Geodesic
On mechanical behavior of the hardening elastoplastic disk affected by a heat source
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 50 (2017), pp. 57-66

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The authors obtained an exact solution of the problem of the stress-strain state of a disk made of an isotropic hardening elastoplastic material affected by a heat source placed in the center of the disk. The disk is in a plane stress state. All mechanical and thermal constants of the material are temperature-independent. All the unknown quantities depend only on the distance to the point heat source due to axial symmetry. The temperature in the heat vicinity of the source is infinitely high. In addition, the same problem without consideration of a hardening process was solved using ANSYS Mechanical engineering package. It should be noted that the analytical solution is unavailable due to infinite temperature in the center of the disk, but ANSYS made it possible to calculate a finite value of the temperature there. As a result, in this paper, an analytical solution of the problem of an ideal elastoplastic disk with the point heat source in the center has been obtained. The analytical solution has been compared with results calculated using the finite element method.
Keywords: Ishlinskii–Prager model, plane stress state, point heat source. 
@article{VTGU_2017_50_a4,
     author = {A. A. Afanas'ev and K. K. Gornostaev and A. V. Kovalev and A. S. Chebotarev},
     title = {On mechanical behavior of the hardening elastoplastic disk affected by a heat source},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {57--66},
     publisher = {mathdoc},
     number = {50},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2017_50_a4/}
}
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A. A. Afanas'ev; K. K. Gornostaev; A. V. Kovalev; A. S. Chebotarev. On mechanical behavior of the hardening elastoplastic disk affected by a heat source. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 50 (2017), pp. 57-66. http://geodesic.mathdoc.fr/item/VTGU_2017_50_a4/