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Projection‐based model reduction for contact problems
Author(s) -
Balajewicz Maciej,
Amsallem David,
Farhat Charbel
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5135
Subject(s) - parametric statistics , robustness (evolution) , nonlinear system , reduction (mathematics) , model order reduction , computational complexity theory , mathematical optimization , finite element method , computer science , projection (relational algebra) , factorization , algorithm , mathematics , engineering , structural engineering , quantum mechanics , biochemistry , statistics , chemistry , physics , geometry , gene
Summary To be feasible for computationally intensive applications such as parametric studies, optimization, and control design, large‐scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that tend to dramatically increase computational complexity. Although significant progress has been achieved in the development of computational approaches for the reduction of nonlinear computational mechanics models, addressing the issue of contact remains a major hurdle. To this effect, this paper introduces a projection‐based model reduction approach for both static and dynamic contact problems. It features the application of a non‐negative matrix factorization scheme to the construction of a positive reduced‐order basis for the contact forces, and a greedy sampling algorithm coupled with an error indicator for achieving robustness with respect to model parameter variations. The proposed approach is successfully demonstrated for the reduction of several two‐dimensional, simple, but representative contact and self contact computational models. Copyright © 2015 John Wiley & Sons, Ltd.