Advertisement

Stability of an explicit time-integration algorithm for hybrid tests, considering stiffness hardening behavior

  • Tao Wang
  • Huimeng Zhou
  • Xipeng Zhang
  • Tianran Ran
Technical Paper
  • 4 Downloads

Abstract

An explicit unconditionally stable algorithm for hybrid tests, which is developed from the traditional HHT-α algorithm, is proposed. The unconditional stability is first proven by the spectral radius method for a linear system. If the value of α is selected within [-0.5, 0], then the algorithm is shown to be unconditionally stable. Next, the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system. The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening. To improve the stability of the proposed method, the structure stiffness is then identified and updated. Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.

Keywords

explicit integration algorithm unconditional stability HHT-α algorithm stiffness identification root locus method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgment

This research is funded by the Scientific Research Fund of the Institute of Engineering Mechanics, CEA (2017A02, 2016B09, 2016A06), the National Sciencetechnology Support Plan Projects (2015BAK17B02), and the National Natural Science Foundation of China (51378478, 51408565, 51678538, 51161120360). Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors, and do not necessarily reflect the views of the sponsors.

References

  1. Bathe KJ and Wison EL (1973), “Stability and Accuracy Analysis of Direct Integration Methods,” Earthquake Engineering and Structural Dynamics, 1: 283–291.CrossRefGoogle Scholar
  2. Bursi OS, Jia C, Vulcan L, Neild SA and Wagg DJ (2011), “Rosenbrock-Based Algorithms and Subcycling Strategies for Real-Time Nonlinear Substructure Testing,” Earthquake Engineering and Structural Dynamics, 40: 1–19.CrossRefGoogle Scholar
  3. Chang SY (2007a), “Improved Explicit Method for Structural Dynamics,” Journal of Engineering Mechanics ASCE, 133(7): 748–760.CrossRefGoogle Scholar
  4. Chang SY (2007b), “Enhanced, Unconditionally Stable, Explicit Pseudodynamic Algorithm,” Journal of Engineering Mechanics, 133(5): 541–554.CrossRefGoogle Scholar
  5. Chen C and Ricles JM (2008), “Stability Analysis of Direct Integration Algorithms Applied to Nonlinear Structural Dynamics,” Journal of Engineering Mechanics, 134(9): 703–711.CrossRefGoogle Scholar
  6. Chen C and Ricles MJ (2012a), “Analysis of Implicit HHT-α Integration Algorithm for Real-Time Hybrid Simulation,” Earthquake Engineering & Structural Dynamics, 41(5): 1021–1041.CrossRefGoogle Scholar
  7. Chen C and Ricles MJ (2012b), “Large-Scale Real-Time Hybrid Simulation Involving Multiple Experimental Substructures and Adaptive Actuator Delay Compensation,” Earthquake Engineering & Structural Dynamics, 41(3): 549–569.CrossRefGoogle Scholar
  8. Chen C, Ricles MJ, Karavasilis TL, Chae Y and Sause R (2012), “Evaluation of a Real-Time Hybrid Simulation System for Performance Evaluation of Structures with Rate Dependent Devices Subjected to Seismic Loading,” Engineering Structures, 35: 71–82.CrossRefGoogle Scholar
  9. Chi F, Wang J and Jin F (2010), “Delay-Dependent Stability and Added Damping of SDOF Real-Time Dynamic Hybrid Testing,” Earthquake Engineering and Engineering Vibration, 9(3): 425–438.CrossRefGoogle Scholar
  10. Chung W and Campbell SD (2007), “Implicit Pseudodynamic Algorithm with an Event-to-Event Solution Scheme,” Engineering Structures, 29(4): 640–648.CrossRefGoogle Scholar
  11. Elkhoraibi T and Mosalam KM (2007), “Towards Error-Free Hybrid Simulation Using Mixed Variables,” Earthquake Engineering and Structural Dynamics, 36(11): 1497–1522.CrossRefGoogle Scholar
  12. Fan J, Lin T and Wei J (2007), “Response and Protection of the Impact of Base-Friction-Isolated Structures and Displacement-Constraint Devices under Near-Fault Earthquakes,” China Civil Engineering Journal, 40(5): 10–16. (in Chinese)Google Scholar
  13. Franklin GF, Powell JD and Naeini AE (2002), Feedback Control of Dynamic System (4th Ed). Prentice-Hall, EnglewoodGoogle Scholar
  14. Cliffs, N.J. Gui Y, Wang J, Jin F, Chen C and Zhou M (2014), “Development of a Family of Explicit Algorithms for Structural Dynamics with Unconditional Stability,” Nonlinear Dynamics, 77(4): 1157–1170.CrossRefGoogle Scholar
  15. Hilber HM, Hughes TJR and Taylor RL (1977), “Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics,” Earthquake Engineering and Structural Dynamics, 5: 283–92.CrossRefGoogle Scholar
  16. Hung CC and Sherif ET (2009), “A Method for Estimating Specimen Tangent Stiffness for Hybrid Simulation,” Earthquake Engineering and Structural Dynamics, 38(1): 115–134.CrossRefGoogle Scholar
  17. Jung RY and Shing PB (2006), “Performance Evaluation of a Real-Time Pseudodynamic Test System,” Earthquake Engineering and Structural Dynamics, 35: 789–810.CrossRefGoogle Scholar
  18. Li Y, Wu B and Ou J (2006), “Stability of Average Acceleration Method for Structures with Nonlinear Damping,” Earthquake Engineering and Engineering Vibration, 5(1): 87–92.CrossRefGoogle Scholar
  19. Liu Y, Goorts K, Ashasi-Sorkhabi A, Mercan O and Narasimhan S (2016), “A State Space-Based Explicit Integration Method for Real-Time Hybrid Simulation,” Structural Control & Health Monitoring, 23(4): 641–658.CrossRefGoogle Scholar
  20. Nakashima M, Kato H and Takaoka E (1992), “Development of Real-Time Pseudo Dynamic Testing,” Earthquake Engineering and Structural Dynamics, 21(1): 79–92.CrossRefGoogle Scholar
  21. Newmark NM (1959), “A Method of Computation for Structural Dynamics,” Journal of the Engineering Mechanics Division, 85(1): 67–94.Google Scholar
  22. Ou G, Prakash A and Dyke S (2015), “Modified Runge-Kutta Integration Algorithm for Improved Stability and Accuracy in Real Time Hybrid Simulation,” Journal of Earthquake Engineering, 19(7): 1–28.CrossRefGoogle Scholar
  23. Pan P, Tada M and Nakashima M (2005), “Online Hybrid Test by Internet Linkage of Distributed Test-Analysis Domains,” Earthquake Engineering and Structural Dynamics, 34: 1407–1425.CrossRefGoogle Scholar
  24. Shing PB (1991), “Implicit Time Integration for Pseudodynamic Tests,” Earthquake Engineering and Structural Dynamics, 20: 551–576.CrossRefGoogle Scholar
  25. Shing PB, Nakashima M and Bursi OS (1996), “Application of Pseudodynamic Test Method to Structural Sesearch,” Earthquake Spectra, 12(1): 29–56.CrossRefGoogle Scholar
  26. Shojaee S, Rostami S and Abbasi A (2015), “An Unconditionally Stable Implicit Time Integration Algorithm: Modified Quartic B-Spline Method,” Computers & Structures, 153 (C): 98–111.CrossRefGoogle Scholar
  27. Takanashi K, Udagawa K, Seki M, Okada T and Tanaka H (1975), “Non-Linear Earthquake Response Analysis of Structures by a Computer-Actuator on-Line System,” Transactions of the Architectural Institute of Japan, 229: 77–83.CrossRefGoogle Scholar
  28. Wallace MI, Sieber J, Neild SA, et al (2005), “Stability Analysis of Real-Time Dynamic Substructuring Using Delay Differential Equation Models,” Earthquake Engineering and Structural Dynamics, 34(15): 1817–1832.CrossRefGoogle Scholar
  29. Wang T, Nakashima M and Pan P (2006), “On-Line Hybrid Test Combining with General-Purpose Finite Element Software,” Earthquake Engineering and Structural Dynamics, 35(12): 1471–1488.CrossRefGoogle Scholar
  30. Wang J, Lu L and Zhu F (2018), “Efficiency Analysis of Numerical Integrations for Finite Element Substructure in Real-Time Hybrid Simulation,” Earthquake Engineering and Engineering Vibration, 17(1): 73–86.CrossRefGoogle Scholar
  31. Wilson EL (1968), “A Computer Program for the Dynamic Stress Analysis of Underground Structure,” SEL Report 68–1 University of California, Berkeley, C.A.Google Scholar
  32. Wu B, Bao H, Ou J and Tian S (2005), “Stability and Accuracy Analysis of the Central Difference Method for Real-Time Substructure Testing,” Earthquake Engineering and Structural Dynamics, 34(7): 705–718.CrossRefGoogle Scholar
  33. Wu B, Wang QY, Shing PB and Ou J (2007), “Equivalent Force Control Method for Generalized Real-Time Substructure Testing with Implicit Integration,” Earthquake Engineering and Structural Dynamics, 36: 1127–1149.CrossRefGoogle Scholar
  34. Zhou H, D Wagg and Wang T (2018), “Velocity Plus Displacement Equivalent Force Control for Real-Time Substructure Testing,” Earthquake Engineering and Engineering Vibration, 17(1): 1–16.CrossRefGoogle Scholar
  35. Zhu F, Wang J, Jin F, et al (2014), “Simulation of Large-Scale Numerical Substructure in Real-Time Dynamic Hybrid Testing,” Earthquake Engineering and Engineering Vibration, 13(4): 599–609.CrossRefGoogle Scholar
  36. Zhu F, Wang J, Jin F, et al (2015), “Stability Analysis of MODF Real-Time Dynamic Hybrid Testing Systems Using the Discrete-Time Root Locus Technique,” Earthquake Engineering and Structural Dynamics, 44: 221–241.CrossRefGoogle Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Tao Wang
    • 1
  • Huimeng Zhou
    • 1
  • Xipeng Zhang
    • 1
  • Tianran Ran
    • 1
  1. 1.Key Laboratory of Earthquake Engineering and Engineering VibrationInstitute of Engineering Mechanics, CEAHarbinChina

Personalised recommendations