Damage of plastic cylinders under localized pressure loading

The purpose of this paper is to develop a general methodology of converting a two-dimensional boundary value problem for a cylindrical shell to an equivalent one-dimensional problem of a plastic string on a non-linear plastic foundation. The shell is subjected to a localized pressure loading, thereby producing large plastic displacements and rotations. The equivalence parameter is defined and evaluated by making assumptions about the shape of the displacement and velocity field in the cross-sectional plane of the cylinder. Closed-form solutions for the deformation and velocity profile in the axial direction of the shell are obtained for two types of pressure loading, a rectangular pressure load and a Gaussian pressure load. The strain distribution and the maximum strains are also calculated for each load case and the possibility of predicting shell fracture is briefly discussed.