Pure bending of helically wound ideal fibre-reinforced cylinders
✍ Scribed by A. J. M. Spencer; R. L. Moss; T. G. Rogers
- Publisher
- Springer Netherlands
- Year
- 1975
- Tongue
- English
- Weight
- 473 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0374-3535
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✦ Synopsis
An ideal fibre-reinforced material is defined to be inextensible in one or more directions through each point of the material. It has been found to be a good model for predicting the deformation and stresses produced in real materials which are very much stronger in resisting extension in those directions than in any other possible mode of deformation.
We consider a circular cylindrical tube of incompressible ideal fibre-reinforced material in which the reinforcement throughout its thickness is directed along two families of helices making angles +05 with the axis of the cylinder. It is shown that the kinematic constraints allow pure bending deformations, and the solution for a linearly elastic reinforced cylinder is explicitly determined. This kinematically admissible deformation is also statically admissible, and can be supported (or produced) solely by the action of bending couples on the ends of the cylinder. The bending moment-curvature relation is deduced, and compared with the Euler-Bernoulli equation for prismatic beams. The effect of different values of the winding angle 05 is discussed, and we show that the case tan 05 = ~/2 is of particular importance.