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Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2023

A Class of One Dimensional Periodic Microstructures Exhibiting Effective Timoshenko Beam Behavior

Jean-Jacques Alibert
  • Function : Author
Emilio Barchiesi
  • Function : Author
Francesco Dell’isola
  • Function : Author

Abstract

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.
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Dates and versions

hal-04165376 , version 1 (18-07-2023)

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Jean-Jacques Alibert, Emilio Barchiesi, Francesco Dell’isola, Pierre Seppecher. A Class of One Dimensional Periodic Microstructures Exhibiting Effective Timoshenko Beam Behavior. ESAIM: Control, Optimisation and Calculus of Variations, 2023, 29, pp.53. ⟨10.1051/cocv/2023048⟩. ⟨hal-04165376⟩

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