# Simon Guest: Bistable Structures

## Bistable Tubes

Bistable tubes are split tubes with essentially the same geometry as a carpenter's tape; however, unlike a carpenter's tape, which is only stable when extended (b), these structures have a second stable state, they are also stable when coiled (a). I have worked on bistable tubes with Sergio Pellegrino, Diana Galletly and Buba Kebadze; we were initially introduced to the problem by Andrew Daton-Lovett of Rolatube Technology Ltd.

There are two ways to make a tube bistable; either by altering the bending stiffnesses of the structure so that it is no longer isotropic, for instance by using a fibre-reinforced composite, or by setting up an initial prestress in the structure.

### Composite bistable tubes

In order to make a tube bistable without prestress, it is necessary to: (i) increase the torsional stiffness, and (ii) increase the coupling between bending in the longitudinal and transverse directions. This can be achieved by ensuring that stiff fibres are at ±45° to the longitudinal axis on the outside of the layup. These tubes coil with same sense curvature, the centre of curvature is on the same side of the structure in both states, as seen above.

### Prestressed bistable tubes

If the correct initial state of self-stress is set up in the tube, the tube will coil into a second stable state with opposite sense curvature.

Khuram Iqbal's project on bistable tubes. Khuram worked with Sergio Pellegrino.
Bi-Stable Structures with Embedded Actuation
Rolatube Technology Ltd.

## Relevant Publications

Guest, S.D. and Pellegrino, S. (2006), "Analytical models for bistable cylindrical shells", submitted to the Proceedings of the Royal Society: Mathematical, Physical & Engineering Sciences. (pdf preprint)

Galletly, D.A. and Guest, S.D. (2004), "Bistable composite slit tubes II: A shell model." International Journal of Solids and Structures. 41(16-17), 4503-4516. doi:10.1016/j.ijsolstr.2004.02.037

Galletly, D.A. and Guest, S.D. (2004), "Bistable composite slit tubes I: A beam model." International Journal of Solids and Structures. 41(16-17), 4517-4533. doi:10.1016/j.ijsolstr.2004.02.036

Kebadze, E., Guest, S.D. and Pellegrino, S. (2004), "Bistable prestressed shell structures." International Journal of Solids and Structures. 41(11-12), 2801-2820. doi:10.1016/j.ijsolstr.2004.01.028

Ekstrom, L., Guest, S.D., and Kellar, E.J.C. (2002) "Infrared Welding of Bistable Composite Pipelines", in Proceeding of the 34th International SAMPE Technical Conference, Baltimore, November 2002.

Shahid, M and Guest, S. D. (2002) "Study of Stepped Joints in Bistable Composite Pipes", in Proceeding of the 34th International SAMPE Technical Conference, Baltimore, November 2002.

Galletly, D. and Guest, S.D. (2000). "Equilibrium and Stability Analysis of Bistable Composite Slit Tubes." Presented at IASS-IACM 2000, Chania, Crete, 4-7 June.

Last updated on the 1st of June, 2005

S.D. Guest - sdg@eng.cam.ac.uk