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Article Dans Une Revue Mathematics and Mechanics of Solids Année : 1998

Two-dimensional models of linearly elastic shells: error estimates between their solutions

Cristinel Mardare
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Résumé

The linear static problem in Ω⊂R3 for a thin shell made from an elastic homogeneous and isotropic material is analyzed. Let the shell thickness 2ϵ be constant, the neutral shell surface S:=θ(ω) be bounded connected and elliptic and the shell edge Γ be clamped. The solution u(ϵ) of the three-dimensional problem, the solution ζ of the corresponding two-dimensional membrane problem and the solution ζ(ϵ) of Koiter's two-dimensional model are compared with each other. The following three estimates are proved for ϵ small enough in the case when the mapping θ(ω) and the boundary γ:=∂ω are of class C4: ||ζ(ϵ)−ζ||H1(ω)×H1(ω)×Hs(ω)≤Cϵ1/5−s/2,s∈[0,2], ||u(ϵ)−ζ||H1(Ω)×H1(Ω)×Hs(Ω)≤Cϵ1/6−s,s∈[0,1], ||u(ϵ)−ζ(ϵ)||H1(Ω)×H1(Ω)×L2(Ω)≤Cϵ1/6−s,s∈[0,1], where in the last two inequalities ζ and ζ(ϵ) are extended to Ω by letting ζ(y,x3)=ζ(y) and ζ(ϵ)(y,x3)=ζ(ϵ)(y) for all (y,x3) ∈ Ω:=ωx(-1,1).
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hal-01478621 , version 1 (28-02-2017)

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  • HAL Id : hal-01478621 , version 1

Citer

Cristinel Mardare. Two-dimensional models of linearly elastic shells: error estimates between their solutions. Mathematics and Mechanics of Solids, 1998, 3, pp.303-318. ⟨hal-01478621⟩
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