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Robustness is formulated as a multiobjective optimization problem in which both the mean and variance of a conventional objective function are minimized simultaneously. Optimal Pareto fronts are obtained and results show a significant improvement in performance stability compared to a standard conventional solution. Möller, Quiroz, Rubinstein and Foschi (Chapter 34) present an efficient methodology for performing performance-based design in earthquake engineering. They take into account various structural and ground motion uncertainties in optimizing design parameters, satisfying multiple performance criteria with target reliabilities and minimizing an objective.

2 Fir s t ord e r r e l i a b i l i t y m e t h o d The first order reliability method (FORM) is an approximate method for assessing the reliability of a structural system. Its basic assumption is to approximate the limit state function (g(Txθ (x)) = 0) of the structural reliability problem by means of a hyperplane which is orthogonal to the design point vector; note that this approximation is constructed in the standard normal space. e. PF ≈ Pˆ F = (−|x∗ |) = (−β) (5) In equation 5, (·) is the standard normal cumulative density function.

Vielma Professor Lisandro Alvarado University, Departamento de Ingeniería Estructural, Decanato de Ingeniería Civil Av. La Salle entre Av. Las Industrias y Av. gr LIII Part 1 Computational Structural Dynamics Chapter 1 Computational stochastic dynamics – some lessons learned Gerhart I. Schuëller University of Innsbruck, Innsbruck, Austria ABSTRACT: This contribution discusses some of the lessons learned in computational stochastic dynamics. Among them is the role of the design point for calculating failure probabilities of systems involving a large number of random variables and structural non linearities.

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