Bending and symmetric pinching of pressurized tubes

Two experiments quantified the forces necessary for large deformation of an inflated cylindrical tube made of a material with a high elastic modulus. In the first experiment, the end force required to maintain a buckled cylin der at a given kink angle was determined. In the second experiment, the lat eral force required to pinch the membrane symmetrically between two flat bl ades was measured. An approximate theory is used, based on the observation that during deforma tion the membrane conserves its initial zero Gaussian curvature in regions free of wrinkling. The novel feature is a simple approximation for the cros s-sectional shape. This permits the volume of the deformed cylinder to be q uickly calculated. For walls that have negligible extensional and bending e nergy, the potential energy consists of only the pressure multiplied by the volume and the work of the prescribed load. Minimization of this potential energy yields results for the indentation and buckling problems that are i n reasonable agreement with the experimental measurements. For small displa cements in the blade pinching experiment, the volume approximation overesti mates the force. It is found that a local solution analogous to the Hertzia n contact problem provides a better approximation. For the kinked tube with end loading, an interesting feature is a decrease in the load when the fol d from one side contacts the opposite side: of the tube. The calculations i ndicate that a minimum potential energy exists with the fold straight. For slightly larger kink angles, however, the fold buckles out of the plane of symmetry. The moment at the single kink, due to the end loads, remains betw een bounds from the analysis of a pressurized elastic tube with nonpositive stresses. (C) 2000 Published by Elsevier Science Ltd.