Incorporation of physical laws into neural networks for solving elasticity problems

Summary

This study investigates the performance of Physics-Informed-Neural-Networks (PINNs) in addressing elasto-static plate bending problems under various boundary conditions. To that effect, the bending of a square isotropic plate was simulated using the Mindlin and Kirchhoff models. The accuracy of the predictions is compared to the established method of Finite Element Analysis (FEA). For ensuring boundary condition compliance, a hard- enforced boundary method is adopted from the literature. Additionally, Fourier Feature Embeddings and Self-Scalable hyperbolic-tangent are employed for increased training stability. The findings confirm the results from previous studies regarding the ability of PINNs to successfully tackle electrostatic problems and confirm that PINNs show great promise as a novel method for solving Partial Differential Equations (PDEs).