Response variability of stochastic frame structures using evolutionary field theory

Papadopoulos, V; Deodatis, G

dc.contributor.author	Papadopoulos, V	en
dc.contributor.author	Deodatis, G	en
dc.date.accessioned	2014-03-01T01:25:05Z
dc.date.available	2014-03-01T01:25:05Z
dc.date.issued	2006	en
dc.identifier.issn	0045-7825	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17533
dc.subject	Monte Carlo simulation	en
dc.subject	Non-homogeneous 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	Evolutionary algorithms	en
dc.subject.other	Finite element method	en
dc.subject.other	Integral equations	en
dc.subject.other	Mathematical models	en
dc.subject.other	Monte Carlo methods	en
dc.subject.other	Probability distributions	en
dc.subject.other	Random processes	en
dc.subject.other	Non-homogeneous stochastic fields	en
dc.subject.other	Spectral density function	en
dc.subject.other	Stochastic finite element analysis	en
dc.subject.other	Upper bounds	en
dc.subject.other	Variability response function (VRF)	en
dc.subject.other	Structural frames	en
dc.subject.other	finite element method	en
dc.subject.other	stochastic method	en
dc.title	Response variability of stochastic frame structures using evolutionary field theory	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cma.2005.04.003	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cma.2005.04.003	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	The integral form for the variance of the response of stochastic statically indeterminate structural systems involving the so-called variability response function (VRF) and the spectral density function of the stochastic field modelling the uncertain system properties is established for the first time in this paper using evolutionary spectra theory. The VRF is a function depending on deterministic parameters related to the geometry, boundary conditions, (mean) material properties and loading of the structural system. No approximations are involved in the derivation of the integral form. However, a conjecture has to be made that is validated using Monte Carlo simulations. The uncertain system property considered is the inverse of the elastic modulus (flexibility). Closed-form expressions can be derived in principle for the VRF of any statically determinate or indeterminate frame system using a flexibility-based formulation. Alternatively, a fast Monte Carlo simulation approach is provided to numerically evaluate the VRF. It is shown in closed-form and numerically that the VRF for statically indeterminate structures is a function of the standard deviation sigma(ff) of the stochastic field modeling the inverse of the elastic modulus. Although the VRF depends on sigma(ff), it appears to be independent of the functional form of the spectral density function of the stochastic field modeling the uncertain system properties. For statically determinate structures, the VRF is independent of sigma(ff). The integral form can be used to compute the variance of the system response as well as its upper bound with minimal computational effort. It also provides an excellent insight into the mechanisms controlling the response variability. The upper bounds for the response variance are spectral- and probability-distribution-free requiring knowledge of only the variance of the inverse of the elastic modulus. The proposed bounds are realizable in the sense that it is possible to determine the probabilistic characteristics of the stochastic field that produces them. Several numerical examples are provided demonstrating the capabilities of the methodology. (c) 2005 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE SA	en
heal.journalName	Computer Methods in Applied Mechanics and Engineering	en
dc.identifier.doi	10.1016/j.cma.2005.04.003	en
dc.identifier.isi	ISI:000234528400012	en
dc.identifier.volume	195	en
dc.identifier.issue	9-12	en
dc.identifier.spage	1050	en
dc.identifier.epage	1074	en