Geometric learning for computational mechanics, Part III : Physics-constrained response surface of geometrically nonlinear shells

This paper presents a graph-manifold iterative algorithm to predict the configurations of geometrically exact shells subjected to external loading. The finite element solutions are first stored in a weighted graph where each graph node stores the nodal displacement and nodal director. This collection of solutions is embedded onto a low-dimensional latent space through a graph isomorphism encoder. This graph embedding step reduces the dimensionality of the nonlinear data and makes it easier for the response surface to be constructed. The decoder, in return, converts an element in the latent space back to a weighted graph that represents a finite element solution. As such, the deformed configuration of the shell can be obtained by decoding the predictions in the latent space without running extra finite element simulations. For engineering applications where the shell is often subjected to concentrated loads or a local portion of the shell structure is of particular interest, we use the solutions stored in a graph to reconstruct a smooth manifold where the balance laws are enforced to control the curvature of the shell. The resultant computer algorithm enjoys both the speed of the nonlinear dimensional reduced solver and the fidelity of the solutions at locations where it matters. & COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a graph-manifold iterative algorithm for predicting the configurations of geometrically exact shells under external loading. Finite element solutions are stored in a weighted graph and embedded onto a low-dimensional latent space. A graph isomorphism encoder reduces the dimensionality of the data, making it easier to construct a response surface. A decoder converts a point in the latent space back to a weighted graph representing a finite element solution. This algorithm allows obtaining the deformed shell configuration without additional finite element simulations and ensures accuracy in important locations.