This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are connected with a Winkler foundation. In particular, forward and inverse problems for the Euler-Bernoulli and Timoshenko partial differential equations (PDEs) are solved using nondimensional equations with the physics-informed loss function. Higher-order complex beam PDEs are efficiently solved for forward problems to compute the transverse displacements and cross-sectional rotations with less than 1e-3 percent error. Furthermore, inverse problems are robustly solved to determine the unknown dimensionless model parameters and applied force in the entire space-time domain, even in the case of noisy data. The results suggest that PINNs are a promising strategy for solving problems in engineering structures and machines involving beam systems.

翻译：本文提出了一种基于物理信息神经网络（PINNs）的新框架，用于模拟由单梁和双梁组成的复杂结构系统——其中双梁通过Winkler地基连接——该框架基于欧拉-伯努利理论和铁木辛柯理论。特别地，采用无量纲方程与物理信息损失函数求解欧拉-伯努利和铁木辛柯偏微分方程（PDEs）的正反问题。针对高阶复杂梁PDEs的正问题，可高效计算横向位移和截面转角，误差低于1e-3%。此外，即便在含噪声数据的情况下，反问题也能稳健求解，确定整个时空域中未知的无量纲模型参数及施加力。结果表明，PINNs是解决涉及梁系统的工程结构与机械问题的有效策略。