Details
| Original language | English |
|---|---|
| Journal | Computational mechanics |
| Early online date | 27 May 2025 |
| Publication status | E-pub ahead of print - 27 May 2025 |
Abstract
This article presents a stochastic ALE framework to solve rolling contact problems with uncertainties. To this end, the classical ALE method used for deterministic rolling contact analysis is extended to a stochastic framework. Within the proposed stochastic ALE framework, stochastic finite element equations are derived and efficiently solved by an iterative algorithm. Specifically, the stochastic solution is approximated by a set of products of random variables and deterministic vectors. An alternating iteration is presented to solve each component of random variable and deterministic vector one by one. Based on a set of obtained deterministic vectors, an equivalent stochastic rolling contact interface system is further constructed, which transforms the original problem into a stochastic rolling contact problem on an interface. Thus, its solution involves fewer degrees of freedom and is cheap enough. The proposed framework is not sensitive to stochastic dimensions and can be applied to high-dimensional stochastic rolling contact problems. Numerical examples demonstrate the promising performance of the proposed framework.
Keywords
- Curse of dimensionality, Stochastic arbitrary Lagrangian–Eulerian method, Stochastic finite element method, Stochastic penalty method, Stochastic rolling contact analysis
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, 27.05.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stochastic arbitrary Lagrangian–Eulerian formalism for stochastic rolling contact analysis
AU - Zheng, Zhibao
AU - Nackenhorst, Udo
N1 - Publisher Copyright: © The Author(s) 2025.
PY - 2025/5/27
Y1 - 2025/5/27
N2 - This article presents a stochastic ALE framework to solve rolling contact problems with uncertainties. To this end, the classical ALE method used for deterministic rolling contact analysis is extended to a stochastic framework. Within the proposed stochastic ALE framework, stochastic finite element equations are derived and efficiently solved by an iterative algorithm. Specifically, the stochastic solution is approximated by a set of products of random variables and deterministic vectors. An alternating iteration is presented to solve each component of random variable and deterministic vector one by one. Based on a set of obtained deterministic vectors, an equivalent stochastic rolling contact interface system is further constructed, which transforms the original problem into a stochastic rolling contact problem on an interface. Thus, its solution involves fewer degrees of freedom and is cheap enough. The proposed framework is not sensitive to stochastic dimensions and can be applied to high-dimensional stochastic rolling contact problems. Numerical examples demonstrate the promising performance of the proposed framework.
AB - This article presents a stochastic ALE framework to solve rolling contact problems with uncertainties. To this end, the classical ALE method used for deterministic rolling contact analysis is extended to a stochastic framework. Within the proposed stochastic ALE framework, stochastic finite element equations are derived and efficiently solved by an iterative algorithm. Specifically, the stochastic solution is approximated by a set of products of random variables and deterministic vectors. An alternating iteration is presented to solve each component of random variable and deterministic vector one by one. Based on a set of obtained deterministic vectors, an equivalent stochastic rolling contact interface system is further constructed, which transforms the original problem into a stochastic rolling contact problem on an interface. Thus, its solution involves fewer degrees of freedom and is cheap enough. The proposed framework is not sensitive to stochastic dimensions and can be applied to high-dimensional stochastic rolling contact problems. Numerical examples demonstrate the promising performance of the proposed framework.
KW - Curse of dimensionality
KW - Stochastic arbitrary Lagrangian–Eulerian method
KW - Stochastic finite element method
KW - Stochastic penalty method
KW - Stochastic rolling contact analysis
UR - http://www.scopus.com/inward/record.url?scp=105006735263&partnerID=8YFLogxK
U2 - 10.1007/s00466-025-02649-7
DO - 10.1007/s00466-025-02649-7
M3 - Article
AN - SCOPUS:105006735263
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
ER -