A new approach to the fundamental theorem of surface theory
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Publication:930410
DOI10.1007/s00205-007-0094-0zbMath1142.53007OpenAlexW2073276349MaRDI QIDQ930410
Liliana Gratie, Christinel Mardare, Philippe G. Ciarlet
Publication date: 30 June 2008
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00205-007-0094-0
Sobolev spaceelastic shellsrotation fieldpolar factorizationGauss and Codazzi-Mainardi equationsrotation fields
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Cites Work
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- On a stress resultant geometrically exact shell model. I: Formulation and optimal parametrization
- The fundamental theorem of surface theory for surfaces with little regularity
- Continuity of a deformation in \(H^{1}\) as a function of its Cauchy-Green tensor in \(L^{1}\)
- On the characterizations of matrix fields as linearized strain tensor fields
- Another approach to the fundamental theorem of Riemannian geometry in \(\mathbb R^{3}\), by way of rotation fields
- On systems of first order linear partial differential equations with \(L^p\) coefficients
- Finite rotations in the description of continuum deformation
- A consistent theory of geometrically nonlinear shells with an independent rotation vector
- Ordinary differential equations of non-linear elasticity. I: Foundations of the theories of non-linearly elastic rods and shells
- Compatibility equations in shell theory
- On the recovery of a surface with prescribed first and second fundamental forms.
- On rigid and infinitesimal rigid displacements in shell theory.
- An introduction to continuum mechanics
- New compatibility conditions for the fundamental theorem of surface theory
- A nonlinear Korn inequality on a surface
- On Pfaff systems with \(L^p\) coefficients and their applications in differential geometry
- RECOVERY OF A SURFACE WITH BOUNDARY AND ITS CONTINUITY AS A FUNCTION OF ITS TWO FUNDAMENTAL FORMS
- The Rotation Associated with Large Strains
- ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY
- Nonlinear Shell Theory With Finite Rotation and Stress-Function Vectors
- On the Embedding Problem in Differential Geometry
