Investigation of rotating hollow cylinders of strain-hardening viscoplastic materials by sequential limit analysis

The paper employs sequential limit analysis to investigate rotating hollow cylinders of nonlinear isotropic strain-hardening viscoplastic materials. A computational optimization procedure was developed to account for hardening material properties and weakening behavior corresponding to the strain-rate sensitivity and widening deformation. A sequence of limit analysis problems was then conducted to seek the corresponding plastic limit angular velocities sequentially by a general algorithm incorporated with an inner and outer iterative sequence. Particularly, analytical solutions of plastic limit angular velocities and the onset of instability were derived for rigorous comparisons. The corresponding stability condition was also obtained explicitly. Specifically, the implicit form of the onset of instability was solved by the fixed point iteration. It is found that the computed limit angular velocities are rigorous upper bounds and match well with analytical solutions.