Convergence of equilibria of planar thin elastic beams

2006/04/26 by Maria Giovanna Mora, Mora, Maria Giovanna, Stefan Mueller +3 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Computer graphics (images) #Computer science #Contact Mechanics and Variational Inequalities #Convergence (economics) #Economics #FOS: Mathematics #Functional Analysis (math.FA) #Materials science #Mathematics #Physics #Planar #Stability and Controllability of Differential Equations #math.FA

paper · pdf · doi:10.48550/arxiv.math/0604554

published in arXiv (Cornell University) (Cornell University) · 19 pages

arxiv created 2006/04/26 · openalex publication_date 2006/04/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider a thin elastic strip of thickness h and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is of order h² converge to stationary points of the Euler-Bernoulli functional. The proof uses the rigidity estimate for low-energy deformations by Friesecke, James, and Mueller (Comm. Pure Appl. Math. 2002), and a compensated compactness argument in a singular geometry. In addition, possible concentration effects are ruled out by a careful truncation argument.

Citations

• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity
• A Hierarchy of Plate Models Derived from Nonlinear Elasticity by Gamma-Convergence

Cited by

• Dimension reduction for time-dependent von Kármán rods
• Derivation of Kirchhoff-type plate theories for elastic materials with voids

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