Про подання розв’язку квазістатичної задачі термопружності для багатошарового циліндра

• Date: 2023
• Main Author: Protsiuk, B. V.; Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України, Львів
• Format: Article
• Language: Ukrainian
• Published: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine 2023
• Subjects: багатошаровий циліндр; нестаціонарне температурне поле; асимптотичний тепловий режим; ряди за власними функціями; термопружність; обернені задачі; узагальнені функції; функції Ґріна; лінійні сплайни; УДК 539.3
• Online Access: http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/apmm2023.21.43-63
• Journal Title: Prykladni Problemy Mekhaniky i Matematyky

The solution of the quasi-static problem of thermoelasticity for a long multi-layered hollow cylinder is constructed in the form of a superposition of dependencies, each of which describes a stressed state caused by a corresponding thermal or force factor. Its application to the determination of the thermoelastic state for various laws of environmental temperature change and heat fluxes and asymptotic regimes, as well as to the solution of inverse problems of thermoelasticity, is illustrated. At the same time, the found exact sums of the series of the eigenfunctions of the thermal conductivity problem for the considered cylinder were used. Three distributions of the ambient temperature inside a twelve-layered hollow cylinder were analyzed, which were determined by the specified distributions of displacement, radial deformation, and ring stress on the limiting outer surface, respectively.  Cite as: B. V. Protsiuk, “On the representation of a solution to the quasistatic problem of thermal elasticity for a multilayer cylinder,” Prykl. Probl. Mekh. Mat., Issue 21, 43–63 (2023) (in Ukrainian), https://doi.org/10.15407/apmm2023.21.43-63