Bifurcation of Elastic-Plastic Circular Cylindrical Shells Under Internal Pressure

The bifurcation of long elastic-plastic cylindrical shells subject to internal pressure is investigated. It is assumed that the end conditions are such that plane strain conditions prevail. For thin shells, simple approximate bifurcation criteria are obtained analytically. The finite-element method is then employed, in conjunction with separation of variables, to obtain the bifurcation conditions for cylindrical shells with arbitrary thickness to radius ratios. For sufficiently thin shells, the numerical and the analytical results are in good agreement for the critical pressure at bifurcation. The numerical and analytical results both indicate that, for sufficiently thin shells, a variety of bifurcation modes are available virtually simultaneously at this critical pressure. However, for thicker shells, the numerical results reveal that there is a single preferred bifurcation mode. The mode number associated with this preferred bifurcation mode depends on the thickness to radius ratio. The possibility of bifurcation occurring before the attainment of the maximum pressure is also explored. For the specific cases investigated here, bifurcation always occurs after the maximum pressure point.