On Elastoplastic Buckling Analysis of Cylinders under Nonproportional Loading by Differential Quadrature Method

Electronic version of an article published as International Journal of Structural Stability and Dynamics, 17(7), DOI: 10.1142/S0219455417500729 © World Scientific Publishing Company 2017 The paper investigates the elastoplastic buckling of thin circular shells subjected to nonproportional loading consisting of axial tensile stress and external pressure. The governing equations of buckling for cylindrical shells derived by Flugge serve as the basis of analysis. To capture the elastic/plastic behavior, two plasticity theories are considered; the flow theory and the deformation theory of plasticity. Plastic buckling pressures for cylinders with various combinations of boundary conditions are presented for which no analytical solutions are available. The results obtained from the flow and deformation theories confirm that, under over-constrained kinematic assumptions, the deformation theory tends to provide lower values of buckling pressure and the discrepancies in the results from the two plasticity theories increase with increasing thickness-to-radius ratios, tensile stresses, boundary clamping and E/σyσy ratios. The plastic buckling results obtained by means of the differential quadrature method are compared with carefully conducted FEA results for both the flow and the deformation theory of plasticity. The reasons underlying the apparent plastic buckling paradox are thus investigated for a vast class of boundary conditions and loads.