Numerical Solution of a Three-Dimensional Coupled Thermoplastic Problem Based on Deformation Theory

The coupled thermodynamic boundary problem of thermo plasticity is formulated on the basis of the Ilyushin theory of small elastoplastic deformations. Note that the related problem consists of the equation of motion, which determines the relations of the Ilyush in deformation theory and the equation of heat influx with the corresponding initial and boundary conditions. In the article, for the problem under consideration, two types of finite difference equations are constructed, namely, explicit schemes reduced to recurrence relations and implicit ones usually solved by the use of the sweep method. Comparisons of numerical results obtained by the two methods show their sufficient proximity, which ensures the reliability of the results obtained.

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