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Title:Stability of finitely deformed cylindrical orthotropic elastic membrane and effect of internal fluid flow
Author(s):Wong, J.S.K.; Shield, Richard T.
Subject(s):Orthotropic Elastic Membrane
Internal Fluid Flow
Abstract:Some stability problems for finitely deformed elastic membranes are considered. The first part treats the stability of a stretched elastic membrane which is orthotropic in its reference state. The stability criteria for a uniformly deformed orthotropic plane sheet under conditions of dead loading are obtained. The potential energy for a uniformly extended and inflated circular cylindrical membrane (the preferred directions being axial and circumferential) with axially symmetric deformations and under constant pressure is found to have the same form as that for an isotropic material. Stability criteria for a long tube are obtained and some numerical results are given through stability diagrams using strain energy functions appropriate for biological tissues. The effect on stability of the flow of an incompressible fluid through the tube is considered next. To model the internal fluid motion, small perturbations superimposed on a state of steady flow with velocity profiles of a slug flow and a Poiseuille flow are assumed, and a one-dimensional analysis is used as a third approach. Equations for the fundamental frequencies of vibration are derived. The fluid motion is found to have a stabilizing or destabilizing influence on the membrane depending on the approach used. The results are compared to Rayleigh's results for a circular liquid jet and they are found to agree for the slug flow and the Poiseuille flow models.
Issue Date:1979-11
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 435
1979-6005
Genre:Technical Report
Type:Text
Language:English
URI:http://hdl.handle.net/2142/112171
ISSN:0073-5264
Rights Information:Copyright 1979 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04


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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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