DOI QR코드

DOI QR Code

A family of dissipative structure-dependent integration methods

  • Chang, Shuenn-Yih (Department of Civil Engineering, National Taipei University of Technology) ;
  • Wu, Tsui-Huang (Department of Civil Engineering, National Taipei University of Technology) ;
  • Tran, Ngoc-Cuong (Department of Civil Engineering, National Taipei University of Technology)
  • Received : 2015.04.15
  • Accepted : 2015.07.27
  • Published : 2015.08.25

Abstract

A new family of structure-dependent integration methods is developed to enhance with desired numerical damping. This family method preserves the most important advantage of the structure-dependent integration method, which can integrate unconditional stability and explicit formulation together, and thus it is very computationally efficient. In addition, its numerical damping can be continuously controlled with a parameter. Consequently, it is best suited to solving an inertia-type problem, where the unimportant high frequency responses can be suppressed or even eliminated by the favorable numerical damping while the low frequency modes can be very accurately integrated.

Keywords

Acknowledgement

Supported by : National Science Council

References

  1. Alamatian, J. (2013), "New implicit higher order time integration for dynamic analysis", Struct. Eng. Mech., 48(5), 711-736. https://doi.org/10.12989/sem.2013.48.5.711
  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., 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
  4. Chang, S.Y. (2001a), "Application of the momentum equations of motion to pseudodynamic testing", Phil. Tran. Royal Soc., Series A, 359(1786), 1801-1827. https://doi.org/10.1098/rsta.2001.0874
  5. 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
  6. 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)
  7. Chang, S.Y. (2002b), "Integrated equations of motion for direct integration methods", Struct. Eng. Mech., 13(5), 569-589. https://doi.org/10.12989/sem.2002.13.5.569
  8. Chang, S.Y. (2007), "Improved explicit method for structural dynamics", J. Eng. Mech., ASCE, 133(7), 748760.
  9. Chang, S.Y. (2009), "An explicit method with improved stability property", Int. J. Numer. Meth. Eng., 77(8), 1100-1120. https://doi.org/10.1002/nme.2452
  10. Chang, S.Y. (2010), "A new family of explicit method for linear structural dynamics", Comput. Struct., 88(11-12), 755-772. https://doi.org/10.1016/j.compstruc.2010.03.002
  11. Chang, S.Y. (2014), "A family of non-iterative integration methods with desired numerical dissipation", Int. J. Numer. Meth. Eng., 100(1), 62-86. https://doi.org/10.1002/nme.4720
  12. Chang, S.Y. (2015), "Dissipative, non-iterative integration algorithms with unconditional stability for mildly nonlinear structural dynamics", Nonlin. Dyn., 79(2), 1625-1649. https://doi.org/10.1007/s11071-014-1765-7
  13. Chen, C. and Robinson, A. (1993), "Improved time-history analysis for structural dynamics. I: treatment of rapid variation of excitation and material nonlinearity", J. Eng. Mech., ASCE, 119(12), 2496-2513. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:12(2496)
  14. Chung, J. and Hulbert, G.M. (1993), "A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-a method", J. Appl. Mech., 60(6), 371-375. https://doi.org/10.1115/1.2900803
  15. Gao, Q., Wu, F., Zhang, H.W., Zhong, W.X., Howson W.P. and Williams, F.W. (2012), "A fast precise integration method for structural dynamics problems", Struct. Eng. Mech., 43(1), 1-13. https://doi.org/10.12989/sem.2012.43.1.001
  16. Goudreau, G.L. and Taylor, R.L. (1972), "Evaluation of numerical integration methods in elasto- dynamics", Comput. Meth. Appl. Mech. Eng., 2, 69-97.
  17. Gui, Y., Wang, J.T., Jin, F., Chen, C. and Zhou, M.X. (2014), "Development of a family of explicit algorithms for structural dynamics with unconditional stability", Nonlin. Dyn., 77, 1157-1170. https://doi.org/10.1007/s11071-014-1368-3
  18. Hadianfard, M.A. (2012), "Using integrated displacement method to time-history analysis of steel frames with nonlinear flexible connections", Struct. Eng. Mech., 41(5), 675-689. https://doi.org/10.12989/sem.2012.41.5.675
  19. 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
  20. Hilber, H.M. and Hughes, T.J.R. (1978), "Collocation, dissipation, and 'overshoot' for time integration schemes in structural dynamics", Earthq. Eng. Struct. Dyn., 6, 99-118. https://doi.org/10.1002/eqe.4290060111
  21. Kolay, C. and Ricles, J.M. (2014), "Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation", Earthq. Eng. Struct. Dyn., 43, 1361-1380. https://doi.org/10.1002/eqe.2401
  22. Krenk, S. (2008), "Extended state-space time integration with high-frequency energy dissipation", Int. J. Numer. Meth. Eng., 73, 1767-1787. https://doi.org/10.1002/nme.2144
  23. Lambert, J.D. (1973), Computational Methods in Ordinary Differential Equations, John Wiley, London.
  24. Loh, C.H., Lee, Z.K., Wu, T.C. and Peng, S.Y. (2000), "Ground motion characteristics of the Chi-Chi earthquake of 21 September 1999", Earthq. Eng. Struct. Dyn., 29, 867-897. https://doi.org/10.1002/(SICI)1096-9845(200006)29:6<867::AID-EQE943>3.0.CO;2-E
  25. Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. Div., ASCE, 85, 67-94.
  26. Robinson, A. and Chen, C. (1993), "Improved time-history analysis for structural dynamics. II: reduction of effective number of degrees of freedom", J. Eng. Mech., ASCE, 119(12), 2514-2530. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:12(2514)
  27. Rezaiee-Pajand, M., Sarafrazi, S.R. and Hashemian, M. (2011), "Improving stability domains of the implicit higher order accuracy method", Int. J. Numer. Meth. Eng., 88, 880-896. https://doi.org/10.1002/nme.3204
  28. Rezaiee-Pajand, M. and Sarafrazi, S.R. (2010), "A mixed and multi-step higher-order implicit time integration family", J. Mech. Eng. Sci., 224, 2097-2108. https://doi.org/10.1243/09544062JMES2093
  29. Wood, W.L., Bossak, M. and Zienkiewicz, O.C. (1981), "An alpha modification of Newmark's method", Int. J. Numer. Meth. Eng., 15, 1562-1566.
  30. Zhou, X. and Tamma, K.K. (2006), "Algorithms by design with illustrations to solid and structural mechanics/dynamics", Int. J. Numer. Meth. Eng., 66, 1738-1790. https://doi.org/10.1002/nme.1559

Cited by

  1. Improved formulation for a structure-dependent integration method vol.60, pp.1, 2016, https://doi.org/10.12989/sem.2016.60.1.149
  2. Assessments of dissipative structure-dependent integration methods vol.62, pp.2, 2015, https://doi.org/10.12989/sem.2017.62.2.151
  3. Extended implicit integration process by utilizing nonlinear dynamics in finite element vol.64, pp.4, 2015, https://doi.org/10.12989/sem.2017.64.4.495
  4. Highly accurate family of time integration method vol.67, pp.6, 2015, https://doi.org/10.12989/sem.2018.67.6.603
  5. An effective locally-defined time marching procedure for structural dynamics vol.73, pp.1, 2015, https://doi.org/10.12989/sem.2020.73.1.065
  6. A dissipative family of eigen-based integration methods for nonlinear dynamic analysis vol.75, pp.5, 2015, https://doi.org/10.12989/sem.2020.75.5.541