Plastic Instability of Cylindrical Shells With Rigid End Closures

Abstract

Solutions are obtained for the large plastic deformations of a cylindrical membrane with rigid end closures subjected to an internal pressure loading. A plastic linearly hardening material obeying Tresca’s yield criterion and the associated flow rule is considered. It is found that, in general, a shell passes through three stages of deformation, finally assuming a spherical shape. The instability pressure (maximum pressure) may be reached in any of the stages depending on the length/diameter ratio of the shell and the hardening modulus of the material. Although numerical integration is required to obtain solutions for shells in the first stages of deformation, the solution in the final stage is given in closed form.