Flexibility-based upper bounds on the response variability of simple beams

Papadopoulos, V; Deodatis, G; Papadrakakis, M

dc.contributor.author	Papadopoulos, V	en
dc.contributor.author	Deodatis, G	en
dc.contributor.author	Papadrakakis, M	en
dc.date.accessioned	2014-03-01T01:22:25Z
dc.date.available	2014-03-01T01:22:25Z
dc.date.issued	2005	en
dc.identifier.issn	0045-7825	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16560
dc.subject	Monte Carlo simulation	en
dc.subject	Optimization	en
dc.subject	Stochastic fields	en
dc.subject	Stochastic finite element analysis	en
dc.subject	Upper bounds	en
dc.subject	Variability response function	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Computer simulation	en
dc.subject.other	Elastic moduli	en
dc.subject.other	Mathematical models	en
dc.subject.other	Monte Carlo methods	en
dc.subject.other	Optimization	en
dc.subject.other	Probability distributions	en
dc.subject.other	Random processes	en
dc.subject.other	Brute-force optimization procedure	en
dc.subject.other	Response displacement	en
dc.subject.other	Response variability	en
dc.subject.other	Stochastic field modeling	en
dc.subject.other	Beams and girders	en
dc.subject.other	Monte Carlo simulation	en
dc.subject.other	stochastic method	en
dc.title	Flexibility-based upper bounds on the response variability of simple beams	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cma.2004.06.040	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cma.2004.06.040	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	Spectral- and probability-distribution-free upper bounds on the response variability of both statically determinate and indeterminate beams are established in the present paper based on exact closed-form analytic expressions derived for the variance of the response displacement. A conjecture has to be made in the case of statically indeterminate beams in order to establish these bounds. The conjecture is supported through an argument postulating the existence of an integral form for the variance of the response displacement and through a brute-force optimization procedure providing numerical validation. Such bounds require knowledge of only the variance of the stochastic field modeling the inverse of the elastic modulus and are realizable in the sense that it is possible to fully determine the probabilistic characteristics of the stochastic field (modeling the inverse of the elastic modulus) that produces them. Furthermore, it is possible to fully determine also the corresponding stochastic field modeling the elastic modulus that produces these bounds. These spectral- and probability-distribution-free bounds can also be computed numerically using a so-called fast Monte Carlo simulation procedure that does not require a closed-form analytic expression for the response displacement, making this approach much more general. Numerical examples are provided involving a statically determinate and a statically indeterminate beam. (C) 2004 Published by Elsevier B.V.	en
heal.publisher	ELSEVIER SCIENCE SA	en
heal.journalName	Computer Methods in Applied Mechanics and Engineering	en
dc.identifier.doi	10.1016/j.cma.2004.06.040	en
dc.identifier.isi	ISI:000227483200006	en
dc.identifier.volume	194	en
dc.identifier.issue	12-16	en
dc.identifier.spage	1385	en
dc.identifier.epage	1404	en