Abstract: Because of the restrictions on mathematical method, analytical solution has been an insuperable barrier in the solid mechanics. From the differential equation of stress equilibrium, geometry equations and the Levy-Mises incremental theory of plasticity, axisymmetrical plane stress problem is analyzed using displacement method. The general solution of displacement for the axisymmetrical plane stress problem in plastic state is given in the form of displacement increment. The research results indicate that displacement solution of axisymmetrical plane stress problem in plastic state has no dependence on the material properties. According to this result, height and diameter variation of generator retaining ring in hydroforming process is analyzed in the combined boundary condition of displacement and stress. And recurrence formula to calculate outer diameter, inner diameter and height of protective-ring is established. Comparing with the experimental data from related literature, the calculation’s results have high precision：The relative error is 0.09% in external diameter and 1.178% in height. It is fully able to meet the actual needs of practical engineering.

Key words: Axisymmetrical plane stress problem, Displacement method, Hydroforming, Plastic state, Turbogenerator’s protective-ring, contact geometry, flat width, impact and vibration, vehicle/rail coupling system dynamics model, three dimensional wheel flat model