Babuška's paradox in a nonlinear bending-folding model

2025/03/21 by Sören Bartels, Bartels, Sören, Andrea Bonito +5 · 1 citation
Computer Science · Engineering · Materials Science · #74K20 74G65 65N30 #Advanced Mathematical Modeling in Engineering #Composite Structure Analysis and Optimization #FOS: Mathematics #Nonlocal and gradient elasticity in micro/nano structures #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2503.17190

openalex publication_date 2025/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

The Babuška 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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