M.A. Valdebenito

Sensitivity estimation of failure probability applying line sampling

Abstract This contribution presents a framework for calculating a sensitivity measure for problems of computational stochastic mechanics. More specifically, the sensitivity measure considered is the derivative of the failure probability with respect to parameters of the probability distributions (e.g. mean value, standard deviation) associated with the random input quantities of a system’s model. The proposed framework is formulated as a post-processing step of Line Sampling, which is a simulation-based method for estimating small failure probabilities. In particular, the proposed framework comprises two different approaches for estimating the sought sensitivity. The application of the proposed framework and comparison of the two aforementioned approaches is discussed through a number of numerical examples. The results obtained indicate that both approaches allow estimating the sought sensitivity measure.

Optimal Design of Base-Isolated Systems Under Stochastic Earthquake Excitation

The development of a general framework for reliability-based design of base-isolated structural systems under uncertain conditions is presented. The uncertainties about the structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. Nonlinear elements composed by hysteretic devices are used for the isolation system. The optimal design problem is formulated as a constrained minimization problem which is solved by a sequential approximate optimization scheme. First excursion probabilities that account for the uncertainties in the system parameters as well as in the excitation are used to characterize the system reliability. The approach explicitly takes into account all non-linear characteristics of the combined structural system (superstructure-isolation system) during the design process. Numerical results highlight the beneficial effects of isolation systems in reducing the superstructure response.

Approximation Concepts For Fuzzy Structural Analysis

This contribution presents an approach for performing fuzzy structural analysis of linear structures subject to static loading where uncertainties are present in both material properties and loadings. The responses of interest are displacements of the structure. The proposed approach is based on a non-linear approximation of these responses. This non-linear approximation is constructed by taking into account the linearity of the displacements with respect to loading and by introducing intervening variables. In this manner, high quality approximations of the structural responses are obtained allowing to determine membership functions performing a single structural analysis.