scholarly journals Intrinsic formulations of the nonlinear Kirchhoff-Love-von Kármán plate theory

2020 ◽  
Vol 144 ◽  
pp. 269-282
Author(s):  
Giuseppe Geymonat ◽  
Françoise Krasucki
Keyword(s):  
Plate Theory ◽  
Von Karman ◽  
Von Kármán Plate ◽  
Von Kármán

The Föppl–von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity

2002 ◽  
Vol 335 (2) ◽  
pp. 201-206 ◽  
Author(s):  
Gero Friesecke ◽  
Richard D James ◽  
Stefan Müller
Keyword(s):  
Nonlinear Elasticity ◽  
Plate Theory ◽  
Low Energy ◽  
Von Karman ◽  
Von Kármán Plate ◽  
Von Kármán

scholarly journals DERIVATION OF A HOMOGENIZED VON-KÁRMÁN PLATE THEORY FROM 3D NONLINEAR ELASTICITY

2013 ◽  
Vol 23 (14) ◽  
pp. 2701-2748 ◽  
Author(s):  
STEFAN NEUKAMM ◽  
IGOR VELČIĆ
Keyword(s):  
Material Properties ◽  
Plate Theory ◽  
Three Dimensional ◽  
Energy Functional ◽  
Oscillatory Behavior ◽  
Von Karman ◽  
Starting Point ◽  
Von Kármán Plate ◽  
Functional Features ◽  
Von Kármán

We rigorously derive a homogenized von-Kármán plate theory as a Γ-limit from nonlinear three-dimensional elasticity by combining homogenization and dimension reduction. Our starting point is an energy functional that describes a nonlinear elastic, three-dimensional plate with spatially periodic material properties. The functional features two small length scales: the period ε of the elastic composite material, and the thickness h of the slender plate. We study the behavior as ε and h simultaneously converge to zero in the von-Kármán scaling regime. The obtained limit is a homogenized von-Kármán plate model. Its effective material properties are determined by a relaxation formula that exposes a non-trivial coupling of the behavior of the out-of-plane displacement with the oscillatory behavior in the in-plane directions. In particular, the homogenized coefficients depend on the relative scaling between h and ε, and different values arise for h ≪ ε, ε ~ h and ε ≪ h.

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