Abstract

A thin anisotropic elastic plate clamped along its lateral side and also supported at a small area θh\theta_{h} of one base is considered; the diameter of θh\theta_{h} is of the same order as the plate relative thickness h≪1h\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 θh\theta_{h}, which with the help of the derived weighted inequality of Korn's type, will provide an error estimate with the bound ch1/2∣ln⁡h∣ch^{1/2}|\ln h|. Ignoring this boundary layer effect reduces the precision order down to ∣ln⁡h∣−1/2|\ln h|^{-1/2}.

Author information

Contact details are reproduced from the original publication and may be historical.

Giuseppe Buttazzo

Dept. of Mathematics, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy

buttazzo@dm.unipi.it

Sergey A. Nazarov

Mathematics and Mechanics Faculty, St. Petersburg State University, Universitetsky pr. 28, Stary Peterhof 198504, Russia
and: Saint-Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, St. Petersburg, 195251, Russia
and: Institute of Problems of Mechanical Engineering RAS, V.O., Bolshoj pr., 61, St. Petersburg, 199178, Russia

srgnazarov@yahoo.co.uk

Keywords

  • Kirchhoff plate
  • small support zones
  • asymptotic analysis
  • boundary layers
  • weighted Korn inequality

Mathematics Subject Classification

74K20, 74B05

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Suggested citation

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 23 (2016), No. 2, 347–386. https://doi.org/10.68381/jca23014

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