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  • Mathematic modeling of the elasto-plastic state of a rotating disk

    Within approaching the plane-stress state the problem of a high-speed rotating disk being under side pressure is considered. Within the model of a perfect rigid-plastic body and the Mises yield criterion the values of external parameters for which the plastic zones appear have been defined. The stresses in plastic zones are obtained from the solution of the Cauchy problem, which includes two differential equations to define the stress tensor nonzero component. In order to estimate the stress state in the elastic zone the equivalent stress is introduced. The maximum allowable values of external parameters are obtained from the solution of the problem when the disk is in the limit state. The numerical results are represented as the stress vector hodograph.

    Keywords: the plane-stress state, Mises yield criterion, the equivalent stress, an elasto-plastic solid, a rotating disk, a stress vector hodograph

  • Mathematic modeling of a thin rotating solid disk being heat and force affected

    Mathematic modeling of the state of a thin round disk being heat and force affected is performed. In the central part of the disk the homogeneous field of temperatures is formed. Within the deformation theory of a perfect elasto-plastic solid the quadratic plasticity condition is chosen. The relationships between the radius of the disk, the temperature of the central part of the disk and the external pressure which defines the appearance of plastic zones have been established. For different values of external parameters of the model the stress vector hodograph and the plots of stresses and equivalent stresses have been introduced.

    Keywords: mathematic modeling, an elastic-plastic solid, the plane-stress state, the deformation theory, thermo-elasto-plasticity, a high-speed rotating disk