# Bi-Stable Structures with Embedded Actuation

## Introduction

This research, started on 1 April 2000, aims to develop structures that
can change their shape in a controlled fashion. Application will include
deployable structures and adaptive surfaces to air flow or lighting in buildings.

**Research team:** Dr. E. Kebadze, D. Galletly , K. Iqbal, Prof. S. Pellegrino, Dr. S.D. Guest

**Collaboration:** Rolatube
Technology Ltd, Arup and Partners

## Background

Rolatube Technology Ltd have developed a way of making laminated composite
tubes that exploit the natural bi-stability of cylindrical shells. By-stable
tubes have two stable configurations, straight (Fig.1a) and rolled up (Fig.1b).
Tubes with different lay-up form coils of different radii. We have conducted
an in-depth study of these laminated composites, leading to a computer model
that predicts those natural radii of coiling.

Figure 1: Bi-stable tube in (a) extended and (b) rolled up configurations.

## Current work

### Bi-stable metallic shells

We have extended this work to metallic shells (Fig.2) and are able to
achieve bi-stability by inducing residual stresses through a forming process.
We have developed a computer model which simulates the forming process and
predicts the natural radii of both configurations.

Figure 2: Bi-stable metallic shell in (a) extended, (b) rolled up configurations,
and (c) between those configurations where it is not stable.

### Finite element simulation

We can also simulate the snap-through behaviour of these shells with
finite element method using ABAQUS package. The residual/initial stresses
which are applied at integration points through the shell thickness are taken
from the model which simulates the forming process (Fig.3a).

If the initial/residual stress signs are reversed, which is equivalent
of applying the forming process in opposite direction, then shell is not
stable anymore and losses its stability through twist (Fig.3b).

Figure 3: Finite element simulation of (a) the snap-through behaviour of
bi-stable shells and (b) losing the stability through the twist.
However, we have discovered that shells with some particular residual
stress distributions have an infinite number of neutrally stable configurations
with different twist angles (Fig.4).

Figure 4: Neutrally stable shell.
### Shell with embedded actuations

We are also working on triggering bi-stable configuration changes in metallic
shells using shape memory alloy wires. Having understood the interaction
between the wires and an isotropic shell the work will be extended to the
more complex composite shells.

[ Cambridge University |
CUED | Structures | Deployable Structures ]

Last updated
on the 4th of April, 2001

E. Kebadze - ek235@eng.cam.ac.uk