FINITE AXISYMMETRICAL DEFORMATIONS OF ELASTIC TUBES - AN APPROXIMATE METHOD


ERBAY H., DEMIRAY H.

JOURNAL OF ENGINEERING MATHEMATICS, vol.29, no.5, pp.451-472, 1995 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 5
  • Publication Date: 1995
  • Doi Number: 10.1007/bf00043978
  • Journal Name: JOURNAL OF ENGINEERING MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.451-472
  • Istanbul Technical University Affiliated: No

Abstract

Finite axisymmetric deformation of a hollow circular cylinder with a finite length, composed of a neo-Hookean material, is studied. The inner surface of the tube is subjected to both normal and tangential tractions, while the outer surface is free of tractions. The cylinder will undergo both radial and axial deformations. An asymptotic-expansion method is used to determine the stress and shape of the deformed tube. The deformed radial and axial coordinates, the stress tenser and the surface tractions are expanded into a power series of an appropriate thickness parameter. A hierarchy of equilibrium equations, boundary conditions and constitutive equation are derived following the usual procedure. The theories corresponding to the lowest two order members in this hierarchy are studied in detail. It is shown that the zeroth-order theory corresponds to the membrane theory. The shape of the deformed tube, up to the second-order in the thickness parameter, is determined in terms of the zeroth-order radial and axial deformations. The zeroth-order radial and axial deformations are governed by a coupled pair of nonlinear ordinary differential equations, both of which are of second order. For illustrative purposes the present approach is then applied to a simple representative problem: simultaneous extension and inflation of a cylindrical elastic tube. Finally, the solutions corresponding to the zeroth and first-order approximations of the present theory and the exact solutions obtained from finite elasticity theory are compared for the above-mentioned problem.