A weak-intrusive stochastic finite element method for stochastic structural dynamics analysis

authored by

Zhibao Zheng, Michael Beer, Hongzhe Dai, Udo Nackenhorst

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.

Organisation(s)

Institute for Risk and Reliability
Institute of Mechanics and Computational Mechanics
International RTG 2657: Computational Mechanics Techniques in High Dimensions

External Organisation(s)

University of Liverpool
Tongji University
Harbin Institute of Technology

Type

Article

Journal

Computer Methods in Applied Mechanics and Engineering

Volume

399

ISSN

0045-7825

Publication date

16.07.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications

Electronic version(s)

https://doi.org/10.1016/j.cma.2022.115360 (Access: Closed)