Zheng, Zhibao, Beer, Michael 
ORCID: 0000-0002-0611-0345, Dai, Hongzhe and Nackenhorst, Udo
(2022)
A weak-intrusive stochastic finite element method for stochastic structural dynamics analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 399.
p. 115360.
|
Text
SD_CMAME_Manuscript.pdf - Author Accepted Manuscript Download (2MB) | Preview |
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Stochastic structural dynamics, Stochastic finite element method, Weak -intrusive approach, Curse of dimensionality |
| Divisions: | Faculty of Science and Engineering > School of Engineering |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 08 Aug 2022 12:36 |
| Last Modified: | 16 Jul 2023 01:30 |
| DOI: | 10.1016/j.cma.2022.115360 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3160703 |
Dimensions
Dimensions
