Volume 29, 2023
|Number of page(s)||28|
|Published online||18 July 2023|
A class of one dimensional periodic microstructures exhibiting effective Timoshenko Beam behavior
Université de Toulon, Institut de Mathématiques de Toulon, Toulon, France
2 Università degli Studi di Sassari, DADU, Alghero, Italy
3 Università degli Studi dell’Aquila, M&MoCS, L’Aquila, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 15 June 2023
We study, from a variational viewpoint, the asymptotic behavior of a planar beam with a periodic wavy shape when the amplitude and the wavelength of the shape tend to zero. We assume that the beam behaves, at the microscopic level, as a compressible Euler–Bernoulli beam and that the material properties have the same period as the geometry. We allow for distributed or concentrated bending compliance and for a non-quadratic extensional energy. The macroscopic Γ-limit that we obtain corresponds to a non-linear model of Timoshenko type.
Mathematics Subject Classification: 26A45 / 34E13 / 74B20 / 74G65
Key words: Γ-convergence / homogenization / Euler–Bernoulli beam / Timoshenko beam
© The authors. Published by EDP Sciences, SMAI 2023
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