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Shock and Vibration
Volume 20 (2013), Issue 5, Pages 933-950

An Energy-Based Limit State Function for Estimation of Structural Reliability in Shock Environments

Michael A. Guthrie

Analytical Structural Dynamics, Org. 1523, Sandia National Laboratories, MS 0346, P.O. Box 5800, Albuquerque, NM 87185, USA

Received 6 September 2012; Revised 17 December 2012; Accepted 13 April 2013

Copyright © 2013 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


limit state function is developed for the estimation of structural reliability in shock environments. This limit state function uses peak modal strain energies to characterize environmental severity and modal strain energies at failure to characterize the structural capacity. The Hasofer-Lind reliability index is briefly reviewed and its computation for the energy-based limit state function is discussed. Applications to two degree of freedom mass-spring systems and to a simple finite element model are considered. For these examples, computation of the reliability index requires little effort beyond a modal analysis, but still accounts for relevant uncertainties in both the structure and environment. For both examples, the reliability index is observed to agree well with the results of Monte Carlo analysis. In situations where fast, qualitative comparison of several candidate designs is required, the reliability index based on the proposed limit state function provides an attractive metric which can be used to compare and control reliability.