On the derivation of homogenized bending plate model

We derive, via simultaneous homogenization and dimension reduction, the Γ -limit for thin elastic plates of thickness h whose energy density oscillates on a scale ε ( h ) such that ε ( h ) 2 ≪ h ≪ ε ( h ) . We consider the energy scaling that corresponds to Kirchhoff’s nonlinear bending theory of pl...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2015-07, Vol.53 (3-4), p.561-586
Main Author: Velcic, Igor
Format: Article
Language:English
Subjects:
Analysis
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Geometry
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Partial differential equations
Systems Theory
Theoretical
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Summary:We derive, via simultaneous homogenization and dimension reduction, the Γ -limit for thin elastic plates of thickness h whose energy density oscillates on a scale ε ( h ) such that ε ( h ) 2 ≪ h ≪ ε ( h ) . We consider the energy scaling that corresponds to Kirchhoff’s nonlinear bending theory of plates.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-014-0758-1