Physics-informed neural networks for analysis of 2D thin-walled structures.

Thin-walled structural problems have been a longstanding computational challenge. The research bottleneck in applying the standard numerical methods for such problems arises from their special geometrical configurations in which the thickness-to-length ratio of the thin-structures is usually up to the order of 10−6 or even smaller. In this paper, we present a method to solve such problems using physics-informed neural networks (PINNs) which are trained to satisfy the differential operator and the corresponding boundary/initial conditions. The PINNs-based method is meshless which is a key feature since mesh-based methods become infeasible for problems with ultra-thin shapes. Instead of using a mesh, the PINNs are trained on batches of randomly sampled collocation points. The algorithm is tested for a class of thin-walled structural problems, including elastic/piezoelectric thin-films as well as ultra-thin coating/substrate structures. We also present comparisons with numerical solutions obtained by using an advanced boundary element method (BEM). Accurate and reliable PINNs results can be achieved for a relative thickness-to-length ratio of the thin structures as small as 10−8, which is sufficient for modeling most of thin structures as used in smart materials. A self-contained MATLAB code and data-sets accompanying this paper are also provided. [ABSTRACT FROM AUTHOR]