Analysis of mean and mean square response of general linear stochastic finite element systems

Papadopoulos, V; Papadrakakis, M; Deodatis, G

dc.contributor.author	Papadopoulos, V	en
dc.contributor.author	Papadrakakis, M	en
dc.contributor.author	Deodatis, G	en
dc.date.accessioned	2014-03-01T01:23:36Z
dc.date.available	2014-03-01T01:23:36Z
dc.date.issued	2006	en
dc.identifier.issn	0045-7825	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17039
dc.subject	Mean response function	en
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	Approximation theory	en
dc.subject.other	Computer simulation	en
dc.subject.other	Monte Carlo methods	en
dc.subject.other	Probability density function	en
dc.subject.other	Random processes	en
dc.subject.other	Non-homogeneous stochastic fields	en
dc.subject.other	Stochastic finite element analysis	en
dc.subject.other	Upper bounds	en
dc.subject.other	Variability response function	en
dc.subject.other	Finite element method	en
dc.subject.other	Approximation theory	en
dc.subject.other	Computer simulation	en
dc.subject.other	Finite element method	en
dc.subject.other	Monte Carlo methods	en
dc.subject.other	Probability density function	en
dc.subject.other	Random processes	en
dc.title	Analysis of mean and mean square response of general linear stochastic finite element systems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cma.2005.11.008	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cma.2005.11.008	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	A general finite element-based formulation is presented for the analysis of the mean and mean square response of stochastic structural systems whose material properties are described by random fields. A flexibility-based formulation is followed that does not involve any approximations. Closed-formed integral expressions for the mean and mean square value of the response displacement of statically indeterminate stochastic structures are introduced in this paper. These integral expressions involve the spectral density function of a stochastic field modeling the uncertain material properties and two new quantities named the mean response function (MRF) and the variability response function for the mean square response (VRFI). The MRF and the VRF1 have many similarities with the classical variability response function (VRF) used to estimate the variance of the response displacement. The existence of the MRF and the VRF1 depends on a conjecture that is validated numerically using a brute force Monte Carlo simulation approach. A so-called finite element method-based fast Monte Carlo simulation procedure (FEM-FMCS) is introduced for the accurate and efficient numerical evaluation of the MRF and the VRF1. This methodology is established for the analysis of stochastic beam/frame structures, as well as for more general stochastic finite element systems (i.e., plane stress and shell problems). Numerical examples are provided including-a statically indeterminate beam, a plane stress problem and a shell structure. The MRF and VRF1 are used to perform sensitivity/parametric analyses with respect to various probabilistic characteristics involved in the problem (i.e., correlation distance, standard deviation) and to establish realizable upper bounds on the mean value of the response displacement. Throughout this paper, the VRF is computed in parallel to the MRF and the VRF I. It should be noted that although the concept of the VRF has been introduced in an earlier work, this is the first time that a flexibility-based approach has been used to estimate the VRF for two-dimensional problems. (c) 2006 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.2005.11.008	en
dc.identifier.isi	ISI:000239190500011	en
dc.identifier.volume	195	en
dc.identifier.issue	41-43	en
dc.identifier.spage	5454	en
dc.identifier.epage	5471	en