Thermal stresses in a rectangular bar

• Datum: 2026
• Hauptverfasser: Tokovyy, Yu., Yuzvyak, M., Токовий, Юрій, Юзв'як, Микола
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2026
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/9873
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 539.37, 517.9 We propose an approach to the construction of an analytic solution to the three-dimensional thermoelasticity problem for a bar with rectangular cross section   infinitely extended in the axial direction under the conditions of stationary distribution of the temperature field. The problem is solved by the method of direct integration with the help of the Vihak functions, for which the governing integrodifferential equations are deduced on the basis of the continuity equations. A procedure for constructing solutions to boundary-value problems for the obtained governing equations is developed with the help of successive approximations. The application of the proposed approach makes it possible to construct the solution to the original problem, which exactly satisfies the boundary conditions and also satisfies the original equations with prescribed accuracy. The numerical investigation of the solution  is performed for a rectangular bar and compared with the limiting cases of a rectangular parallelepiped and a layer with infinite (in plan) cross section.