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
published in: Indiana University mathematics journal, 56 (2007) 5, p. 2413-2438
DOI number (of the published article): 10.1512/iumj.2007.56.3023
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We consider a thin elastic strip , and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is bounded by converge to stationary points of the Euler-Bernoulli functional where , with , and where . This corresponds to the equilibrium equation , where is the primitive of g. The proof uses the rigidity estimate for low-energy deformations  and a compensated compactness argument in a singular geometry. In addition, possible concentration effects are ruled out by a careful truncation argument.