Knowledge-Dominated and Data-Driven Rigid-Flexible Coupling Dynamics for Rotating Flexible Structure

Solving a rigid–flexible coupling nonlinear dynamic equation necessitates updating dynamic quantities in each time step, which is the main factor that hampers computational efficiency. Therefore, this study develops an innovative framework that combines knowledge-based and data-driven solutions, for which a data-driven numerical integration (DDNI) method is established to update the mass matrix and load vector. The DDNI model is obtained from offline training based on a deep neural network model and is embedded in the floating frame of reference formulation for online simulation of rigid–flexible coupling problems. As benchmark cases, planar and curved shell structures are analyzed, and the results show that the DDNI method exhibits excellent performance in terms of accuracy and adaptability. In particular, compared to a fully numeric integration (FNI) scheme, the DDNI method shows significantly improved efficiency, surpassing that of commercial software. These noteworthy characteristics aid the investigation of intricate structures in engineering problems. We utilize the developed DDNI method in a rigid–flexible coupling analysis of a manipulator, which shows that it is highly time-efficient, approximately 20 times faster than the FNI scheme, while producing results that are consistent with those of experiments.