Elastic-Plastic, Axisymmetric Analysis of a Thin-Walled Cylindrical Shell Subjected to a Radial Pressure Difference

Abstract

An analysis is given for the axisymmetric behavior of a thin-walled cylinder with direction-fixed ends subjected to increasing radial pressure, the material being elastic-pure plastic and yielding according to the Tresca (maximum stress difference) criterion. The presence of end pressure as well as radial pressure would involve only an extension to the analysis. A step-by-step, finite-difference technique is adopted, and is illustrated by application to two cylinders, enabling the development of plasticity in the walls of the cylinders to be traced in detail. The two cylinders considered were also tested experimentally and the theoretical pressures necessary to cause full yield conditions over the central sections of the cylinder lengths are shown to be in good agreement with the experimental results. Experimentally, cylindrical shells, which are insufficiently slender to fail by elastic instability when loaded with external pressure, are found to collapse when the central region of the shell length reaches a yield condition, a phenomenon which is not well understood. The theory presented here indicates the load level at which this central yielding takes place and can therefore be used to estimate the experimental collapse load. The relationship of the analysis to the rigid-plastic solution (10) of the same problem is discussed.