<strong>Paper Title</strong><br>
Wkb Solution and The Buckling Analysis of a Neo-Hookean Elastic Cylindrical Shell<br>
<br>

<strong>Abstract</strong><br>
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.