Asymptotic behavior of structures made of straight rods

Abstract

This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2δ$ when $δ$ tends to 0. This analysis relies on the decomposition of the large deformation of a single rod introduced in [6] and on the extension of this technique to a multi-structure. We characterize the asymptotic behavior of the infimum of the total elastic energy as the minimum of a limit functional for an energy of order $δ^β$ ($2<β\le 4$).