A comparison of stability and bifurcation criteria for inflated spherical elastic shells

Haughton, D. M. & Kirkinis, E. (2003) A comparison of stability and bifurcation criteria for inflated spherical elastic shells. Mathematics and Mechanics of Solids, 8(5), pp. 561-572.

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Abstract

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

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7 citations in Web of Science®

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ID Code: 73437
Item Type: Journal Article
Refereed: Yes
Keywords: Bifurcation (mathematics), Nonlinear equations, Numerical methods, Ordinary differential equations, Plastic deformation, Nonlinear stability analysis, Spherical elastic shells, Thin shells, Third order nonlinear ordinary differential equation, Elasticity
DOI: 10.1177/10812865030085008
ISSN: 10812865 (ISSN)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 07 Jul 2014 22:53
Last Modified: 07 Jul 2014 22:53

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