On the general homogenization of von Kármán plate equations from three-dimensional nonlinear elasticity

2016 ◽  
Vol 15 (01) ◽  
pp. 1-49 ◽  
Author(s):  
Igor Velčić
Keyword(s):  
Nonlinear Elasticity ◽  
Three Dimensional ◽  
Von Karman ◽  
Elasticity Equations ◽  
Plate Equations ◽  
Von Kármán Plate ◽  
Von Kármán ◽  
Three Dimensional Elasticity

Starting from three-dimensional elasticity equations we derive the model of the homogenized von Kármán plate by means of [Formula: see text]-convergence. This generalizes the recent results, where the material oscillations were assumed to be periodic.

On the Range of Applicability of von Karman Plate Equations

1989 ◽  
Vol 56 (3) ◽  
pp. 724-726 ◽  
Author(s):  
You-He Zhou ◽  
Xiao-Jing Zheng
Keyword(s):  
Von Karman ◽  
Plate Equations ◽  
Von Kármán Plate ◽  
Von Kármán

scholarly journals A hierarchy of multilayered plate models

2020 ◽  
Author(s):  
Miguel de Benito Delgado ◽  
Bernd Schmidt
Keyword(s):  
Nonlinear Elasticity ◽  
Curvature Tensor ◽  
Elastic Constants ◽  
Three Dimensional ◽  
Spontaneous Curvature ◽  
Multilayered Plate ◽  
Von Karman ◽  
Plate Models ◽  
Γ Convergence ◽  
Von Kármán

We derive a hierarchy of plate theories for heterogeneous multilayers from three dimensional nonlinear elasticity by means of Γ-convergence. We allow for layers composed of different materials whose constitutive assumptions may vary significantly in the small film direction and which also may have a (small) pre-stress. By computing the Γ-limits in the energy regimes in which the scaling of the pre-stress is non-trivial, we arrive at linearised Kirchhoff, von Kármán, and fully linear plate theories, respectively, which contain an additional spontaneous curvature tensor. The effective (homogenised) elastic constants of the plates will turn out to be given in terms of the moments of the pointwise elastic constants of the materials.

scholarly journals Conservative numerical methods for the Full von Kármán plate equations

2015 ◽  
Vol 31 (6) ◽  
pp. 1948-1970 ◽  
Author(s):  
Stefan Bilbao ◽  
Olivier Thomas ◽  
Cyril Touzé ◽  
Michele Ducceschi
Keyword(s):  
Numerical Methods ◽  
Von Karman ◽  
Plate Equations ◽  
Von Kármán Plate ◽  
Von Kármán
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