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Multiscale homogenization in Kirchhoff's nonlinear plate theory

Laura Bufford

Department of Mathematics, Carnegie Mellon University, Forbes Avenue, Pittsburgh, PA 15213, USA

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Elisa Davoli

Department of Mathematics, Carnegie Mellon University, Forbes Avenue, Pittsburgh, PA 15213, USA

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, and

Irene Fonseca

Department of Mathematics, Carnegie Mellon University, Forbes Avenue, Pittsburgh, PA 15213, USA

Corresponding author.

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https://doi.org/10.1142/S0218202515500451Cited by:7 (Source: Crossref)

Abstract

The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff's nonlinear bending theory for plates. Different limit models are deduced depending on the relative ratio between the thickness parameter h and the two homogenization scales ε and ε².

Keywords:

AMSC: 35B27, 49J45, 74B20, 74E30

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