SAINT VENANT COMPATIBILITY EQUATIONS ON A SURFACE APPLICATION TO INTRINSIC SHELL THEORY

DOI10.1142/S0218202508002644zbMath1172.53002MaRDI QIDQ3521648

Ming Shen, Liliana Gratie, Christinel Mardare, Philippe G. Ciarlet

Publication date: 26 August 2008

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

Saint Venant compatibility conditionDifferential geometry of surfacesintrinsic shell theory

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Shells (74K25) Applications of differential geometry to physics (53Z05) Surfaces in Euclidean and related spaces (53A05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (11)

Intrinsic formulation of the displacement-traction problem in linear shell theory ⋮ An intrinsic formulation of the Kirchhoff–Love theory of linearly elastic plates ⋮ Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates ⋮ Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors ⋮ Asymptotic justification of the intrinsic equations of Koiter's model of a linearly elastic shell ⋮ Donati compatibility conditions on a surface -- application to shell theory ⋮ Explicit reconstruction of a displacement field on a surface by means of its linearized change of metric and change of curvature tensors ⋮ An intrinsic approach to a nonlinear model in shell theory ⋮ NONLINEAR SAINT–VENANT COMPATIBILITY CONDITIONS AND THE INTRINSIC APPROACH FOR NONLINEARLY ELASTIC PLATES ⋮ Poincaré's lemma on some non-Euclidean structures ⋮ CESÀRO–VOLTERRA PATH INTEGRAL FORMULA ON A SURFACE

Cites Work

• Intrinsic equations for non-linear deformation and stability of thin elastic shells
• Existence theorems for two-dimensional linear shell theories
• On rigid and infinitesimal rigid displacements in shell theory.
• On Pfaff systems with \(L^p\) coefficients and their applications in differential geometry
• Existence and uniqueness for the linear Koiter model for shells with little regularity
• ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY
• A NEW APPROACH TO LINEAR SHELL THEORY
• Unnamed Item

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