基于有限元网络分析的时间瞬态模拟：理论公式与数值验证
Time transient Simulations via Finite Element Network Analysis: Theoretical Formulation and Numerical Validation
AI总结：
本研究将有限元网络分析扩展到动态时间瞬态模拟，提出超级有限网络单元与时间维网络拼接方法，经一维结构瞬态模拟验证，在1%左右误差下实现了极高计算效率。
摘要：
本文将有限元网络分析（FENA）扩展至包含动态时间瞬态公式的形式。FENA最初是针对一维和二维弹性结构的线性静力分析提出的。通过引入超级有限网络单元的概念，本文为将FENA扩展应用于均质和非均质区域的线性时间瞬态模拟提供了必要基础。原本用于在空间上组合代表不同结构构件的网络的神经网络拼接概念，被拓展到了时间维度。时间维度的网络拼接使得研究人员可以基于有限时间范围内的可用数据训练神经网络模型，随后利用训练好的网络模拟系统在训练数据集所特有的初始时间窗口之外的演化过程。研究通过将FENA应用于一维结构单元（如杆和梁）的瞬态模拟，并将结果与解析解或有限元解进行对比，对所提方法进行了验证。结果证实，FENA能够准确预测物理系统的动力响应，尽管（与控制微分方程的解析解或计算解相比）会引入约1%的误差，但它具备极高的计算效率。
英文摘要：
This paper extends the finite element network analysis (FENA) to include a dynamic time-transient formulation. FENA was initially formulated in the context of the linear static analysis of 1D and 2D elastic structures. By introducing the concept of super finite network element, this paper provides the necessary foundation to extend FENA to linear time-transient simulations for both homogeneous and inhomogeneous domains. The concept of neural network concatenation, originally formulated to combine networks representative of different structural components in space, is extended to the time domain. Network concatenation in time enables training neural network models based on data available in a limited time frame and then using the trained networks to simulate the system evolution beyond the initial time window characteristic of the training data set. The proposed methodology is validated by applying FENA to the transient simulation of one-dimensional structural elements (such as rods and beams) and by comparing the results with either analytical or finite element solutions. Results confirm that FENA accurately predicts the dynamic response of the physical system and, while introducing an error on the order of 1% (compared to analytical or computational solutions of the governing differential equations), it is capable of delivering extreme computational efficiency.
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