Asymptotic analysis for domains separated by a thin layer made of periodic vertical beams

Georges Griso (1) , Anastasia Migunova (2) , Julia Orlik (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Fraunhofer ITWM - Fraunhofer Institute of Industrial Mathematics

We consider a thin heterogeneous layer consisting of thin beams (of radius r) and study the limit behaviour of this problem as the period ε, the thickness δ and the radius r of the beams tend to zero. The decomposition of the displacement field into beams developed in [10] is used, which allows to obtain a priori estimates. Two types of unfolding operators are introduced to deal with different parts of the decomposition. In conclusion, we obtain the limit problem together with transmission conditions across the interface.

Mots clés: linear elasticity; junctions; decomposition of beam displacements; interface; homogenization

Domaines: Analyse numérique [math.NA]

Georges Griso, Anastasia Migunova, Julia Orlik. Asymptotic analysis for domains separated by a thin layer made of periodic vertical beams. 2016. ⟨hal-01449381⟩