Criteria for assessing dynamic collapse of elastoplastic structural systems

Y. Araki, K. D. Hjelmstad

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


Criteria are presented for assessing the propensity for dynamic collapse of elastoplastic structural systems. To detect the onset of dynamic collapse, three key concepts are introduced. First, the equations of motion are linearized and time shifted rel ative to a reference time in a dynamic process. Second, we study the free vibration of the system after the reference time. Third, we use a modal decomposition of the response. We suggest that dynamic collapse is likely if (1) there exist negative eigenvalues of the Hessian of the total potential energy and (2) the direction of motion is consistent with the loading direction of the elastoplastic material. The direction of motion is determined by using the gradient of total potential energy and the eig enmodes corresponding to the negative eigenvalues. The fidelity of the present criteria is demonstrated through numerical examples for which the non-linear equations of motion can be integrated exactly. With the present approach, it becomes apparent that p-delta effects, the tangent stiffness, the internal resistance, and the direction of unloading all play key roles in the dynamic collapse of structures. Copyright (C) 2000 John Wiley and Sons, Ltd.

Original languageEnglish (US)
Pages (from-to)1177-1198
Number of pages22
JournalEarthquake Engineering and Structural Dynamics
Issue number8
StatePublished - 2000
Externally publishedYes


  • Dynamic collapse
  • Elastoplastic structures
  • Geometrical non-linearity
  • Linearization
  • Modal decomposition
  • Time shifting

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Earth and Planetary Sciences (miscellaneous)


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