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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
     year = {2017},
     number = {50},
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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/

[1] Sokolovskiy V. V., Theory of plasticity, Vysshaya shkola, M., 1969

[2] Artemov M. A., Yakubenko A. P., “Mathematical modeling of mechanical behavior of a rotating disk”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Fizika i matematika – Proceedings of Voronezh State University. Phisics and mathematics, 2014, no. 1, 30–38

[3] Sporykhin A. N., Perturbation method in the problems of stability of complex media, Izdatel'stvo Voronezh. un-ta, Voronezh, 1997

[4] Aleksandrov S. E., “Solution of the thermoelastoplastic problem for a thin disk of plastically compressible material subjected to thermal loading”, Doklady Physics, 57:3 (2012), 136–139 | DOI

[5] Parkus H., Nonsteady temperature stresses, Fizmatgiz, M., 1963

[6] Melan E., Heinz P., Thermal Stresses due to Stationary Temperature Fields, Fizmatgiz, M., 1958

[7] Kozlovskiy S. N., “Mathematical modelling of the temperature field at contact spot welding”, Vestnik Sibirskogo Gosudarstvennogo Aerokosmicheskogo Universiteta im. akademika M. F. Reshetneva - Vestnik of the Siberian State University of Science and Technology Named after academician M. F. Reshetnev, 2006, no. 6, 4–10

[8] Borisenko E. A., Shakhmanova V. A., Belyakov N. N., Kozlovskiy S. N., “Computational temperature determination in spot welding”, Aktual'nye problemy aviatsii i kosmonavtiki. Obshchie i kompleksnye problemy tekhnicheskikh i prikladnykh nauk i otrasley narodnogo khozyaystva – Topical problems of aviation and cosmonautics. General and complex problems of technical and applied sciences and branches of national economy, 10:1 (2014), 93–94

[9] Manakhov P. V., Fedoseev O. B., “Optimization of calculations of plastic deformations in nonlinear problems of deformable solid mechanics”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics, 2013, no. 3(23), 96–103

[10] Gotsev D. V., Perunov N. S., “Mathematical model of the stress-strain state of an elastic cylindrical body with a porous filler”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics, 47 (2017), 43–50 | DOI

[11] Ishlinskiy A. Yu., “General theory of plasticity with a linear hardening”, Ukrainskiy Matematicheskiy Zhurnal – Ukrainian Mathematical Journal, 6:3 (1964), 314–325

[12] Prager W., Hodge P. G., Theory of perfectly plastic solids, John Wiley Sons, 1951 | MR | Zbl