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.
The nonlinear stability analysis introduced by Chen and Haughton  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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|Item Type:||Journal Article|
|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|
|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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