Axisymmetric Elastic-Plastic Buckling of Axial and Pressure Loaded Cylinders

Abstract

An analytical approach to the axisymmetric elastic buckling of isotropic cylinders, under arbitrary combinations of radial pressure and axial loading, is used as the basis of a first surface yield and a first full plasticity criterion of plastic collapse. Bending disturbances caused by the boundary constraint of both Poisson bulging under axial loading and the effects of arbitrary radial pressure loading are combined with any prescribed initial geometric errors to provide total ‘equivalent imperfection parameters’ on an otherwise perfectly cylindrical prebuckling state. Elasto-plastic collapse loads are then summarized in terms of just three parameters: the total equivalent membrane and bending imperfections parameters and the ratio of the minimum elastic classical critical axial stress to the material yield stress. The ease with which shells of arbitrary end conditions or internal ring stiffener supports can be treated, the consideration that the results so closely reproduce and extend the more elaborate numerical solutions, and the possible simplifications of the method, make it an ideal basis for design against axisymmetric collapse.