Proceedings of the International scientific and practical conference ―Current Issues in Science‖ (January 9-11, 2026) / Publisher website: www.naukainfo.com. – Dresden, Germany, 2026. – 179 p.

155 differ from those of the interacting bodies, and by the microgeometry of their surfaces in the contact zone, may be used for mathematical description of contact. The solution of the problem of thermoelasticity for a half-plane is obtained by means of the Fourier integral transformation. Heat conductivity problem for the punch is solved by method of straight lines. The system obtained of dual integral equations is reduced to the system of linear algebraic equations by means of points collocation method. Formulas for thermal fields, heat fluxes and contact stresses are proposed. In order to obtain the unknown contact area, the iterative scheme based on a control of a sign of normal stresses in the immediate contact interaction zones is used. Method of moving line of separation of boundary conditions is proposed. REFERENCES: 1. Levyts‘kyi V.P., Onyshkevych V.M. Investigation of the influence of properties of a ―third body‖ on heat generation due to friction. J. Maths. Sci., 2020. Vol. 109, no. 1. P. 1251-1256. 2. Onyshkevych V.M, Sulym G.T. The problem about thermoelastic contact of half-plane and rectangular punch with heat generation account of friction. Bull. of T. Shevchenko Nat. Univ. of Kyiv. Ser.: Phys. & Math., 2017. Vol. 3. P. 165- 168. 3. Levytskyi V.P., Onyshkevych V.M. Plane contact problem with heat generation account of friction. Int. J. Engng Sci., 1996. Vol. 34, no. 1. P. 101-112. 4. Onyshkevych V.M., Barabash G.M. Modelling of contact interaction by ―third body‖ in tribological problems. Bull. of T. Shevchenko Nat. Univ. of Kyiv. Ser.: Phys. & Math., 2021. Vol. 3. P. 85-88, 2021.