Reduced order model-based uncertainty modeling of structures with localized response

Pengchao Song, Marc Mignolet

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

This paper focuses on the introduction of uncertainty in reduced order models of structures exhibiting a localized static response in the neighborhood of the excitation. A straightforward application of the maximum entropy framework is first considered to carry out the stochastic modeling of the uncertainty. Quite consistently with the maximization of the entropy, it is found that this modeling may lead to a "globalization" of the response and thus an extension of the nonparametric stochastic modeling approach is sought. To this end, the eigenvalues and eigenvectors of the stiffness matrix of structures exhibiting this localization property are first studied. It is found that their lowest eigenvalues are closely spaced when the corresponding eigenvectors are extended to the entire structure. On this basis, a novel version of the nonparametric stochastic modeling approach is introduced to randomize the entire stiffness matrix while distorting only slightly the closely spaced eigenvalue structure. The above concepts are demonstrated on a thin annulus clamped at its inner radius and a localization of the uncertain response is indeed observed using the proposed approach.

Original languageEnglish (US)
Title of host publicationUNCECOMP 2017 - Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering
EditorsGeorge Stefanou, M. Papadrakakis, Vissarion Papadopoulos
PublisherNational Technical University of Athens
Pages531-542
Number of pages12
ISBN (Electronic)9786188284449
DOIs
StatePublished - Jan 1 2017
Event2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2017 - Rhodes Island, Greece
Duration: Jun 15 2017Jun 17 2017

Publication series

NameUNCECOMP 2017 - Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering
Volume2017-January

Other

Other2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2017
CountryGreece
CityRhodes Island
Period6/15/176/17/17

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Keywords

  • Localized Response.
  • Maximum Entropy
  • Reduced Order Modeling
  • Structural Uncertainty
  • Uncertainty Modeling

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Theoretical Computer Science

Cite this

Song, P., & Mignolet, M. (2017). Reduced order model-based uncertainty modeling of structures with localized response. In G. Stefanou, M. Papadrakakis, & V. Papadopoulos (Eds.), UNCECOMP 2017 - Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (pp. 531-542). (UNCECOMP 2017 - Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering; Vol. 2017-January). National Technical University of Athens. https://doi.org/10.7712/120217.5389.17224