Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

verfasst von

Zhibao Zheng, Michael Beer, Udo Nackenhorst

Abstract

This article presents unified and efficient stochastic modal decomposition methods to solve stochastic structural static and dynamic problems. We extend the idea of deterministic modal decomposition method for structural dynamic analysis to stochastic cases. Standard/generalized stochastic eigenvalue equations are adopted to calculate the stochastic subspaces for stochastic static/dynamic problems and they are solved by an efficient reduced-order method. The stochastic solutions of both static and dynamic equations are approximated by stochastic bases of the stochastic subspaces. Original stochastic static/dynamic equations are then transformed into a set of single-degree-of-freedom (SDoF) stochastic static/dynamic equations, which are efficiently solved by the proposed non-intrusive methods. Specifically, a non-intrusive stochastic Newmark method is developed for the solution of SDoF stochastic dynamic equations, and the element-wise division of sample vectors is used to solve the SDoF stochastic static equations. All of these methods have low computational effort and are weakly sensitive to the stochastic dimension, thus the proposed methods avoid the curse of dimensionality successfully. Two numerical examples, including two- and three-dimensional spatial problems with low and high stochastic dimensions, are given to show the efficiency and accuracy of the proposed methods.

Organisationseinheit(en)

Institut für Baumechanik und Numerische Mechanik
Institut für Risiko und Zuverlässigkeit

Externe Organisation(en)

The University of Liverpool
Tongji University

Typ

Artikel

Journal

International Journal for Numerical Methods in Engineering

Band

125

Anzahl der Seiten

22

ISSN

0029-5981

Publikationsdatum

06.03.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Numerische Mathematik, Ingenieurwesen (insg.), Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.1002/nme.7469 (Zugang: Offen)