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COMPUTATIONAL ISSUES IN FORM WITH UNIFORM RANDOM VARIABLES

Beck, André. T.;

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The First Order Reliability Method is well accepted as an efficient way to solving structural reliability problems with linear or moderately non-linear limit state functions. High non-linearity is introduced in reliability problems by non-linear mechanical responses, but also by correlation between the random variables and by highly non-Gaussian probability distribution functions. Correlation and non-Gaussian distributions introduce non-linearities in the mapping to the standard Gaussian space, hence making search for the design point more challenging. This article discusses computational issues in finding the design point in problems involving uniform and other bounded random variables. The discussion covers the Principle of Normal Tail Approximation, and the mapping to standard Gaussian space. It addresses three different techniques to impose the domain of bounded random variables, when mapping them back from standard Gaussian to original design space. A simple but challenging academic problem is presented, involving a simply-supported beam subject to a concentrated load of random intensity. The concentrated load can occupy a random position over the beam, following an uniform distribution. Although the underlying mechanical problem is very simple, the uniform distribution introduces severe non-linearities, which makes finding the design point a very demanding task. The article also addresses algorithms that can be used to find the design point in highly non-linear problems. It is shown that the Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm fails to converge. The performance of the improved HRFL (iHLRF) and of the Sequential Quadratic Programming algorithms are investigated with respect to two alternative mappings to standard Gaussian space and to three techniques to impose the bounds in the inverse probability mapping.

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Palavras-chave: structural reliability, FORM, design point, probability mapping, normal tail approximation, standard Gaussian space.,

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DOI: 10.5151/meceng-wccm2012-18315

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Como citar:

Beck, André. T.; "COMPUTATIONAL ISSUES IN FORM WITH UNIFORM RANDOM VARIABLES", p. 1228-1244 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18315

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