Elastic-Plastic Ring-Loaded Cylindrical Shells

Abstract

The elastic-plastic solution for an infinitely long cylindrical shell with an axisymmetric ring load is presented. Except for the material nonlinearity, the standard assumptions of small deflection shell theory were made. Because the principal directions are known for the axisymmetric problem, the Tresca yield condition wasused. This made it possible to obtain closed-form expressions for the elastic-plastic, moment-curvature relations, greatly simplfying the computational task. The actual stress distribution through the thickness was used, making these relations exact. Yielding was contained near the load. Thus, for the analysis the cylinder was divided along its axis into elastic-plastic and purely elastic regions. Solutions were obtained for each region which were then matched at their intersection to give the complete solution. All results are given in dimensionless form so that they may be applied to any shell.