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C R Acad Sci Paris t SOrie I p Probkmes mathematiques de la mCcanique Mathematica Problems in Mechanics

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6 Pages
English

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C. R. Acad. Sci. Paris, t. 324, SOrie I, p. 839-844, 1997 Probkmes mathematiques de la mCcanique/Mathematica/ Problems in Mechanics RCsumC. On donne une d6monstration simple de l'existence et de I'unicite de la solution du mod& de Nagdhi pour une coque dont la surface moyenne peut avoir des courbures diacontinucs. cc qui ameliore les d6monstrations antCrieures de Cixlet et Mix:\ et de Bernadou. Ciarlet et Miara pour des surfaces moyennes de classe c”‘. Abridged English Version Greek indices their values in { I. 2) and Latin indices in ( I. 2. 3). Unless otherwise specified. the Einstein summation is LIW~. Let ti be a domain of R2. We consider a shell whose midsurface is given by S = P(W). where g g 11“‘.‘(ti: R”) is an injective mapping. Let (I., be the covariant basis and rf: , be the Christoffel symbols of S. We denote II, = /(/,,A(Lz~~. If II, I' E II' (w; W”) are respectively a displacement of the midsurface and a rotation of the unit normal vector to the surface, the linearized strain tensor, the linearized change of curvature tensor and the linearized transverse shear strain are given componentwise respectively by (1) (2) and (:I) Note pr&entCe par Philippe G.

  • covariant basis

  • existence

  • espace i‘

  • dkrivkes covariantes des compoantcs de i' et des composantes tangentielles

  • base orthonormale canonique de l'espace euclidien

  • base covariante

  • coque

  • discontinuitcs de courbure pour la surface


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