Model order reduction for large-scale structures with local nonlinearities
(2019) In Computer Methods in Applied Mechanics and Engineering 353. p.491-515- Abstract
In solid mechanics, linear structures often exhibit (local) nonlinear behavior when close to failure. For instance, the elastic deformation of a structure becomes plastic after being deformed beyond recovery. To properly assess such problems in a real-life application, we need fast and multi-query evaluations of coupled linear and nonlinear structural systems, whose approximations are not straight forward and often computationally expensive. In this work, we propose a linear–nonlinear domain decomposition, where the two systems are coupled through the solutions on a prescribed linear–nonlinear interface. After necessary sensitivity analysis, e.g. for structures with a high dimensional parameter space, we adopt a non-intrusive method,... (More)
In solid mechanics, linear structures often exhibit (local) nonlinear behavior when close to failure. For instance, the elastic deformation of a structure becomes plastic after being deformed beyond recovery. To properly assess such problems in a real-life application, we need fast and multi-query evaluations of coupled linear and nonlinear structural systems, whose approximations are not straight forward and often computationally expensive. In this work, we propose a linear–nonlinear domain decomposition, where the two systems are coupled through the solutions on a prescribed linear–nonlinear interface. After necessary sensitivity analysis, e.g. for structures with a high dimensional parameter space, we adopt a non-intrusive method, e.g. Gaussian processes regression (GPR), to solve for the solution on the interface. We then utilize different model order reduction techniques to address the linear and nonlinear problems individually. To accelerate the approximation, we employ again the non-intrusive GPR for the nonlinearity, while intrusive model order reduction methods, e.g. the conventional reduced basis (RB) method or the static-condensation reduced-basis-element (SCRBE) method, are employed for the solution in the linear subdomain. The proposed method is applicable for problems with pre-determined linear–nonlinear domain decomposition. We provide several numerical examples to demonstrate the effectiveness of our method.
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- author
- Zhang, Zhenying ; Guo, Mengwu LU and Hesthaven, Jan S.
- publishing date
- 2019-08-15
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Gaussian process regression, Machine learning, Model order reduction, Nonlinear structural analysis, Reduced basis method
- in
- Computer Methods in Applied Mechanics and Engineering
- volume
- 353
- pages
- 25 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85066480471
- ISSN
- 0045-7825
- DOI
- 10.1016/j.cma.2019.04.042
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2019 Elsevier B.V.
- id
- 199a1923-3723-495c-b716-7b8eaf9a5c8f
- date added to LUP
- 2024-03-19 12:27:43
- date last changed
- 2024-04-17 15:22:50
@article{199a1923-3723-495c-b716-7b8eaf9a5c8f,
abstract = {{<p>In solid mechanics, linear structures often exhibit (local) nonlinear behavior when close to failure. For instance, the elastic deformation of a structure becomes plastic after being deformed beyond recovery. To properly assess such problems in a real-life application, we need fast and multi-query evaluations of coupled linear and nonlinear structural systems, whose approximations are not straight forward and often computationally expensive. In this work, we propose a linear–nonlinear domain decomposition, where the two systems are coupled through the solutions on a prescribed linear–nonlinear interface. After necessary sensitivity analysis, e.g. for structures with a high dimensional parameter space, we adopt a non-intrusive method, e.g. Gaussian processes regression (GPR), to solve for the solution on the interface. We then utilize different model order reduction techniques to address the linear and nonlinear problems individually. To accelerate the approximation, we employ again the non-intrusive GPR for the nonlinearity, while intrusive model order reduction methods, e.g. the conventional reduced basis (RB) method or the static-condensation reduced-basis-element (SCRBE) method, are employed for the solution in the linear subdomain. The proposed method is applicable for problems with pre-determined linear–nonlinear domain decomposition. We provide several numerical examples to demonstrate the effectiveness of our method.</p>}},
author = {{Zhang, Zhenying and Guo, Mengwu and Hesthaven, Jan S.}},
issn = {{0045-7825}},
keywords = {{Gaussian process regression; Machine learning; Model order reduction; Nonlinear structural analysis; Reduced basis method}},
language = {{eng}},
month = {{08}},
pages = {{491--515}},
publisher = {{Elsevier}},
series = {{Computer Methods in Applied Mechanics and Engineering}},
title = {{Model order reduction for large-scale structures with local nonlinearities}},
url = {{http://dx.doi.org/10.1016/j.cma.2019.04.042}},
doi = {{10.1016/j.cma.2019.04.042}},
volume = {{353}},
year = {{2019}},
}