Buckling Analysis of a Neo-Hookean Elastic Cylindrical Shell by WKB Method

Abstract

Our focus in this article is to consider the axisymmetric deformation of an incompressible, isotropic thick-walled circular cylindrical shell. This neo-Hookean elastic shell is subjected to combined axial loading and internal pressure. For finding the rate of change of the inner radius (  and the outer radius , concerning the variations of the wall thickness (A/B) for different mode numbers and axial stretches, the incremental equilibrium equations derived by Haughton and Ogden are solved with the asymptotic WKB method, (where A and B are the un-deformed and and are the deformed inner and outer radii respectively). The graph of the eigenvalues which shows the radius changes concerning the changes of the wall thickness has been plotted. Our derived asymptotic results are shown to agree with the counterpart data obtained by using the numerical compound matrix method.