Skip to main content

Optimal Design of Base-Isolated Systems Under Stochastic Earthquake Excitation

  • Chapter
Computational Methods in Stochastic Dynamics

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 26))

Abstract

The development of a general framework for reliability-based design of base-isolated structural systems under uncertain conditions is presented. The uncertainties about the structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. Nonlinear elements composed by hysteretic devices are used for the isolation system. The optimal design problem is formulated as a constrained minimization problem which is solved by a sequential approximate optimization scheme. First excursion probabilities that account for the uncertainties in the system parameters as well as in the excitation are used to characterize the system reliability. The approach explicitly takes into account all non-linear characteristics of the combined structural system (superstructure-isolation system) during the design process. Numerical results highlight the beneficial effects of isolation systems in reducing the superstructure response.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alexandrov, N.M., Dennis, J.E. Jr., Lewis, R.M., Torczon, V.: A trust-region framework for managing the use of approximation models in optimization. Struct. Optim. 15(1), 16–23 (1998)

    Article  Google Scholar 

  2. Anderson, J.G., Hough, S.E.: A model for the shape of fhe Fourier amplitude spectrum of acceleration at high frequencies. Bull. Seismol. Soc. Am. 74(5), 1969–1993 (1984)

    Google Scholar 

  3. Atkinson, G.M., Silva, W.: Stochastic modeling of California ground motions. Bull. Seismol. Soc. Am. 90(2), 255–274 (2000)

    Article  Google Scholar 

  4. Au, S.K., Beck, J.L.: Estimation of small failure probabilities in high dimensions by subset simulation. Probab. Eng. Mech. 16(4), 263–277 (2001)

    Article  Google Scholar 

  5. Baber, T.T., Wen, Y.: Random vibration hysteretic, degrading systems. J. Eng. Mech. Div. 107(6), 1069–1087 (1981)

    Google Scholar 

  6. Boore, D.M.: Simulation of ground motion using the stochastic method. Pure Appl. Geophys. 160(3–4), 635–676 (2003)

    Article  Google Scholar 

  7. Boore, D.M., Joyner, W.B., Fumal, T.E.: Equations for estimating horizontal response spectra and peak acceleration from western North American earthquakes: a summary of recent work. Seismol. Res. Lett. 68(1), 128–153 (1997)

    Article  Google Scholar 

  8. Ceccoli, C., Mazzotti, C., Savoia, M.: Non-linear seismic analysis of base-isolated rc frame structures. Earthquake Eng. Struct. Dyn. 28(6), 633–653 (1999)

    Article  Google Scholar 

  9. Chickermane, H., Gea, H.C.: Structural optimization using a new local approximation method. Int. J. Numer. Methods Eng. 39, 829–846 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chopra, A.K.: Dynamics of Structures: Theory and Applications to Earthquake Engineering. Prentice Hall, New York (1995)

    MATH  Google Scholar 

  11. De Luca, A., Mele, E., Molina, J., Verzeletti, G., Pinto, A.V.: Base isolation for retrofitting historic buildings: evaluation of seismic performance through experimental investigation. Earthquake Eng. Struct. Dyn. 30(8), 1125–1145 (2001)

    Article  Google Scholar 

  12. Der Kiureghian, A.: Analysis of structural reliability under parameter uncertainties. Probab. Eng. Mech. 23(4), 351–358 (2008)

    Article  Google Scholar 

  13. Ditlevsen, O., Madsen, H.O.: Structural Reliability Methods. Wiley, New York (1996)

    Google Scholar 

  14. Fleury, C., Braibant, V.: Structural optimization: a new dual method using mixed variables. Int. J. Numer. Methods Eng. 23(3), 409–428 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  15. Freudenthal, A.M.: Safety and the probability of structural failure. Trans. Am. Soc. Civ. Eng. 121, 1337–1397 (1956)

    Google Scholar 

  16. Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  17. Groenwold, A.A., Etman, L.F.P., Snyman, J.A., Rooda, J.E.: Incomplete series expansion for function approximation. Struct. Multidiscip. Optim. 34(1), 21–40 (2007)

    Article  MathSciNet  Google Scholar 

  18. Groenwold, A.A., Wood, D.W., Etman, L.F.P., Tosserams, S.: Globally convergent optimization algorithm using conservative convex separable diagonal quadratic approximations. AIAA J. 47(11), 2649–2657 (2009)

    Article  Google Scholar 

  19. Haftka, R.T., Gürdal, Z.: Elements of Structural Optimization, 3rd edn. Kluwer Academic, Norwell (1992)

    Book  MATH  Google Scholar 

  20. Jensen, H.A.: Structural optimization of non-linear systems under stochastic excitation. Probab. Eng. Mech. 21(4), 397–409 (2006)

    Article  Google Scholar 

  21. Jensen, H.A., Sepulveda, J.G.: Structural optimization of uncertain dynamical systems considering mixed-design variables. Probab. Eng. Mech. 26(2), 269–280 (2011)

    Article  Google Scholar 

  22. Jensen, H.A., Valdebenito, M.A., Schuëller, G.I., Kusanovic, D.S.: Reliability-based optimization of stochastic systems using line search. Comput. Methods Appl. Mech. Eng. 198(49–52), 3915–3924 (2009)

    Article  MATH  Google Scholar 

  23. Kelly, J.M.: Aseismic base isolation: review and bibliography. Soil Dyn. Earthq. Eng. 5(4), 202–216 (1986)

    Article  Google Scholar 

  24. Kramer, S.L.: Geotechnical Earthquake Engineering. Prentince Hall, New York (2003)

    Google Scholar 

  25. Mavroeidis, G.P., Papageorgiou, A.S.: A mathematical representation of near-fault ground motions. Bull. Seismol. Soc. Am. 93(3), 1099–1131 (2003)

    Article  Google Scholar 

  26. Mokha, A.S., Amin, N., Constantinou, M.C., Zayas, V.: Seismic isolation retrofit of large historic building. J. Struct. Eng. 122(3), 298–308 (1996)

    Article  Google Scholar 

  27. Prasad, B.: Approximation, adaptation and automation concepts for large scale structural optimization. Eng. Optim. 6(3), 129–140 (1983)

    Article  Google Scholar 

  28. Saragoni, G.R., Hart, G.C.: Simulation of artificial earthquakes. Earthquake Eng. Struct. Dyn. 2(3), 249–267 (1974)

    Article  Google Scholar 

  29. Schittkowski, K., Zillober, C., Zotemantel, R.: Numerical comparison of nonlinear programming algorithms for structural optimization. Struct. Optim. 7(1–2), 1–19 (1994)

    Article  Google Scholar 

  30. Taflanidis, A.A.: Robust stochastic design of viscous dampers for base isolation applications. In: Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN), 22–24 June, Rhodes, Greece (2009)

    Google Scholar 

  31. Taflanidis, A.A., Beck, J.L.: Stochastic subset optimization for optimal reliability problems. Probab. Eng. Mech. 23(2–3), 324–338 (2008)

    Article  Google Scholar 

  32. Valdebenito, M.A., Schuëller, G.I.: Efficient strategies for reliability-based optimization involving non linear, dynamical structures. Comput. Struct. 89(19–20), 1797–1811 (2011)

    Article  Google Scholar 

  33. Zou, X.-K., Wang, Q., Li, G., Chan, C.-M.: Integrated reliability-based seismic drift design optimization of base-isolated concrete buildings. J. Struct. Eng. 136(10), 1282–1295 (2010)

    Article  Google Scholar 

Download references

Acknowledgements

This research was partially supported by CONICYT (National Commission for Scientific and Technological Research) under grant 1110061. This support is gratefully acknowledged by the authors.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hector A. Jensen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Jensen, H.A., Valdebenito, M.A., Sepulveda, J.G. (2013). Optimal Design of Base-Isolated Systems Under Stochastic Earthquake Excitation. In: Papadrakakis, M., Stefanou, G., Papadopoulos, V. (eds) Computational Methods in Stochastic Dynamics. Computational Methods in Applied Sciences, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5134-7_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-5134-7_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5133-0

  • Online ISBN: 978-94-007-5134-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics