Reduction of the two-dimensional thermoelasticity problems for solids with corner points to key integrodifferential equations

• Дата: 2026
• Автори: Kushnir, R. M., Tokovyi, Yu. V., Yuzvyak, M. Y., Yasinskyi, A. V., Кушнир, Роман, Юзвяк, Николай, Кушнір , Р. М., Токовий , Ю. В., Юзв'як, М. Й., Ясінський, А. В.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2026
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/6784
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDK 539.3 A generalization of the direct integration method is given with regard to solving the original equations of two-dimensional thermoelasticity problems for solids with corner points (i.e., plane problems for a rectangular domain and an annular sector and the axisymmetric problem for a solid cylinder of finite length). The problems are thereby reduced to a governing integrodifferential equation for a key function, which is unique for each problem. By making use of equilibrium equations, the expressions for stress-tensor components are derived in terms of the key function, while the complete sets of boundary conditions are identically reduced to the corresponding sets of integral conditions for the key function. The algorithms for separating variables in the derived governing equations are suggested by utilizing the complete sets of the eigen- and associated functions in order to construct the solutions to the formulated problems in the form of explicit dependencies on thermal loading in view of the boundary conditions.