2015/03/03 by Maciej Balajewicz, Balajewicz, Maciej, David Amsallem +3 · 2 citations
Decision Sciences · Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Structural Health Monitoring Techniques
paper · pdf · doi:10.48550/arxiv.1503.01000
openalex publication_date 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.