University of Illinois Urbana-Champaign

Stability of finitely deformed cylindrical orthotropic elastic membrane and effect of internal fluid flow

Wong, J.S.K.; Shield, Richard T.

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https://hdl.handle.net/2142/112171

Description

Title
Stability of finitely deformed cylindrical orthotropic elastic membrane and effect of internal fluid flow
Author(s)
  • Wong, J.S.K.
  • Shield, Richard T.
Issue Date
1979-11
Keyword(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.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 435
  • 1979-6005
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112171
Copyright and License Information
Copyright 1979 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
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.