Neural networks for the approximation of Euler’s elastica
Celledoni E, Çokaj E, Leone A, Leyendecker S, Murari D, Owren B, Sato Martin de Almagro R, Stavole M (2025)
Publication Type: Journal article, Original article
Publication year: 2025
Journal
Book Volume: 435
Article Number: 117584
DOI: 10.1016/j.cma.2024.117584
Abstract
Euler’s elastica is a classical model of flexible slender structures relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions to this problem can be challenging due to nonlinearity and constraints. We here present two neural network-based approaches for simulating Euler’s elastica. Starting from a data set of solutions of the discretised static equilibria, we train the neural networks to produce solutions for unseen boundary conditions. We present a discrete approach learning discrete solutions from the discrete data. We then consider a continuous approach using the same training data set but learning continuous solutions to the problem. We present numerical evidence that the proposed neural networks can effectively approximate configurations of the planar Euler’s elastica for a range of different boundary conditions.
Authors with CRIS profile
Sigrid Leyendecker
Institute of Applied Dynamics
Rodrigo Sato Martin de Almagro
Institute of Applied Dynamics
Martina Stavole
Institute of Applied Dynamics
Related research project(s)
Involved external institutions
Norway (NO)How to cite
APA:
Celledoni, E., Çokaj, E., Leone, A., Leyendecker, S., Murari, D., Owren, B.,... Stavole, M. (2025). Neural networks for the approximation of Euler’s elastica. Computer Methods in Applied Mechanics and Engineering, 435. https://doi.org/10.1016/j.cma.2024.117584
MLA:
Celledoni, Elena, et al. "Neural networks for the approximation of Euler’s elastica." Computer Methods in Applied Mechanics and Engineering 435 (2025).
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