Limit analysis of flaws in pressurized pipes and cylindrical vessels. Part I: Axial defects

Within the theory of plasticity recently developed primal-dual limit analyses with the finite element method (FEM) give upper and lower bounds of the limit load. The method can be iterated until both bounds have converged to the same value which is then considered the exact plastic collapse load. This new numerical method is used in part I of the paper to derive improved lower bound limit load formulae for axial defects in pressurized cylinders for any defect geometry and loading. Based on the observation that even long slits in thick pipes have a residual strength a simple formula for the stress magnification factor is justified also for thick pipes. Global collapse loads are compared with primal-dual FEM limit analyses and with a large number of burst tests. For axial defects it is possible to find corresponding local collapse loads. Part II of the paper will discuss the FEM discretization of the limit load theorems and will consider circumferential defects.