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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

• ## The limit state of a rotating disk

Within 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 allowable boundaries of external parameters have been defined. Within the model of a perfect elasto-plastic solid and the Mises yield criterion the limit state of the disk has been considered. The displacements and the deformations are assumed to be negligible quantity; deformation plasticity theory is chosen. The problem of defining the stresses is ecstatically determined. The displacements are determined together with the stresses. In order to define the displacements as single-valued within the model of a perfect elasto-plastic solid when the disk is in the limit state it is chosen the condition that the plastic deformations inside the disk side surface are equal to zero. For the model of a perfect rigid-plastic body in order to define the displacements as single-valued the displacements values inside the side surface of the disk are needed to be determined. Plots of numerical calculations for the stresses, the deformations, the displacements and the stress vector hodograph have been introduced.

Keywords: the plane-stress state, Mises yield criterion, the limit state, a rigid-plastic body, 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