基于投影的接触问题模型降阶
Projection-based model reduction for contact problems
AI总结：
本文提出基于投影的模型降阶方法，用于静态和动态接触问题，通过非负矩阵分解构建正的降阶基，结合贪心采样算法和误差指标提高鲁棒性，验证了其在二维接触问题中的有效性。
摘要：
为使参数研究、优化和控制设计等计算密集型应用可行，大规模有限元分析需要模型降阶。这在非线性设置中尤为突出，因为非线性问题显著增加计算复杂性。尽管在非线性计算力学模型降阶方面已取得显著进展，但解决接触问题仍是一个主要障碍。为此，本文介绍了一种基于投影的模型降阶方法，用于静态和动态接触问题。该方法应用非负矩阵分解方案构建接触力的正降阶基，并结合贪心采样算法和误差指标，以实现对模型参数变化的鲁棒性。所提出的方法成功应用于几种二维简单但具有代表性的接触和自接触计算模型的降阶。
英文摘要：
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.
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