Stationary points of nonlinear plate theories

DOI10.1016/j.jfa.2017.04.010zbMath1368.74014OpenAlexW2609962039WikidataQ125378788 ScholiaQ125378788MaRDI QIDQ2357085

Peter Hornung

Publication date: 19 June 2017

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2017.04.010

zbMATH Keywords

Willmore functionalinfinitesimal bendingsnon-Euclidean plates

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Qualitative behavior of solutions of equilibrium problems in solid mechanics (74G55)

Related Items (3)

Regularity of intrinsically convex \(W^{2,2}\) surfaces and a derivation of a homogenized bending theory of convex shells ⋮ On singularities of stationary isometric deformations ⋮ On material optimisation for nonlinearly elastic plates and shells

Cites Work

• Variational models for prestrained plates with Monge-Ampère constraint.
• Fine level set structure of flat isometric immersions
• The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
• Elastic theory of unconstrained non-Euclidean plates
• Constrained Willmore surfaces
• Analysis aspects of Willmore surfaces
• Functional analysis, Sobolev spaces and partial differential equations
• Extensions of infinitesimal bendings of higher orders of a simply connected surface of positive curvature
• Surface deformation. I
• The space of inextensional displacements for a partially clamped linearly elastic shell with an elliptic middle surface
• Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence.
• On the Sobolev space of isometric immersions
• Removability of point singularities of Willmore surfaces
• Willmore surfaces
• Gradient flow for the Willmore functional
• On the rigidity of certains surfaces with folds and applications to shell theory
• Existence of surfaces minimizing the Willmore functional
• Bending of surfaces. II
• A Riemannian approach to reduced plate, shell, and rod theories
• Willmore minimizers with prescribed isoperimetric ratio
• Equilibrium shapes with stress localisation for inextensible elastic Möbius and other strips
• Bending paper and the Möbius strip
• Non-Euclidean ribbons
• The Willmore boundary problem
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• Extension of infinitesimal bendings of surfaces to analytic bendings under external constraints
• Continuation of Infinitesimal Bendings on Developable Surfaces and Equilibrium Equations for Nonlinear Bending Theory of Plates
• Euler-lagrange equation and regularity for flat minimizers of the Willmore functional
• Triangular buckling patterns of twisted inextensible strips
• Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics
• On Spherical Image Maps Whose Jacobians Do Not Change Sign
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• A remark on constrained von Kármán theories
• The Weyl and Minkowski problems in differential geometry in the large
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