Structural Engineering and Mechanics

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Integrated equations of motion for direct integration methods

  • Chang, Shuenn-Yih (National Center for Research on Earthquake Engineering, National Taiwan University)
  • Received : 2000.04.07
  • Accepted : 2002.03.06
  • Published : 2002.05.25
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Abstract

In performing the dynamic analysis, the step size used in a step-by-step integration method might be much smaller than that required by the accuracy consideration in order to capture the rapid chances of dynamic loading or to eliminate the linearization errors. It was first found by Chen and Robinson that these difficulties might be overcome by integrating the equations of motion with respect to time once. A further study of this technique is conducted herein. This include the theoretical evaluation and comparison of the capability to capture the rapid changes of dynamic loading if using the constant average acceleration method and its integral form and the exploration of the superiority of the time integration to reduce the linearization error. In addition, its advantage in the solution of the impact problems or the wave propagation problems is also numerically demonstrated. It seems that this time integration technique can be applicable to all the currently available direct integration methods.

Keywords

Acknowledgement

Supported by : National Science Council, Taiwan

References

  1. Bathe, K.J. and Wilson, E.L. (1973). "Stability and accuracy analysis of direct integration methods", Earthq.Eng. and Struct. Dyn., 1, 283-291.
  2. Bathe, K.J. (1982). Finite Element Procedures in Engineering Analysis, Prentice-Hall, Inc., Englewood Cliffs,New Jersey.
  3. Belytschko, T. and Hughes, T.J.R. (1983). Computational Methods for Transient Analysis, Elsevier SciencePublishers B.V., North-Holland.
  4. Chang, S.Y. (1994). "Improved dynamic analysis for linear and nonlinear systems", Ph.D. Thesis, Department ofCivil Engineering, University of Illinois, Urbana-Champaign.
  5. Chang, S.Y. (1996). "A series of energy conserving algorithms for structural dynamics", J. Chinese Inst. Eng.,19(2).
  6. Chang, S.Y., Tsai, K.C. and Chen, K.C. (1998). "Improved time integration for pseudo-dynamic tests", Earthq.Eng. and Struct. Dyn., 27, 711-730. https://doi.org/10.1002/(SICI)1096-9845(199807)27:7<711::AID-EQE753>3.0.CO;2-6
  7. Chang, S.Y. (1996). "The smoothing effect in structural dynamics and pseudodynamic tests", NCREE Report,NCREE-96-008, National Center for Research on Earthquake Engineering. Taipei, Taiwan, Republic of China.
  8. Chen, C.C. and Robinson, A.R. (1993). "Improved time history analysis for structural dynamics. I: Treatment ofrapid variation of excitation and material nonlinearity", J. Eng. Mech., 119(12), 2496-2513. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:12(2496)
  9. Clough, R.W. and Penzien, J. (1967). Dynamics of Structures, McGraw-Hill, New York.
  10. Hilber, H.M., Hughes, T.J.R. and Taylor, R.L. (1977). "Improved numerical dissipation for time integrationalgorithms in structural dynamics", Earthq. Eng. and Struct. Dyn., 5, 283-292. https://doi.org/10.1002/eqe.4290050306
  11. Houbolt, J.C. (1950). "A recurrence matrix solution for the dynamic response of elastic aircraft", J. AeronauticalSci., 17, 540-550. https://doi.org/10.2514/8.1722
  12. Hughes, T.J.R. (1987). The Finite Element Method, Prentice-Hall, Inc., Englewood Cliffs, N.J.
  13. Newmark, N.M. (1959). "A method of computation for structural dynamics", J. Eng. Mech. Div., ASCE, 85, 67-94.
  14. Park, K.C. (1975). "An improved stiffly stable method for direct integration of nonlinear structural dynamicequations", J. Appl. Mech., 42, 464-470. https://doi.org/10.1115/1.3423600
  15. Shing, P.B. and Mahin, S.A. (1984). "Pseudodynamic method for seismic performance testing: theory andimplementation", UCB/EERC-84/01, Earthquake Engineering Research Center, University of California,Berkeley, CA.
  16. Shing, P.B. and Mahin, S.A. (1987). "Cumulative experimental errors in pseudo-dynamic tests", Earthq. Eng.and Struct. Dyn., 15, 409-424. https://doi.org/10.1002/eqe.4290150402
  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. Strang, G. (1986). Linear Algebra and Its Applications, Harcourt Brace Jovanovich, San Diego.
  19. Zienkiewicz, O.C. (1977). The Finite Element Methods, McGraw-Hill Book Company, UK.
  20. Zienkiewicz, O.C. (1977). "A new look at the Newmark, Houbolt and other time stepping formulas. A weightedresidual approach", Earthq. Eng. and Struct. Dyn., 5, 413-418. https://doi.org/10.1002/eqe.4290050407

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