 2, 515-524.
  14. Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. Div., ASCE, 67-94.
  15. Shing, P.B. and Mahin, S.A. (1987), "Cumulative experimental errors in pseudodynamic tests", Earthq. Eng. Struct. Dyn., 15, 409-424. https://doi.org/10.1002/eqe.4290150402
  16. Shing, P.B. and Mahin, S.A. (1987), "Elimination of spurious higher-mode response in pseudodynamic tests", Earthq. Eng. Struct. Dyn., 15, 425-445. https://doi.org/10.1002/eqe.4290150403
  17. Shing, P.B. and Mahin, S.A. (1990), "Experimental error effects in pseudodynamic testing", J. Eng. Mech., ASCE, 116, 805-821. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:4(805)
  18. Shing, P.B., Vannan, M.T. and Carter, E. (1991), "Implicit time integration for pseudodynamic tests", Earthq. Eng. Struct. Dyn., 20, 551-576. https://doi.org/10.1002/eqe.4290200605
  19. Strang, G. (1986), Linear Algebra and Its Applications, Harcourt Brace Jovanovich, San Diego.
  20. Thewalt, C.R. and Mahin, S.A. (1995), "An unconditionally stable hybrid pseudodynamic algorithm", Earthq. Eng. Struct. Dyn., 24, 723-731. https://doi.org/10.1002/eqe.4290240508

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