Derivation of a homogenized nonlinear plate theory from 3d elasticity

We derive, via simultaneous homogenization and dimension reduction, the Γ -limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the energy scaling that corresponds to Kirchhoff’s nonlinear bending...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 51; no. 3-4; pp. 677 - 699
Main Authors Hornung, Peter, Neukamm, Stefan, Velčić, Igor
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014
Springer Nature B.V
Subjects
Analysis
Bending theory
Calculus
Calculus of variations
Calculus of Variations and Optimal Control; Optimization
Control
Derivation
Film thickness
Homogenizing
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonlinearity
Partial differential equations
Plate theory
Systems Theory
Texts
Theoretical
49J45
35B27
74E30
74Q05
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Summary:We derive, via simultaneous homogenization and dimension reduction, the Γ -limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the energy scaling that corresponds to Kirchhoff’s nonlinear bending theory of plates.
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ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-013-0691-8