The model-free distance-minimizing data-driven computational method has recently become a novel paradigm for solving various mechanics problems. However, the paradigm may suffer from low efficiency since tremendous iterative searches of key data points in the material dataset are needed during the solution process. A fast data-driven solver is therefore proposed here for the accurate and efficient analysis of multi-material structural responses to dynamic loading. In the proposed approach, a multi-material database (MMD) with different kinds of constituents is constructed, and a multi-level K-d tree (MKT) is developed for effective data addition and fast data search in the MMD. An efficient data-driven dynamics solver (DDDS) is then designed based on the MMD/MKT, which can deal with the complicated dynamic analysis of different structures containing multiple material datasets. Representative types of dynamic problems are considered to verify and demonstrate the capability of the proposed approach. Numerical results demonstrate that the MMD/MKT and the corresponding DDDS possess high accuracy and efficiency, which might be further developed for the dynamic analysis of composite structures containing constituents at different scales.

中文翻译：

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基于多层次Kd树的数据驱动计算方法的多材料结构动力分析

无模型的距离最小化数据驱动的计算方法最近已成为解决各种力学问题的新颖范例。但是，该范式可能会效率低下，因为在求解过程中需要对材质数据集中的关键数据点进行大量的迭代搜索。因此，在此提出一种快速的数据驱动求解器，用于对多材料结构对动态载荷的响应进行准确而有效的分析。在所提出的方法中，建立了具有不同种类成分的多材料数据库（MMD），并开发了多级Kd树（MKT）以在MMD中进行有效的数据添加和快速的数据搜索。然后，基于MMD / MKT设计了一种高效的数据驱动动力学求解器（DDDS），它可以处理包含多个材料数据集的不同结构的复杂动态分析。动态问题的代表性类型被认为可以验证和证明所提出方法的能力。数值结果表明，MMD / MKT和相应的DDDS具有较高的准确度和效率，可以进一步开发用于动态分析包含不同比例成分的复合结构。