A machine learning approach to simulate flexible body dynamics

Flexible body dynamics simulations are powerful tools to realistically analyze vehicles, machines, mechanics, etc. However, the inherently nonlinear governing equations often require tailor-made and computationally expense solution strategies. Employing artificial neural networks for forward dynamics analyses of flexible bodies may be not only useful as a model reduction tool, since evaluating a network is frequently faster compared to solving physics-based models, but also to enhance models with experimental data. In this realm four primary strategies have emerged: (i) Incorporating time as an input to the artificial neural network to predict the desired solution variables at that specific time. (ii) Utilizing an entire time series as input, the network generates the corresponding time series of the desired solution variables in a single pass through the artificial neural network. (iii) Employing an artificial neural network to advance one time step into the future using the states as input. (iv) Leveraging the artificial neural network solely for learning the equations of motion or energetic quantities, e.g., Lagrangian/Hamiltonian, coupled with standard techniques from analytical dynamics and time integration. Approaches (iii) and (iv) can be considered advantageous owing to their inherent physics-informed nature, greater flexibility in adopting varying time steps, and ease of integration with classical simulation techniques. This contribution, therefore, presents a method to predict flexible body dynamics one step at a time using two complimentary artificial neural networks. One network predicts the equations of motion relationship between positions, velocities, and accelerations, while a second network or numerical integrator propagates the system states forwards in time. This work demonstrates the feasibility of the developed approach on the testcase of a flexible beam. Various parameter studies and alternative solutions are presented to highlight the performance of the developed approach. The robustness and ability to extrapolate are also explored to determine the practical viability of this solution. The intention of this single-body work is to enable the future embedding in a multibody context.