Response Variability and Reliability of Structures

Abstract

Computational methods, such as the finite element method, are nowadays necessary for the analysis and design of large-scale engineering systems. The considerable influence of inherent uncertainties on system behavior has also led the scientific community to recognize the importance of a stochastic approach to engineering problems. Engineering experience has shown that uncertainties are involved not only in the loading but also in the material and geometric properties of engineering systems. The rational treatment of these uncertainties cannot be addressed rigorously in the framework of the traditional deterministic approach. Stochastic methods do provide this possibility at the expense of increasing the complexity of the system model and, consequently, of the required computational effort for the solution of the problem. Therefore, the exploitation of the available computational resources and the development of enhanced solution algorithms are of paramount importance in the application of stochastic methods to real-world problems and to their further dissemination to the engineering community. The problems of response variability and reliability of structures with stochastic properties under dynamic loading are currently the subject of extensive research in the fields of computational stochastic dynamics and earthquake engineering. Both problems deal with the computation of the statistical characteristics of the response (statistical moments, probability of failure), and their solution is time consuming, particularly in the case of large-scale realistic structures. An important practical application of structural response variability and reliability is the estimation of seismic fragility curves used to assess the vulnerability of structures due to earthquakes. Fragility curves provide the probability of exceeding a prescribed level of damage for a wide range of ground motion intensity, usually expressed in terms of peak ground or spectral accelerations. The existing analytical methods for the evaluation of structural response variability and reliability can only be used in few special cases and are not applicable to realistic engineering problems. Therefore, this chapter will be focused on approximate methods and simulation. The first class of methods is mostly based on the approximation of the underlying Fokker–Planck–Kolmogorov equation or of the limit state function, while the second comprises the direct Monte Carlo simulation and its variants. In sections “Response Variability of Stochastic Systems” and “Reliability of