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On the Korn Inequalities on Thin Periodic Frames
Authors:V V Zhikov  S E Pastukhova
Institution:(1) Vladimir State Pedagogical University, USA;(2) Moscow Institute of Radio Technology, Electronics, and Authomatics (Technical University), Moscow
Abstract:Korn-type inequalities for thin periodic structures of period epsi and width epsih(epsi) with h(epsi) rarr 0 are presented. Periodic meshes, three-dimensional road structures, and three-dimensional box structures are considered. A particular attention is paid to structures with the so-called critical width when 
$$\mathop {lim}\limits_{\varepsilon  \to 0} h\left( \varepsilon  \right)\varepsilon ^{ - 1}  > 0$$
.
Keywords:
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