Upper and lower bound limit and shakedown loads for hollow tubes with axisymmetric internal projections under axial loading

In this paper, the elastic compensation method proposed by Mackenzie and Bo yle is used to estimate the upper and lower bound limit (collapse) loads an d the upper and lower bound shakedown loads for hollow tubes with axisymmet ric internal projections subjected to axial loading. The method is based on an iterative elastic analysis procedure and the application of lower and u pper bound limit load theorems. Four different geometries with a range of s tress concentration factors (from low to high) are considered. Elastic-plas tic finite element predictions for collapse and shakedown pressure are foun d to be within these upper and lower bound estimates. The method is particularly useful because it is founded on an iterative ela stic approach and does not require extensive and complex elastic-plastic fi nite element computations.