Low-rank model order reduction strategies for contact mechanics show limited dimensionality reduction due to linear inseparability of contact pressure field. Therefore, a dictionary based strategy is explored for creating efficient models for frictionless non-adhesive contact. A large dictionary of contact pressure trajectories is generated using a high-fidelity finite element model, while approximating the online query with a small number of dictionary entries. This is achieved by inducing sparsity in the approximation. Accuracy, computational effort and limitations of such methods are demonstrated on few numerical examples.

翻译：针对接触力学的低秩模型降阶策略，由于接触压力场的线性不可分离性，其维度约减能力有限。因此，本文探索了一种基于字典的策略，用于建立无摩擦非黏附接触的高效模型。通过高保真有限元模型生成包含大量接触压力轨迹的字典，并利用少量字典条目对在线查询进行近似。这一目标通过诱导近似中的稀疏性实现。本文通过若干数值算例展示了此类方法的精度、计算代价与局限性。