We consider an ε-parametrized collection of cylinders of cross section εÏ, where Ïâ2, and of fixed length â. By Korn's inequality, there exists a positive constant Kε such that â«Î©Îµ|symu|2d3xâ¤Kεâ«Î©Îµ|u|2d3x provided that uH1(Ω;â3) satisfies a condition that rules out infinitesimal rotations. We show that Kε?ε2 converges to a strictly positive limit, and we characterize this limit in terms of certain parameters that depend on the geometry of Ï and on â. © The Author(s) 2012.
On Korn's constant for thin cylindrical domains
Paroni, Roberto;
2014-01-01
Abstract
We consider an ε-parametrized collection of cylinders of cross section εÏ, where Ïâ2, and of fixed length â. By Korn's inequality, there exists a positive constant Kε such that â«Î©Îµ|symu|2d3xâ¤Kεâ«Î©Îµ|u|2d3x provided that uH1(Ω;â3) satisfies a condition that rules out infinitesimal rotations. We show that Kε?ε2 converges to a strictly positive limit, and we characterize this limit in terms of certain parameters that depend on the geometry of Ï and on â. © The Author(s) 2012.File in questo prodotto:
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