The Point-Load Solution Using Linearized von Kármán Plate Theory for a Spinning Flexible Disk Near a Baseplate

1992 ◽  
Vol 35 (3) ◽  
pp. 473-481 ◽  
Author(s):  
J. F. Maher ◽  
G. G. Adams
2002 ◽  
Vol 335 (2) ◽  
pp. 201-206 ◽  
Author(s):  
Gero Friesecke ◽  
Richard D James ◽  
Stefan Müller

2013 ◽  
Vol 23 (14) ◽  
pp. 2701-2748 ◽  
Author(s):  
STEFAN NEUKAMM ◽  
IGOR VELČIĆ

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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