INITIALLY DEFORMED DISSIMILAR ELASTIC TUBES CONTAINING FLUID-FLOW

This paper consists of two parts. In the first part, a review of the a uthors' recent work is given. This concerns a study of the mechanics o f thin membranes, under internal pressure, which are composed of elast ically dissimilar straight cylindrical tubes joined end-to-end longitu dinally. Both static pressure fields and pressure fields arising from fluid flow through the tube are considered, and stresses at tile joint s can be calculated. In the case of fluid flow, a coupled fluid/elasti c problem arises. It is hoped that tile work will ultimately aid the d esign of arterial grafts. The case of pulsatile flow is considered usi ng the fluid solution for harmonic waves following that of Womersley. The membrane solutions are derived either from the equations formulate d in Green and Adkins for finite deformations or from a linearized ver sion of these equations. In die second part a short study is made of w ave propagation in initially deformed thin elastic tubes containing in viscid flow. Applying the long wavelength approximation, we predict an alytically that for any frequency if the tube is predeformed, there ar e values of the principal stretches for which the wave will not propag ate, in addition to wave cut-off frequencies shown by Rubinow and Kell er. This analytic procedure is much simpler than the corresponding num erical calculation for viscous fluid and the results, at least for rit e cut-off frequencies, are very similar.