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Mat. Sb., 2004, Volume 195, Number 4, Pages 97–126 (Mi msb815)  

This article is cited in 10 scientific papers (total in 10 papers)

Weighted anisotropic Korn's inequality for a junction of a plate and a rod

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: Korn's inequality is proved for an elastic body obtained by attaching to a plate several rods with clamped farther ends. The thickness of the plate and the diameters of the rods are characterized by a single small parameter $h$, which also gauges the distinctions in the elastic properties of the elements of the junction. The selection of the weighted anisotropic norms distinguishing the longitudinal and transverse directions in the plate and in a rod ensures the asymptotic accuracy of the inequality, which is substantiated by examples of particular constructions. New results on single plates and rods are obtained in the course of the proof.


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English version:
Sbornik: Mathematics, 2004, 195:4, 553–583

Bibliographic databases:

UDC: 517.946
MSC: Primary 74K30, 74B05; Secondary 74K99
Received: 30.10.2002 and 01.12.2003

Citation: S. A. Nazarov, “Weighted anisotropic Korn's inequality for a junction of a plate and a rod”, Mat. Sb., 195:4 (2004), 97–126; Sb. Math., 195:4 (2004), 553–583

Citation in format AMSBIB
\by S.~A.~Nazarov
\paper Weighted anisotropic Korn's inequality for a~junction of a~plate and a~rod
\jour Mat. Sb.
\yr 2004
\vol 195
\issue 4
\pages 97--126
\jour Sb. Math.
\yr 2004
\vol 195
\issue 4
\pages 553--583

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    This publication is cited in the following articles:
    1. S. A. Nazarov, “Korn's inequalities for junctions of elastic bodies with thin plates”, Siberian Math. J., 46:4 (2005), 695–706  mathnet  crossref  mathscinet  zmath  isi  elib
    2. Izotova O.V., Nazarov S.A., Sweers G.H., “Weighted Korn inequalities for thin-walled elastic structures”, Comptes Rendus Mécanique, 334:12 (2006), 707–712  crossref  adsnasa  isi  elib
    3. S. A. Nazarov, “Korn inequalities for elastic junctions of massive bodies, thin plates, and rods”, Russian Math. Surveys, 63:1 (2008), 35–107  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Durante T., Kardone D., Nazarov S.A., “Modelirovanie sochlenenii plastin i sterzhnei posredstvom samosopryazhennykh rasshirenii”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1: Matem., Mekh., Astronom., 2009, no. 2, 3–14  mathscinet  zmath  elib
    5. Nazarov S.A., Slutskij A.S., Sweers G.H., “Korn Inequalities for a Reinforced Plate”, Journal of Elasticity, 106:1 (2012), 43–69  crossref  mathscinet  zmath  isi
    6. Yu. Grabovsky, D. Harutyunyan, “Exact scaling exponents in Korn and Korn-type inequalities for cylindrical shells”, SIAM J. Math. Anal., 46:5 (2014), 3277–3295  crossref  mathscinet  zmath  isi
    7. Buttazzo G. Cardone G. Nazarov S.A., “Thin Elastic Plates Supported Over Small Areas. i: Korn'S Inequalities and Boundary Layers”, J. Convex Anal., 23:2 (2016), 347–386  mathscinet  zmath  isi
    8. Harutyunyan D., “Sharp Weighted Korn and Korn-Like Inequalities and an Application to Washers”, J. Elast., 127:1 (2017), 59–77  crossref  mathscinet  zmath  isi  scopus
    9. Grabovsky Yu., Harutyunyan D., “Korn Inequalities For Shells With Zero Gaussian Curvature”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 35:1 (2018), 267–282  crossref  mathscinet  zmath  isi
    10. Harutyunyan D., Mikayelyan H., “Weighted Asymptotic Korn and Interpolation Korn Inequalities With Singular Weights”, Proc. Amer. Math. Soc., 147:8 (2019), 3635–3647  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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