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fractal ribbons

European Journal of Applied Mathematics (1)

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Dimension reduction analysis of a three-dimensional thin elastic plate reinforced with fractal ribbons
Part of
Mustapha El Jarroudi, Mhamed El Merzguioui, Mustapha Er-Riani, Aadil Lahrouz, Jamal El Amrani
Journal:

European Journal of Applied Mathematics / Volume 34 / Issue 4 / August 2023

Published online by Cambridge University Press:

02 March 2023, pp. 838-869
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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.