Physics-Informed Neural Networks for Shell Structures

Abstract

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

24 pages, 16 figures

References in corpus (4)

• Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates
• A Physics-Guided Neural Network Framework for Elastic Plates: Comparison of Governing Equations-Based and Energy-Based Approaches
• Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy
• Physics-informed Neural Networks for Elliptic Partial Differential Equations on 3D Manifolds

Cited by in corpus (8)

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• k-space Physics-informed Neural Network (k-PINN) for Compressed Spectral Mapping and Efficient Inversion of Vibrations in Thin Composite Laminates
• When invariants matter: The role of I1 and I2 in neural network models of incompressible hyperelasticity
• Variational PINNs with tree-based integration and boundary element data in the modeling of multi-phase architected materials
• Precise, efficient and flexible modeling of crystallizing elastomers based on physics-augmented neural networks
• A physics-augmented neural network framework for finite strain incompressible viscoelasticity