Introduction to linear and nonlinear programming

http://www.ukm.my/kamal3/psm/pfpstochastics.pdf

The stochastic finite element method: Past, present and future

Reliability-based Optimization is a most appropriate and advantageous methodology for structural design. Its main feature is that it allows determining the best design solution (with respect to prescribed criteria) while explicitly considering the unavoidable effects of uncertainty. In general, the application of this methodology is numerically involved, as it implies the simultaneous solution of an optimization problem and also the use of specialized algorithms for quantifying the effects of uncertainties. In view of this fact, several approaches have been developed in the literature for applying this methodology in problems of practical interest. This contribution provides a survey on approaches for performing Reliability-based Optimization, with emphasis on the theoretical foundations and the main assumptions involved. Early approaches as well as the most recently developed methods are covered. In addition, a qualitative comparison is performed in order to provide some general guidelines on the range of applicability on the different approaches discussed in this contribution.

A survey on approaches for reliability-based optimization

A fully nonstationary stochastic model for strong earthquake ground motion is developed. The model employs filtering of a discretized white-noise process. Nonstationarity is achieved by modulating the intensity and varying the filter properties in time. The formulation has the important advantage of separating the temporal and spectral nonstationary characteristics of the process, thereby allowing flexibility and ease in modeling and parameter estimation. The model is fitted to target ground motions by matching a set of statistical characteristics, including the mean-square intensity, the cumulative mean number of zero-level up-crossings and a measure of the bandwidth, all expressed as functions of time. Post-processing by a second filter assures zero residual velocity and displacement, and improves the match to response spectral ordinates for long periods. Copyright © 2008 John Wiley & Sons, Ltd.

A stochastic ground motion model with separable temporal and spectral nonstationarities

Application of line sampling simulation method to reliability benchmark problems

Tail equivalent linearization method for nonlinear random vibration

Structural reliability software at the University of California, Berkeley

Design-point excitation for non-linear random vibrations

A new approach for computing seismic fragility curves for nonlinear structures for use in performance-based earthquake engineering analysis is proposed. The approach makes use of a recently developed method for nonlinear stochastic dynamic analysis by tail-equivalent linearization. The ground motion is modeled as a discretized stochastic process with a set of parameters that characterizes its evolutionary intensity and frequency content. For each selected response (seismic demand) threshold, a linear system is defined that has the same tail probability as the nonlinear response in first-order approximation. Simple linear random vibration analysis with the tail-equivalent linear system then yields the fragility curve. The approach has the advantage of avoiding the selection and scaling of recorded accelerograms and repeated time-history analyses, which is the current practice for developing fragility curves. Copyright © 2009 John Wiley & Sons, Ltd.

Kazuya Fujimura

Papers

Tail equivalent linearization method for nonlinear random vibration

Structural reliability software at the University of California, Berkeley

Design-point excitation for non-linear random vibrations

Nonlinear stochastic dynamic analysis for performance‐based earthquake engineering