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This paper summarizes the development of the methods and a computer program to compute the probability of instability of dynamic systems that can be represented by a system of second-order ordinary linear differential equations. Two instability criteria based upon the eigenvalues or Routh-Hurwitz test functions are investigated. Computational methods based on a fast probability integration concept and an efficient adaptive importance sampling method are proposed to perform efficient probabilistic analysis. A numerical example is provided to demonstrate the methods.

The purpose in doing probabilistic structural analysis is to provide the designer with a more realistic ability to assess the importance of uncertainty in the structural response. This paper provides an overview of the methodology and discusses validation of modular structural analysis packages capable of predicting the probabilistic response distribution for key structural variables such as stress, displacement, natural frequencies, buckling loads, transient responses, etc. The structural analysis solution is in terms of the cumulative distribution function (CDF). Probabilistic structural analysis methods (PSAM) can be used to estimate structural safety and reliability, while providing the engineer with information on the confidence that should be given to the predicted behavior.