Internally Pressurized Machined Domed Ends—a Comparison of the Plastic Buckling Predictions of the Deformation and Flow Theories

Abstract

The present series of tests, involving six machined steel torispherical shells subjected to internal pressure, was designed to highlight the difference in the buckling predictions of the deformation and the flow theories of plasticity. For the geometries selected, deformation theory predicted that bifurcation buckling would occur for all the domes tested, whereas flow theory predicted buckling in only two of them. In the tests, low-amplitude waves (detected by probes) appeared in all six of the domes. In four of the domes, the low-amplitude waves grew with increasing pressure and became buckles which were visible to the naked eye. Assuming that the occurrence of low-amplitude waves can be considered as buckling of a dome, then deformation theory predicted the failure mode correctly in all six cases. Flow theory was correct in only two cases. The agreement between the initial experimental buckling pressures and those predicted by deformation theory was reasonably good, the ratios varying between 0.71 and 0.94. For three of the domes, the buckling pressures were also found by the Southwell plot technique. These latter agreed best with the deformation theory predictions. The shell buckling program used for analysis purposes was BOSOR 5 and its predictions were checked using five other independent shell buckling programs. One reason for the incorrect prediction of the failure mode by flow theory may be the neglect of initial geometric imperfections in the analysis. Some preliminary calculations including them seem to confirm the hypothesis.