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：本文提出一种基于物理信息神经网络(PINNs)的新框架，用于模拟由基于欧拉-伯努利和铁木辛柯理论的单梁与双梁组成的复杂结构系统，其中双梁通过温克勒地基连接。特别地，利用无量纲化方程和物理信息损失函数，求解了欧拉-伯努利和铁木辛柯偏微分方程的正问题与反问题。在正问题中，高阶复杂梁偏微分方程得到高效求解，横向位移和截面转角的计算误差小于1e-3%。此外，即使在含噪声数据的情况下，反问题也得到稳健求解，能够确定全时空域中未知的无量纲模型参数及施加的力。结果表明，PINNs是求解涉及梁系统的工程结构与机械问题的一种有前景的策略。