Mechanics of Bi-stable Composite Shells

Khuram Iqbal

Abstract:

Bi-stable composite shells are straight, thin-walled ribs with a semi/full circular cross-section. They are configurable between two stable states, a coiled state in which the shell is folded along its length and an extended state in which the shell is unfolded. These shells can be used for large deployable structures as deployment actuators in a similar manner to tape-springs. But unlike tape-springs, they do not need any drum to roll upon. Among the many other uses to which these bi-stable shells can be put are water pipes, extendible handles and probes, vehicle hoods, roll up ladders, aerial masts, camera mounts, microphone booms, conveyor belts, telecommunications or computer cable ducting and tent poles. It is found that the shell stretches more along its length than in the transverse length when changes from flattened surface to curved.

It is also found that the radius of shell's cross-section in its extended state is almost equal to the inner radius of the shell in its coiled state. A theoretical model is proposed for the total strain energy, including the bending strain energy and membrane strain energy, contained by the shell as a function of the longitudinal curvature, the transverse curvature, the radius of the shell and the angle subtended by the shell's cross-section.

According to this model, the strain energy increases as we move away from the zero energy point, (0, 1/R). This increase is particularly sensitive to the variations in the longitudinal curvature of the shell and less so to variations in the transverse curvature. Tension, bending and torsion tests were performed to obtain the stress-strain and moment-curvature relationships which show almost linear behaviour of the material for large strains except for a small non-linearity near the initial point. The 'laminate theory' is used to calculate the extensional, coupling and bending compliances which are compared to the compliances measured from the experiments. Finally the strain energy plots are obtained using stiffnesses measured from the experiments and it is shown that both energy minima appear at nearly equal values of the longitudinal and transverse curvatures; this supports the radii measured experimentally for shell's cross-section and the coiled shell.