A new approach to the fundamental theorem of surface theory, by means of the Darboux-Vallée-Fortuné compatibility relation

DOI10.1016/J.MATPUR.2009.01.004zbMath1170.53002OpenAlexW2165986425MaRDI QIDQ1017645

Philippe G. Ciarlet, Oana Iosifescu

Publication date: 12 May 2009

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2009.01.004

zbMATH Keywords

nonlinear shell theoryfundamental theorem of surface theory

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Surfaces in Euclidean and related spaces (53A05)

Related Items (2)

Isometric immersions into warped product spaces ⋮ Justification of the Darboux-Vallée-Fortuné compatibility relation in the theory of surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Determination of the midsurface of a deformed shell from prescribed surface strains and bendings via the polar decomposition
• The fundamental theorem of surface theory for surfaces with little regularity
• Lectures on three-dimensional elasticity. Notes by S. Kesavan
• Another approach to the fundamental theorem of Riemannian geometry in \(\mathbb R^{3}\), by way of rotation fields
• Modeling and analysis of an elastic problem with large displacements and small strains
• A new approach to the fundamental theorem of surface theory
• On systems of first order linear partial differential equations with \(L^p\) coefficients
• Justification of the Darboux-Vallée-Fortuné compatibility relation in the theory of surfaces
• A consistent theory of geometrically nonlinear shells with an independent rotation vector
• Compatibility equations for large deformations
• Existence theorems for two-dimensional linear shell theories
• Compatibility equations in shell theory
• On the recovery of a surface with prescribed first and second fundamental forms.
• An introduction to continuum mechanics
• Determination of the midsurface of a deformed shell from prescribed fields of surface strains and bendings
• On Pfaff systems with \(L^p\) coefficients and their applications in differential geometry
• The Rotation Associated with Large Strains
• ON THE RECOVERY OF A MANIFOLD WITH PRESCRIBED METRIC TENSOR
• A method of shell theory in determination of the surface from components of its two fundamental forms
• Nonlinear Shell Theory With Finite Rotation and Stress-Function Vectors
• Micropolar Flow past a Slightly Deformed Fluid Sphere
• Nonlinear problems of elasticity

This page was built for publication: A new approach to the fundamental theorem of surface theory, by means of the Darboux-Vallée-Fortuné compatibility relation