Elasto-plastic Analysis of Thick-walled Cylinder using Perturbation Technique and Radial Return Method

In this paper, the elasto-plastic behavior of thick-walled cylindrical shell under uniform pressure is studied. Mirsky-Herman shear deformation theory, in which shear deformations are considered, has been used to obtain elastic equations using energy and virtual work methods. The studied cylindrical shell is axially symmetric and has clamp-clamp boundary condition at two ends. The material state of the shell is fully elastic-plastic, and the Prandtl-Reuss flow rule has been used to express the material behavior in plastic state, and the von Mises yield criterion has been used to determine the beginning of plasticization of the cylinder in the middle layer. The radial return mapping method has been investigated to obtain the stresses in the plastic state and to correct and restore the stress to the yield surface. To solve the obtained equations, the eigenvalue problem method and MAM perturbation technique are used. Also, the obtained results, including the yield stress and cylinder stresses in the middle layer, have been compared with the finite element method using Abaqus software. The obtained results show that the MAM perturbation technique and using Mirsky-Herman shear deformation theory has a good accuracy in the elasto-plastic solution of thick-walled cylinders.