Convergence of equilibria of planar thin elastic beams
Maria Giovanna Mora, Stefan Mueller, Maximilian G. Schultz
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.
Create a lesson
Related papers
Truncated Moment Problems and the Extension Property on Monomial Curves
Rajkamal Nailwal, Aljaž Zalar, Igor Zobovič
Optimal stability of regularized spectral differentiation in Sobolev spaces
Teemu Tyni
Modular Topologies on Vector Spaces: Structure and Normability
M. Khamsi, J. Lang, O. Mendez
Critical Norm Profiles for Finite-Prime Composition Operators on the Hardy Space of Dirichlet Series
Xiang Fang, Feng Guo, Aman Mishra et al.
Sparse Operators and their boundedness on Morrey-type Spaces: An Expository Note
Manasa N. Vempati
Sharp Concave-Function Transfer for Lee-Type Schatten Norm Inequalities
Xing Li