Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | e7469 |
| Seitenumfang | 22 |
| Fachzeitschrift | International Journal for Numerical Methods in Engineering |
| Jahrgang | 125 |
| Ausgabenummer | 12 |
| Publikationsstatus | Veröffentlicht - 7 Mai 2024 |
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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Numerische Mathematik
- Ingenieurwesen (insg.)
- Mathematik (insg.)
- Angewandte Mathematik
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in: International Journal for Numerical Methods in Engineering, Jahrgang 125, Nr. 12, e7469, 07.05.2024.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses
AU - Zheng, Zhibao
AU - Beer, Michael
AU - Nackenhorst, Udo
N1 - Publisher Copyright: © 2024 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
PY - 2024/5/7
Y1 - 2024/5/7
N2 - 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.
AB - 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.
KW - curse of dimensionality
KW - stochastic eigenvalue problems
KW - stochastic Newmark method
KW - stochastic reduced-order equations
KW - stochastic static and dynamic analyses
UR - http://www.scopus.com/inward/record.url?scp=85187121351&partnerID=8YFLogxK
U2 - 10.1002/nme.7469
DO - 10.1002/nme.7469
M3 - Article
AN - SCOPUS:85187121351
VL - 125
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 12
M1 - e7469
ER -