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arXiv · 2503.17190

Babu\v{s}ka's paradox in a nonlinear bending-folding model

Sören Bartels·Andrea Bonito·Peter Hornung·Michael Neunteufel
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Abstract

The Babu\v{s}ka or plate paradox concerns the failure of convergence when a domain with curved boundary is approximated by polygonal domains in linear bending problems with simply supported boundary conditions. It can be explained via a boundary integral representation of the total Gaussian curvature that is part of the Kirchhoff--Love bending energy. It is shown that the paradox also occurs for a nonlinear bending-folding model which enforces vanishing Gaussian curvature. A simple remedy that is compatible with simplicial finite element methods to avoid incorrect convergence is devised.

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Sören Bartels, Andrea Bonito, Peter Hornung, Michael Neunteufel. 2025-03-21. Babu\v{s}ka's paradox in a nonlinear bending-folding model. https://arxiv.org/abs/2503.17190

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