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  2025, Vol. 46 Issue (2): 275-285    
  研究论文 本期目录 | 过刊浏览 | 高级检索 |
求解结构动力响应的距离最小化数据驱动法
董标,徐国林,盛冬发
西南林业大学
Distance-minimizing data-driven method for solving structural dynamic response
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摘要 距离最小化数据驱动法作为计算力学的新范式,在预测结构力学行为方面优势显著。该方法直接输入离散的材料数据集(一组应力-应变对),绕开了传统经验本构建模,通过定义解集到材料数据集的距离泛函,并从材料数据集中搜索满足应变-位移关系和平衡方程的泛函极值,实现边值问题求解。距离最小化数据驱动法在无阻尼振动分析中已取得成功,但还不能用于求解有阻尼振动问题。本研究采用含阻尼项的结构动力平衡方程作为距离泛函的约束条件,并使用上时刻的终值作为当前时刻的初值代替随机初值方案,提出一种求解结构动力响应的距离最小化数据驱动法。以单自由度体系和多自由度桁架为例,通过线性和非线性材料动力响应分析,验证了本文方法的准确性和高效性。
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董标
徐国林
盛冬发
关键词 数据驱动计算力学,非线性动力学,力学变分法,泛函极值,离散本构Data-driven computational mechanics,nonlinear dynamics,mechanical variation,functional extremum,Discrete constitutive model    
Abstract:As a new paradigm of computational mechanics, distance minimizing data-driven method has significant advantages in predicting structural mechanics behavior. This method directly inputs the discrete material datasets (a set of stress-strain pairs), bypasses the conventional empirical constitutive modeling. The boundary value problem is solved by defining the distance functional from the solution set to the material dataset, and searching the functional extreme value from the material dataset to satisfy the strain-displacement relationship and the equilibrium equation. The distance minimizing data-driven method has been successful in solving undamped vibration problems, but it cannot be used for damped vibration problems. This study adopts the structural dynamic equilibrium equation with damping term as the constraint condition of the distance functional, uses the final value at the previous time step as the initial value at the current time step to replace the random initial value scheme, proposes a distance minimizing data-driven method for solving the structural dynamic response. Taking single-degree-of-freedom system and multi-degree-of-freedom truss as examples, the effectiveness and efficiency of the proposed method are verified by the dynamic response analysis of linear and nonlinear materials.
收稿日期: 2024-08-31      出版日期: 2025-04-23
基金资助:数据驱动计算力学的算法优化研究
通讯作者: 盛冬发     E-mail: shengdf@swfu.edu.cn
引用本文:   
董标 徐国林 盛冬发. 求解结构动力响应的距离最小化数据驱动法[J]. , 2025, 46(2): 275-285.
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