[Univ of Cambridge] [Dept of Engineering]

Modelling the Equilibrium and Stability of Slit Tubes

by Diana Galletly


A novel shell structure, a bi-stable composite slit tube, is presented.  This structure is formed like a coilable tape measure; unlike tape measures, however, it is stable in both the extended form and the coiled form, without any need for a spindle or casing to hold it in either position.

The structure is initially modelled linearly, as a beam.  Various applications of this model are presented: an algorithm for rapidly locating the second equilibrium point, the investigation of the strain state as the path is followed from one equilibrium state to the second, and generalised plots throughout longitudinal curvature--transverse curvature space.  Various examples (two composites with layups which are anti-symmetric about the middle layer, one which is symmetric about the middle layer, and an isotropic case) are presented.  The inability of this model to determine the stability of an equilibrium is noted, as the results for the anti-symmetric and symmetric cases appear to be similar, whilst their experimental behaviour is very different. The model is then extended to incorporate non-linear geometric effects, and stability criteria are determined.  The examples considered for the original model are re-evaluated using the new model; the equilibrium locations for the anti-symmetric and isotropic cases are found to be unchanged, whilst the
symmetric case develops more twist.  The stability of the anti-symmetric layups, and the instability of the symmetric layup and the isotropic case, are accurately predicted.
The structure is then modelled as a shell of arbitrary cross-section.  An expression for this cross-sectional shape is derived, and the same examples once again examined.  The stability of the anti-symmetric layups, and the instability of the symmetric and isotropic cases, are again predicted correctly.  The constant transverse curvature assumption of the extended beam model is found to be valid for cross-sectional angles greater than about 180 degrees.
Various reasons for the disparity between the experimental and theoretical results are then investigated, including inaccuracies in the material properties and inelasticity in the matrix.  It is thought that matrix inelasticity is the cause of the difference and initial results to support this are presented.

[Cambridge University | CUED | Structures Group | Geotechnical Group]

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