Earthquake Engineering and Engineering Vibration

, Volume 16, Issue 4, pp 745–759 | Cite as

Evaluation of integration methods for hybrid simulation of complex structural systems through collapse

  • Maikol Del Carpio R.
  • M. Javad Hashemi
  • Gilberto Mosqueda
Special Section: State-of-the-Art of Hybrid Testing Method


This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration (iterative) and the operator-splitting (non-iterative) is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom (SDOF) cantilever column with replaceable steel coupons that provides repeatable highlynonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1:2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model of a 1:2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.


Hybrid simulation collapse integration methods unbalance forces stability and accuracy numerical errors 


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This work was primarily supported by the National Science Foundation (NSF) under grant CMMI-0748111 with additional support from the NEES equipment at the University at Buffalo supported by NSF. This support is gratefully acknowledged. Any opinions, findings, and conclusion or recommendation expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.


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Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Maikol Del Carpio R.
    • 1
  • M. Javad Hashemi
    • 2
  • Gilberto Mosqueda
    • 3
  1. 1.KPFF Consulting EngineersLos AngelesUSA
  2. 2.Faculty of Science, Engineering and TechnologySwinburne University of TechnologyMelbourneAustralia
  3. 3.Department of Structural EngineeringUniversity of CaliforniaSan DiegoUSA

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