| 郑勇刚,吴哲同,张涵博,刘振海,叶宏飞,张洪武.基于弹性力学第一性原理的数据驱动力学建模[J].计算力学学报,2024,41(1):73~80 |
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| 基于弹性力学第一性原理的数据驱动力学建模 |
| Data-driven mechanical modeling based on the first principles of elasticity |
| 投稿时间：2023-08-11 修订日期：2023-10-08 |
| DOI：10.7511/jslx20230811001 |
| 中文关键词: 结构力学模型 数据驱动 方程识别 Timoshenko梁 第一性原理 |
| 英文关键词:structural mechanics model data-driven method equation identification Timoshenko beam first principles |
| 基金项目:国家重点研发计划（2022YFB4201200）；国家自然科学基金（12072061；12072062；11972108）资助项目. |
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| 中文摘要: |
| 提出了一种基于弹性力学第一性原理的数据驱动力学建模方法，其能够从基于弹性力学方程的数值计算结果建立简洁且能准确捕捉变形机制的力学模型。基于有限元计算得到的高精度数据和无监督数据驱动控制方程识别方法Seq-SVF，从梁的载荷和位移数据中自动识别出了Timoshenko梁形式的弯曲控制微分方程，得到了三种不同加载条件下剪切影响系数关于结构尺寸和力学参数的函数表达式。揭示了经典模型适用的加载条件，同时还给出了一种未发现的新模型。通过将基于弹性力学的第一性原理计算与数据驱动范式相结合，克服了传统建模方法的局限性和对人类经验的强依赖性，为建立简洁的力学模型提供了一种新途径。 |
| 英文摘要: |
| A data-driven mechanical modeling method based on the first principles of elasticity is proposed in this paper, which enables the identification of concise mechanical models that can accurately capture the deformation mechanism from the numerical simulation results of elasticity.Based on the high-precision data obtained from finite element calculations and the unsupervised data-driven identification method of Seq-SVF, the governing differential equation to describe the bending deformation in the form of Timoshenko beam is automatically identified from the load and displacement data, and the expressions of the shear correction coefficient as a function of structural dimension and mechanical parameters under three different loading conditions are identified.The results reveal the applicability of classical beam models in cases of different loading conditions, and a new model is also established.By combining the first-principle calculation of elasticity with the data-driven paradigm, a new approach is provided for building and analyzing complex mechanical models, which can overcome the limitations and the strong dependence on human experience of traditional modeling methods. |
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