Treffer: Aplicació de la tecnologia 'Physics Informed Neural Networks' a l'enginyeria estructural

This thesis explores the application of physics-informed neural networks (PINNs) for solving solid mechanics problems governed by the Euler-Bernoulli beam theory. The primary objective was to develop a Python-based framework capable of constructing PINNs to approximate solutions to differential equations and incorporate boundary and initial conditions, all integrated into a loss function. A training dataset derived from the domain of the governing equation enabled the PINN to iteratively train and converge toward the analytical solution. The developed framework was applied to a range of solid mechanics models, including a rod under distributed force, a simply supported beam, a cantilever beam, and a simply supported cantilever beam. The results demonstrated highly accurate approximations, with minimal errors when compared to analytical solutions. These findings validate the effectiveness of PINNs in solving static solid mechanics problems. To investigate the impact of network parameters on convergence, a principal component analysis (PCA) biplot was conducted on the rod with a distributed force model. A total of 250 PINNs were evaluated with varying neurons, collocation points, batch sizes, and activation functions. The analysis revealed that increasing collocation points reduced the number of epochs required for convergence, while larger batch sizes shortened training times. Additionally, activation functions exhibited distinct clustering patterns, with sigmoid showing consistent behavior and tanh displaying greater variability. These insights highlight the importance of careful parameter tuning for optimizing PINN performance. Challenges emerged for transient problems involving multiple domains, such as the transient cantilever beam, where PINNs failed to converge to valid solutions due to the presence of multiple solutions. Issues with loss term scaling were also identified, as imbalanced loss components hindered efficient training. Addressing these challenges offers opportunities for future research, ...