Physics-Informed Neural Networks for shell structures

The numerical modeling of thin shell structures is a challenge, which has been met by variety finite element (FE) and other formulations -- many give rise to new challenges, from complex implementations artificial locking. As potential alternative, we use machine learning present Physics-Informed Neural Network (PINN) predict the small-strain response arbitrarily curved shells. To this end, midsurface described chart, mechanical fields are derived in curvilinear coordinate frame adopting Naghdi's theory. Unlike typical PINN applications, corresponding strong or weak form must therefore be solved non-Euclidean domain. We investigate performance proposed three distinct scenarios, including well-known Scordelis-Lo roof setting widely used test FE elements against Results show that can accurately identify solution field all benchmarks if equations presented their form, while it may fail do so when using form. In thin-thickness limit, where classical methods susceptible locking, training time notably increases as differences scaling membrane, shear, bending energies lead adverse stiffness gradient flow dynamics. Nevertheless, match ground truth performs well benchmark, highlighting its for drastically simplified alternative designing locking-free formulations.