Preprint 48/2006

Convergence of equilibria of planar thin elastic beams

Maria Giovanna Mora, Stefan Müller, and Maximilian G. Schultz

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Submission date: 13. May. 2006
Pages: 21
published in: Indiana University mathematics journal, 56 (2007) 5, p. 2413-2438 
DOI number (of the published article): 10.1512/iumj.2007.56.3023
MSC-Numbers: 74K10
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We consider a thin elastic strip formula28, and we show that stationary points of the nonlinear elastic energy (per unit height) formula30 whose energy is bounded by formula32 converge to stationary points of the Euler-Bernoulli functional formula34 where formula36, with formula38, and where formula40. This corresponds to the equilibrium equation formula42, where formula44 is the primitive of g. The proof uses the rigidity estimate for low-energy deformations [4] and a compensated compactness argument in a singular geometry. In addition, possible concentration effects are ruled out by a careful truncation argument.

18.10.2019, 02:13