A thin circular disk is considered, the material of which exhibits elastic and plastic properties under thermal and force influences. In the central part of the disk, the temperature field is uniform. At the boundary of the disk, pressure and a constant temperature are set. Approximation of a plane stress state is adopted. The additive form of the connection of full, elastic, plastic deformations and deformations under free thermal expansion is considered. Elastic deformations are expressed in terms of stresses according to Hooke's law. A linear approximation of the dependence of the plasticity limit on temperature is proposed. The possibility of neutral loading of the central region of the disk and its external boundary is shown. Especially distinguished is the condition for the plasticity of Tresca.
Keywords: mathematical modeling, elastoplastic body, plane stress state, piecewise-linear plasticity conditions, plastic flow theory, thermoelastic plasticity
The steps of constructing an algorithm for calculating the stressed and strained state of a thin circular disk experiencing thermal and force effects are discussed. A homogeneous temperature field is created in the central part of the disk. Within the framework of the theory of the flow of an ideal elastoplastic body, conditions of general plasticity are considered. It is assumed that the plasticity limit for uniaxial tension is common for all plasticity conditions. Dependencies between the disk radius, the temperature of the central region of the disk and the external pressure, which determine the appearance of plastic regions, are established. For piecewise-linear plasticity conditions of general form, analogous dependences are defined, when singular plasticity regimes are realized at elastoplastic boundaries. For different values of the input parameters of the problem, the stresses, equivalent stresses and the hodograph of the stress vector are given.
Keywords: mathematical modeling, elastoplastic body, plane stress state, piecewise linear plasticity conditions, plastic flow theory, thermoelastic plasticity