Convergence of equilibria for incompressible elastic plates in the von Kármán regime

DOI10.3934/cpaa.2015.14.143zbMath1317.74058arXiv1211.3942OpenAlexW2963356972MaRDI QIDQ2347695

Hui Li, Marta Lewicka

Publication date: 5 June 2015

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.3942

zbMATH Keywords

nonlinear elasticitycalculus of variationsgamma convergenceconvergence of equilibriaplate theories

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Plates (74K20)

Related Items

Mathematical Problems in Thin Elastic Sheets: Scaling Limits, Packing, Crumpling and Singularities, Gaussian curvature as an identifier of shell rigidity, Plates with incompatible prestrain of high order, Theories for incompressible rods: A rigorous derivation via Γ-convergence

Cites Work

• Unnamed Item
• Unnamed Item
• The von Kármán theory for incompressible elastic shells
• Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density
• The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
• Derivation of a plate theory for incompressible materials
• \(\Gamma \)-convergence for incompressible elastic plates
• Les equations de von Kármán
• Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence.
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry
• The Föppl-von Kármán equations for plates with incompatible strains
• Scaling laws for non-Euclidean plates and theW^2,2isometric immersions of Riemannian metrics
• Some Open Problems in Elasticity
• Convergence of Equilibria of Thin Elastic Plates - The Von Karman Case
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• The Infinite Hierarchy of Elastic Shell Models: Some Recent Results and a Conjecture
• Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity
• Convergence of equilibria for planar thin elastic beams