FSCE 文章速递 基于物理信息神经网络的各向异性复合材料板新型解法。论文标题：A novelty solution for orthotropic composite plate based on physics informed neural network
期刊：Frontiers of Structural and Civil Engineering
作者：Hoang-Le MINH, Thanh SANG-TO, Binh LE-VAN, Thanh CUONG-LE
发表时间：15 Jan 2025
DOI：10.1007/s11709-025-1178-3
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文章亮点/Highlights
采用数值方法对交叉铺设复合材料层合板进行建模一直是一项具有挑战性的任务，这促使了多种有限元方法及其他解析解的发展。随着材料科学的进步，这一问题变得更加复杂，亟要可靠且创新的解决方法。
本研究首次提出利用机器学习，特别是物理信息神经网络（PINN）来研究复合材料板的行为。通过求解基于虚功平衡原理推导的偏微分方程组，采用广义强形式方法实现方程求解。为了解决损失函数不平衡的问题，本研究还提出了相应的调整方法。训练完成的PINN可作为代理模型，用于预测交叉铺设层合板的位移和应力分布。为了验证PINN的有效性和可靠性，本研究选取了两种具有不同材料分布和边界条件（包括位移边界条件和应力边界条件）的层合板案例，将计算结果与基准Navier解进行对比。研究
结果表明，PINN具有优异的性能和精度，展现了其作为解决交叉铺设层合板相关问题的代理模型的潜力。
绝对无量纲位移：（a）为Navier解;（b）在板的中心线处使用PINN（1）模型;（c）使用PINN（1）模型在板的整个域;（d）使用PINN的误差谱（1）模型;（e）在板的中心线处使用PINN（2）模型;（f）使用PINN的整个板域（2）模型;（g）使用PINN（2）模型的误差谱
摘要/Abstract
The modeling of cross-ply composite laminates using numerical methods has been a difficult task, leading to the development of various finite element method and other analytical solutions. However, as materials science advances, this problem has become more complex, presenting new challenges that require reliable and novel approaches. In this study, we propose the utilization of machine learning, specifically physics informed neural networks (PINN), for the first time to examine the behavior of composite plate. By solving a system of partial differential equations derived from the virtual work equilibrium principle, PINN are employed as a method to solve these equations using a generalized strong-form approach. To address the issue of imbalanced loss functions, we also propose adjusting the loss function in this research. Once trained, PINN serve as a surrogate model capable of predicting displacements and stresses in cross-ply composite laminates. To demonstrate the effectiveness and reliability of PINN, we investigate two examples of laminates with different material distributions and boundary conditions including boundary conditions on displacement and boundary conditions on stress, comparing the results with the benchmark Navier solution. The research and obtained results showcase the performance and accuracy of PINN, highlighting their potential as a surrogate model for solving problems related to cross-ply composite laminates.
关键词/Keywords
PINN; loss function; laminate plates; Navier solution
引用信息/Citation Information
Hoang-Le MINH, Thanh SANG-TO, Binh LE-VAN, Thanh CUONG-LE. A novelty solution for orthotropic composite plate based on physics informed neural network. Front. Struct. Civ. Eng., 2025, 19(5): 718–741 https://doi.org/10.1007/s11709-025-1178-3
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https://doi.org/10.1007/s11709-025-1178-3
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来源：Frontiers of Structural and Civil Engineering
