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{uncover https://cdn.pixabay.com/photo/2017/04/09/10/44/sea-shells-2215408_960_720.jpg 100 400 Sea shell}

_h1 thin shells

_h3 1) equililibrium equations of an elastic medium in S{sup 3}
 
{{code_block}
∇{sub j}n{sup ij} + F{sup i} = 0 
i,j ∈ [1,2,3]
;;n{sub k}n{sub 0}{sup ik} + F{sub 0}{sup i} = 0   boundary conditions
}

_p This system with 3 equations and 6 unknowns (n{sup ij} is symetric) is hyperstatic.

_h3 2) equilibrium equations for thin shells

{{code_block}
∇{sub j}N{sup ij} + F{sup i} = 0
ω{sub ij}N{sup ij} - P = 0
i,j ∈ [1,2]
}

_p This system, with 3 equations and 3 unknowns, (N{sup ij} is symetric) is isostatic.

_h3 3) source

{iframe {@ src="data/coques.pdf" width="100%" height="810"}}

_ul [[coques minces|http://marty.alain.free.fr/recherche/articles/coques.pdf]]
_ul [[eta|https://www.w3schools.com/charsets/ref_utf_greek.asp]]

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