Asymptotic behavior of structures made of straight rods

TL;DR

This paper analyzes the asymptotic deformation and elastic energy of structures composed of thin straight rods as their thickness approaches zero, extending single-rod deformation techniques to complex multi-structures.

Contribution

It introduces a method to characterize the asymptotic elastic energy behavior of rod structures, generalizing previous single-rod deformation analysis to multi-structures.

Findings

Characterizes the limit of elastic energy as rod thickness tends to zero.

Extends deformation decomposition techniques to multi-structure configurations.

Identifies the order of energy scaling with respect to rod thickness.

Abstract

This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ 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 $\delta^\beta$ ($2<\beta\le 4$).