Numerical and analytical investigation into the plastic buckling paradox for metal cylinders

Abstract

It is widely accepted that, for many buckling problems of plates and shells in the plastic range, the flow theory of plasticity either fails to predict buckling or significantly overestimates buckling stresses and strains, while the deformation theory, which fails to capture important aspects of the underlying physics of plastic deformation, provides results that are more in line with experimental findings and is therefore generally recommended for use in practical applications. This thesis aims to contribute further understanding of the reasons behind the seeming differences between the predictions provided by these two theories, and therefore provide some explanation of this so-called ‘plastic buckling paradox’. The study focuses on circular cylindrical shells subjected to either axial compression or non-proportional loading, the latter consisting of combined axial tensile stress and increasing external pressure. In these two cases, geometrically nonlinear finite-element (FE) analyses for perfect and imperfect cylinders are conducted using both the flow and the deformation theories of plasticity, and the numerical results are compared with data from widely cited physical tests and with analytical results. The plastic buckling pressures for cylinders subjected to non-proportional loading, with various combinations of boundary conditions, tensile stresses, material properties and cylinder’s geometries, are also obtained with the help of the differential quadrature method (DQM). These results are compared with those obtained using the code BOSOR5 and with nonlinear FE results obtained using both the flow and deformation theories of plasticity. It is found that, contrary to common belief, by using a geometrically nonlinear FE formulation with carefully determined and validated constitutive laws, very good agreement between numerical and test results can be obtained in the case of the physically more sound flow theory of plasticity. The reason for the ‘plastic buckling paradox’ appears to be the over-constrained kinematics assumed in many analytical and numerical treatments, such as BOSOR5 and NAPAS, whereby a harmonic buckling shape in the circumferential direction is prescribed.