Wkb Solution and The Buckling Analysis of a Neo-Hookean Elastic Cylindrical Shell
The deformation of a thick-walled circular cylindrical shell of incompressible, isotropic, elastic material is
considered. The shell, which is made of neo-Hookean strain energy function is subjected to the combined internal and axial
loading pressures. For finding the eigen-values which are = / and = / (where and are the un-deformed and
and are the deformed inner and outer radii respectively), the incremental equilibrium equations derived by Haughton and
Ogden are solved with the asymptotic WKB method. Finally we have shown the eigen-values by plotting the radius changes
with respect to the wall thickness. Our derived asymptotic results are similar to the counter-part data obtained by using the
numerical compound matrix method.
Keywords: Compound Matrix method, Eigen-values, neo-Hookean material, WKB method.