On Boundary Layers in a Pressurized Mooney Cylinder

Abstract

Asymptotic expansions are developed for the equations governing large axisymmetric deformation of a circular cylindrical shell composed of a Mooney material. The shell equations allow large normal strains and thickness changes but ignore transverse shear deformation. For a pressurized cylinder with rigid end plugs, results are presented to illustrate the development of a primary and a secondary boundary layer as generalizations of those that occur in small-strain shell theory. The form of the WKB-type expansion divides the secondary layer into bending and stretching components, which lie within the wider primary boundary layer. While the bending component of the secondary layer can become significant when strains are still small, the stretching component emerges as a consequence of large geometry changes in the edge zone, becoming significant as strains grow large and material nonlinearity becomes important.