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Annals of Solid and Structural Mechanics

, Volume 11, Issue 1–2, pp 11–24 | Cite as

2D dynamic and earthquake response analysis of base isolation systems using a convex optimization framework

  • Nicholas D. OlivetoEmail author
  • Anastasia Athanasiou
Original Article
  • 42 Downloads

Abstract

A formulation is presented for the 2D dynamic analysis and earthquake response simulation of base isolation systems. The approach is force-based and consists of casting the computation in each time increment as a convex optimization problem. Interaction between the two horizontal components of response is considered in an elegant and simple way through yield functions appearing as constraints of the optimization problem. Numerical examples are carried out to illustrate the approach. These comprise bidirectional shearing of a high damping rubber bearing and earthquake simulations of a real-world base isolation system.

Keywords

Nonlinear dynamics Seismic isolation Convex optimization 

Notes

Acknowledgements

The authors gratefully acknowledge financial support by ReLUIS (Italian National Network of University Earthquake Engineering Laboratories), ‘Project D.P.C-ReLUIS 2014–2018’.

Compliance with ethical standards

Conflict of interest

All authors have read and approved submission of the manuscript. The manuscript has not been published nor is it being considered for publication by other journals. The authors declare that they have no conflict of interest.

References

  1. 1.
    Markou AA, Oliveto ND, Athanasiou A (2017) Modelling of high damping rubber bearings. In: Sextos A, Manolis G (eds) Dynamic response of infrastructures to environmentally induced loads. Lecture notes in civil engineering, vol 2. Springer, ChamGoogle Scholar
  2. 2.
    Calvi PM, Calvi GM (2018) Historical development of friction-based seismic isolation systems. Soil Dyn Earthq Eng 106:14–30CrossRefGoogle Scholar
  3. 3.
    Grant DN, Fenves GL, Whittaker AS (2004) Bidirectional modeling of high-damping rubber bearings. J Earthq Eng 8(S1):161–185Google Scholar
  4. 4.
    Park YJ, Wen YK, Ang AHS (1986) Random vibration of hysteretic systems under bi-directional ground motions. Earthq Eng Struct Dyn 14:543–557CrossRefGoogle Scholar
  5. 5.
    Kumar M, Whittaker AS, Constantinou MC (2014) An advanced numerical model of elastomeric seismic isolation bearings. Earthq Eng Struct Dyn 43(13):1955–1974CrossRefGoogle Scholar
  6. 6.
    Oliveto ND, Markou AA, Athanasiou A (2019) Modeling of high damping rubber bearings under bidirectional shear loading. Soil Dyn Earthq Eng 118:179–190CrossRefGoogle Scholar
  7. 7.
    Bouc R (1971) Modele mathematique d’hysteresis. Acustica 24:16–25zbMATHGoogle Scholar
  8. 8.
    Wen Y (1976) Method for random vibration of hysteretic systems. J Eng Mech Div ASCE 102(2):249–263Google Scholar
  9. 9.
    Hwang J, Wu J, Pan TC, Yang G (2002) A mathematical hysteretic model for elastomeric isolation bearings. Earthq Eng Struct Dyn 31(4):771–789CrossRefGoogle Scholar
  10. 10.
    Vaiana N, Sessa S, Marmo F, Rosati L (2018) A class of uniaxial phenomenological models for simulating hysteretic phenomena in rate-independent mechanical systems and materials. Nonlinear Dyn 93(3):1647–1669CrossRefGoogle Scholar
  11. 11.
    Vaiana N, Sessa S, Marmo F, Rosati L (2019) An accurate and computationally efficient uniaxial phenomenological model for steel and fiber reinforced elastomeric bearings. Compos Struct 211:196–212CrossRefGoogle Scholar
  12. 12.
    Abe M, Yoshida J, Fujino Y (2004) Multiaxial behaviors of laminated rubber bearings and their modeling. I: experimental study. J Struct Eng 130:1119–1132CrossRefGoogle Scholar
  13. 13.
    Yamamoto M, Minewaki S, Yoneda H, Higashino M (2012) Nonlinear behavior of high-damping rubber bearings under horizontal bidirectional loading: full-scale tests and analytical modeling. Earthq Eng Struct Dyn 41:1845–1860CrossRefGoogle Scholar
  14. 14.
    Chopra AK (2012) Dynamics of structures: theory and applications to earthquake engineering. Prentice Hall, New JerseyGoogle Scholar
  15. 15.
    Nagarajaiah S, Reinhorn AM, Constantinou MC (1991) Nonlinear dynamic analysis of 3-D base-isolated structures. J Struct Eng ASCE 117(7):2035–2054CrossRefGoogle Scholar
  16. 16.
    Greco F, Luciano R, Serino G, Vaiana N (2018) A mixed explicit-implicit time integration approach for nonlinear analysis of base-isolated structures. Ann Solid Struct Mech 10(1–2):17–29CrossRefGoogle Scholar
  17. 17.
    Boyd SP, Vandenberghe L (2004) Convex optimization. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  18. 18.
    Nocedal J, Wright SJ (2006) Numerical optimization, 2nd edn. Springer, New YorkzbMATHGoogle Scholar
  19. 19.
    Kanno Y (2011) Nonsmooth mechanics and convex optimization. CRC Press, Boca RatonCrossRefGoogle Scholar
  20. 20.
    Cohn MZ, Maier G, Grierson DE (1979) Engineering plasticity by mathematical programming. In: Proceedings of the NATO Advanced Study Institute, University of Waterloo, Waterloo, Canada, 2–12 August 1977. Pergamon Press. New YorkGoogle Scholar
  21. 21.
    Maier GA (1970) Matrix structural theory of piecewise linear elastoplasticity with interacting yield planes. Meccanica 5(1):54CrossRefGoogle Scholar
  22. 22.
    Sivaselvan MV, Lavan O, Dargush GF, Kurino H, Hyodo Y, Fukuda R, Sato K, Apostolakis G, Reinhorn AM (2009) Numerical collapse simulation of large-scale structural systems using an optimization-based algorithm. Earthq Eng Struct Dyn 38(5):655–677CrossRefGoogle Scholar
  23. 23.
    Sivaselvan MV (2011) Complementarity framework for non-linear dynamic analysis of skeletal structures with softening hinges. Int J Numer Meth Eng 86:182–223MathSciNetCrossRefGoogle Scholar
  24. 24.
    Oliveto ND, Sivaselvan MV (2011) Dynamic analysis of tensegrity structures using a complementarity framework. Comput Struct 89:2471–2483CrossRefGoogle Scholar
  25. 25.
    Halphen B, Nguyen Quoc S (1975) Sur les materiaux standard generalises. Journal de Mecanique 14(1):39zbMATHGoogle Scholar
  26. 26.
    Mielke A (2006) A mathematical framework for generalized standard materials in the rate-independent case. In: Multifield problems in solid and fluid mechanics. Springer, Berlin, pp 399–428Google Scholar
  27. 27.
    Architectural Institute of Japan (AIJ) (2016) Design recommendations for seismically isolated buildings. Committee for Seismically Isolated Structures, JapanGoogle Scholar
  28. 28.
    Rockafellar RT (1970) Convex analysis. Princeton University Press, PrincetonCrossRefGoogle Scholar
  29. 29.
    Hiriart-Urruty JB, Lemarechal C (1993) Convex analysis and minimization algorithms. Grundlehren der Mathematischen Wissenschaften. Springer, Berlin, pp 305–306CrossRefGoogle Scholar
  30. 30.
    Sivaselvan MV, Reinhorn AM (2006) Lagrangian approach to structural collapse simulation. J Eng Mech (ASCE) 132(8):795–805CrossRefGoogle Scholar
  31. 31.
    MATLAB Release (2011a) The MathWorks, Inc. Natick, MA, United States (2011)Google Scholar
  32. 32.
    Mehrotra S (1992) On the implementation of a primal-dual interior point method. SIAM J Optim 2:575–601MathSciNetCrossRefGoogle Scholar
  33. 33.
    Byrd RH, Gilbert JC, Nocedal J (2000) A trust region method based on interior point techniques for nonlinear programming. Math Program 89(1):149–185MathSciNetCrossRefGoogle Scholar
  34. 34.
    Byrd RH, Hribar ME, Nocedal J (1999) An interior point algorithm for large-scale nonlinear programming. SIAM J Optim 9(4):877–900MathSciNetCrossRefGoogle Scholar
  35. 35.
    Waltz RA, Morales JL, Nocedal J, Orban D (2006) An interior algorithm for nonlinear optimization that combines line search and trust region steps. Math Program 107(3):391–408MathSciNetCrossRefGoogle Scholar
  36. 36.
    Oliveto G, Granata M, Buda G, Sciacca P (2004) Preliminary results from full-scale free vibration tests on a four story reinforced concrete building after seismic rehabilitation by base isolation. In: JSSI 10th anniversary symposium on performance of response controlled buildings, Yokohama, JapanGoogle Scholar
  37. 37.
    Oliveto ND, Scalia G, Oliveto G (2008) Dynamic identification of structural systems with viscous and friction damping. J Sound Vib 318:911–926CrossRefGoogle Scholar
  38. 38.
    Oliveto ND, Scalia G, Oliveto G (2010) Time domain identification of hybrid base isolation systems using free vibration tests. Earthq Eng Struct Dyn 39:1015–1038Google Scholar
  39. 39.
    Athanasiou A, De Felice M, Oliveto G, Oliveto PS (2011) Evolutionary algorithms for the identification of structural systems in earthquake engineering. In: Proceedings of International Conference on Evolutionary Computation Theory and Applications (ECTA 11), FranceGoogle Scholar
  40. 40.
    Athanasiou A, De Felice M, Oliveto G, Oliveto PS (2013) Dynamical modeling and parameter identification of seismic isolation systems by evolution strategies. In: Studies in computational intelligence, vol 465. Springer, Berlin, pp 101–18CrossRefGoogle Scholar
  41. 41.
    Oliveto G, Athanasiou A, Oliveto ND (2012) Analytical earthquake response of 1D hybrid base isolation systems. Soil Dyn Earthq Eng 43:1–15CrossRefGoogle Scholar
  42. 42.
    Oliveto G, Oliveto ND, Athanasiou A (2014) Constrained optimization for 1-D dynamic and earthquake response analysis of hybrid base-isolation systems. Soil Dyn Earthq Eng 67:44–53CrossRefGoogle Scholar
  43. 43.
    Markou AA, Oliveto G, Mossucca A, Ponzo FC (2014) Laboratory experimental tests on elastomeric bearings from the Solarino project. Task 1.1. report, WP1 Isolamento Sismico: Rapporto tecnico prove sperimentali progetto JETBIS e prove/analisi su isolatori elastomerici. DPC-ReLUIS project, pp 159–192Google Scholar
  44. 44.
    SAP2000. Computers and Structures, Inc. Walnut Creek, CA, United StatesGoogle Scholar
  45. 45.
    Oliveto G, Athanasiou A, Marino G, Granata M, Markou AA, Oliveto ND (2016) Adeguamento sismico degli edifici di Solarino. Prodotto finale del WP1: Progettazione di strutture sismicamente isolate. DPC-ReLUIS project, pp 15–77Google Scholar
  46. 46.
    Thompson ACT (1998) High damping rubber seismic isolation bearings—behavior and design implications. CE299 report, University of California, BerkeleyGoogle Scholar
  47. 47.
    Morgan TA (2000) Characterization and seismic performance of high-damping rubber isolation bearings. CE299 report, University of California, BerkeleyGoogle Scholar
  48. 48.
    Huang WH (2002) Bi-directional testing, modeling, and system response of seismically isolated bridges. Ph.D. Thesis, University of California, BerkeleyGoogle Scholar
  49. 49.
    Presidenza del Consiglio Superiore dei Lavori Pubblici—Servizio Tecnico Centrale (1998) Linee Guida per Progettazione, Esecuzione e Collaudo di Strutture Isolate dal SismaGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil and Architectural EngineeringUniversity of CataniaCataniaItaly
  2. 2.Department of Building, Civil and Environmental EngineeringConcordia UniversityMontrealCanada

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