Hinged and supported plates with corners

  • Sergey A. Nazarov
  • Athanasios Stylianou
  • Guido Sweers
Article
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Abstract

We consider the Kirchhoff–Love model for the supported plate, that is, the fourth-order differential equation Δ2 u = f with appropriate boundary conditions. Due to the expectation that a downwardly directed force f will imply that the plate, which is supported at its boundary, touches that support everywhere, one commonly identifies those boundary conditions with the ones for the so-called hinged plate: u = 0 = Δu − (1 − σ ) κ u n . Structural engineers however are usually aware that rectangular roofs tend to bend upwards near the corners, and this would mean that u = 0 is not appropriate. We will confirm this behavior and show the difference of the supported and the hinged plates in case of domains with corners.

Mathematics Subject Classification (2010)

Primary: 35J86 35J35 Secondary: 74K20 

Keywords

Supported plate Hinged plate Biharmonic operator Unilateral boundary conditions Variational inequality 
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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Sergey A. Nazarov
    • 1
  • Athanasios Stylianou
    • 2
  • Guido Sweers
    • 2
  1. 1.Institute for Problems of Mechanical EngineeringSt. PetersburgRussia
  2. 2.Athanasios Stylianou and Guido Sweers, Mathematisches InstitutUniversität zu KölnCologneGermany

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