Geodesic
Thin Elastic Plates Supported over Small Areas. I: Korn's Inequalities and Boundary Layers
Journal of convex analysis, Tome 23 (2016) no. 2, pp. 347-386
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A thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base is considered; the diameter of $\theta_{h}$ is of the same order as the plate relative thickness $h\ll 1$. In addition to the standard Kirchhoff model with the Sobolev point condition, a three-dimensional boundary layer is investigated in the vicinity of the support $\theta_{h}$, which with the help of the derived weighted inequality of Korn's type, will provide an error estimate with the bound $ch^{1/2}|\ln h|$. Ignoring this boundary layer effect reduces the precision order down to $|\ln h|^{-1/2}$.
Classification : 74K20, 74B05
Mots-clés : Kirchhoff plate, small support zones, asymptotic analysis, boundary layers, weighted Korn inequality 
@article{JCA_2016_23_2_JCA_2016_23_2_a2,
     author = {G. Buttazzo and G. Cardone and S. A. Nazarov},
     title = {Thin {Elastic} {Plates} {Supported} over {Small} {Areas.} {I:} {Korn's} {Inequalities} and {Boundary} {Layers}},
     journal = {Journal of convex analysis},
     pages = {347--386},
     year = {2016},
     volume = {23},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_2_JCA_2016_23_2_a2/}
}
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G. Buttazzo; G. Cardone; S. A. Nazarov. Thin Elastic Plates Supported over Small Areas. I: Korn's Inequalities and Boundary Layers. Journal of convex analysis, Tome 23 (2016) no. 2, pp. 347-386. http://geodesic.mathdoc.fr/item/JCA_2016_23_2_JCA_2016_23_2_a2/