Colloquia

Summary

The inherent complexity of analyzing geometrically nonlinear structures imposes significant limitations on their applicability in optimization and control projects. To address this challenge, physics-informed neural networks offer a promising approach by providing accurate and efficient surrogate models with enhanced interpretability and generalization compared to conventional feed-forward architectures. This study investigates the use of Hamiltonian neural networks (HNNs) as an alternative method for modeling highly flexible slender beams. The full and reduced-order models of the beams are developed using a lumped-mass finite element approach and validated against existing literature. Subsequently, three different neural networks are trained using datasets generated from simulation samples: a simple feed-forward neural network, an HNN, and a modified version of the HNN that incorporates dissipation effects. The surrogate models based on HNNs demonstrate reasonable accuracy and reduced computational costs in specific scenarios while preserving the energy conservation nature expected from the Hamiltonian formulation. However, challenges in hyperparameter tuning and limitations in handling external forces restrict their applicability to low-dimensional problems.