Sequential limit analysis of rotating hollow cylinders of nonlinear isotropic hardening

Abstract

Plastic limit angular velocity of rotating hollow cylinders made of the von Mises materials with nonlinear isotropic hardening is investigated numerically and analytically in the paper. The paper applies sequential limit analysis to deal with the rotating problems involving hardening material property and weakening behavior resulted from the widening deformation. By sequential limit analysis, the paper treats the plasticity problems as a sequence of limit analysis problems stated in the upper bound formulation. Rigorous upper bounds are acquired iteratively through a computational optimization procedure with the angular velocity factor as the objective function. Especially, rigorous validation was conducted by numerical and analytical studies of rotating hollow cylinders in terms of the plastic limit angular velocity as well as the onset of instability. It is found that the computed limit angular velocities are rigorous upper bounds and agree very well with the analytical solutions.