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Dimension reduction analysis of a three-dimensional thin elastic plate reinforced with fractal ribbons

Part of: Partial differential equations Elliptic equations and systems Classical measure theory

Published online by Cambridge University Press:  02 March 2023

Mustapha El Jarroudi Open the ORCID record for Mustapha El Jarroudi [Opens in a new window] ,
Mhamed El Merzguioui ,
Mustapha Er-Riani ,
Aadil Lahrouz  and
Jamal El Amrani
Mustapha El Jarroudi*
Affiliation:
Abdelmalek Essaâdi University, LMA, FST Tanger, B.P. 416, Tangier, Morocco
Mhamed El Merzguioui
Affiliation:
Abdelmalek Essaâdi University, LMA, FST Tanger, B.P. 416, Tangier, Morocco
Mustapha Er-Riani
Affiliation:
Abdelmalek Essaâdi University, LMA, FST Tanger, B.P. 416, Tangier, Morocco
Aadil Lahrouz
Affiliation:
Abdelmalek Essaâdi University, LMA, FST Tanger, B.P. 416, Tangier, Morocco
Jamal El Amrani
Affiliation:
Abdelmalek Essaâdi University, LMA, FST Tanger, B.P. 416, Tangier, Morocco
*
*Correspondence author. Email: eljarroudi@hotmail.com
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Abstract

The aim of this paper is to study the dimension reduction analysis of an elastic plate with small thickness reinforced with increasing number of thin ribbons developing fractal geometry. We prove the $\Gamma $-convergence of the energy functionals to a two-dimensional effective energy including singular terms supported within the Sierpinski carpet.

Keywords

Thin elastic platesfractal ribbonsdimension reduction analysismicroscopic interactionseffective material

MSC classification

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 28A80: Fractals 35J20: Variational methods for second-order elliptic equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 34 , Issue 4 , August 2023 , pp. 838 - 869
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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