Bifurcation of elastic–plastic thick-walled cylindrical structures

Abstract

This article presents theoretical analysis of the bifurcation behavior of metallic thick-walled cylindrical structures, extremely loaded by combined pressure and axial force. The analysis, which is based on the continuum theory, takes into account large elastic–plastic deformations and non-linear isotropic hardening. Bifurcation analysis investigates the uniqueness of the velocity field in the fundamental state, which adopts a constitutive law is based on the von Mises yield criterion. The solution successfully predicts load and deformation limits associated with the onset of bulging and buckling bifurcation of thick-walled cylindrical structures. The theoretical solution is validated by comparing the theoretically obtained results with those obtained independently using nonlinear finite element simulations utilizing the commercial FEA software Abaqus. As an example, the numerical solution is presented for a thick, relatively long cylinder. The results show that, for axially compressed long cylinders, axial deformations at column buckling increase with additional internal or external pressure. The results also explain and quantify the transition from axisymmetric bulging to column buckling bifurcation modes. It also explains the occurrence of non-symmetric (localized) bulging, which follows the axisymmetric bulging. The findings provide valuable information in the safety design of extremely loaded hollow cylindrical columns, thick-walled pressure vessels, piping and other cylindrical structures.