On the bifurcation and post-bifurcation behaviour of thick circular elastic-plastic tubes under lateral pressure

Abstract

Abstract The nonaxisymmetric bifurcation and post-bifurcation behaviour of circular tubes subjected to external pressure are investigated numerically. It is assumed that the tubes are made of elastic-plastic workhardening material with a smooth yield surface and that they deform under a plane strain condition. Hill's uniqueness theory along with the Prandtl-Reuss equation and the separation of the variables are employed to obtain the bifurcation point and corresponding mode. The influence of the workhardening rate upon the bifurcation behaviour is investigated, and comparison is made with a classical buckling pressure. For thin to thick tubes, the post-bifurcation behaviour and the influence of thickness imperfection upon the deformation behaviour are numerically investigated. The differences which exist in the behaviour of thin and thick tubes, the development of the unloading region, and the collapse after the maximum pressure point with ribbon type deformation mode accompanied by the rapid reduction of the supporting pressure, are clarified.