Analysis of certain unilateral problems in von karman plate theory by a penalty method-part 2. Approximation and numerical analysis

1980 ◽  
Vol 24 (3) ◽  
pp. 317-337 ◽  
Author(s):  
K. Ohtake ◽  
J.T. Oden ◽  
N. Kikuchi
Keyword(s):  
Numerical Analysis ◽  
Penalty Method ◽  
Plate Theory ◽  
Von Karman ◽  
Von Kármán Plate ◽  
Unilateral Problems ◽  
Von Kármán

A $$C^0$$ C 0 interior penalty method for a von Kármán plate

2016 ◽  
Vol 135 (3) ◽  
pp. 803-832 ◽  
Author(s):  
Susanne C. Brenner ◽  
Michael Neilan ◽  
Armin Reiser ◽  
Li-Yeng Sung
Keyword(s):  
Penalty Method ◽  
Interior Penalty ◽  
Von Karman ◽  
Von Kármán Plate ◽  
Interior Penalty Method ◽  
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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