Interaction and multiscale mechanics

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Ellipsoidal bounds for static response of framed structures against interactive uncertainties

  • Kanno, Yoshihiro (Department of Mathematical Informatics, University of Tokyo) ;
  • Takewaki, Izuru (Department of Urban and Environmental Engineering, Kyoto University)
  • Received : 2007.04.13
  • Accepted : 2007.11.05
  • Published : 2008.03.25
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Abstract

This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the $\mathcal{S}$-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.

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References

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Cited by

  1. Semidefinite programming for dynamic steady-state analysis of structures under uncertain harmonic loads vol.198, pp.41-44, 2009, https://doi.org/10.1016/j.cma.2009.06.005