Convergence of equilibria of planar thin elastic beams

Mora, Maria Giovanna; Mueller, Stefan; Schultz, Maximilian G.

Convergence of equilibria of planar thin elastic beams

Authors

Mora, Maria Giovanna

Mueller, Stefan

Schultz, Maximilian G.

Description

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 h^2 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.
19 pages