A weak-intrusive stochastic finite element method for stochastic structural dynamics analysis
Abstract
This paper presents a weak-intrusive stochastic finite element method for solving stochastic structural dynamics equations. In this method, the stochastic solution is decomposed into the summation of a series of products of random variables, spatial vectors and temporal functions. An iterative algorithm is proposed to compute each triplet of the random variable, spatial vector and temporal function one by one. The original stochastic dynamics problem is firstly transformed into spatial–temporal coupled problems (i.e. deterministic structural dynamics equations), which can be solved efficiently by existing FEM solvers. Based on the solution of the spatial–temporal coupled problem, the original problem is then transformed into stochastic-temporal coupled problems (i.e. one-dimensional second-order stochastic ordinary differential equations), which are solved by a proposed sampling method. All random sources are embedded into the stochastic-temporal coupled problems. The proposed sampling method can solve the stochastic-temporal problems of hundreds of dimensions with low computational costs. Thus the curse of dimensionality in high-dimensional stochastic spaces is avoided with great success. Three numerical examples, including low- and high-dimensional stochastic problems, are used to demonstrate the good accuracy and the high efficiency of the proposed method.
Details
- Organisationseinheit(en)
-
Institut für Risiko und Zuverlässigkeit
Institut für Baumechanik und Numerische Mechanik
Internationales GRK 2657: Methoden der Numerischen Mechanik in höheren Dimensionen
- Externe Organisation(en)
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The University of Liverpool
Tongji University
Harbin Institute of Technology
- Typ
- Artikel
- Journal
- Computer Methods in Applied Mechanics and Engineering
- Band
- 399
- ISSN
- 0045-7825
- Publikationsdatum
- 01.09.2022
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Allgemeine Physik und Astronomie, Angewandte Informatik
- Elektronische Version(en)
-
https://doi.org/10.1016/j.cma.2022.115360 (Zugang:
Geschlossen
)
