Design and stability of a family of deployable structures

TL;DR

This paper introduces a new class of deployable filamentary structures made from elastic rods, models their equilibrium and stability using variational principles and geometric methods, and applies the theory to the Bristol ladder.

Contribution

It develops a variational framework and a geometric stability analysis for a family of elastic rod-based deployable structures, including the Bristol ladder.

Findings

Equilibrium equations derived from a variational principle.

Stability conditions established using a novel geometric method.

All equilibria of the Bristol ladder shown to be stable or unstable as characterized.

Abstract

A large family of deployable filamentary structures can be built by connecting two elastic rods along their length. The resulting structure has interesting shapes that can be stabilized by tuning the material properties of each rod. To model this structure and study its stability, we show that the equilibrium equations describing unloaded states can be derived from a variational principle. We then use a novel geometric method to study the stability of the resulting equilibria. As an example we apply the theory to establish the stability of all possible equilibria of the Bristol ladder.