Mathematical Models of Thermal Reaction of Viscoelastic Bodies

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Abstract

This paper examines mathematical models of the thermal response of viscoelastic bodies under intense heating of the solid boundary (temperature heat ing; thermal heating; heating by the environment). The proposed theory is based on the linear rheological models of Maxwell and Kelvin, introducing stress and strain deviators. A generalized model is considered, incorporating three coordi nate systems simultaneously: Cartesian coordinates – a massive body bounded by a flat surface; spherical coordinates – a massive body with an internal spherical cavity; and cylindrical coordinates – a massive body with an internal cylindrical cavity. Numerical experiments are presented, and the influence of the domain topology on the magnitude of the corresponding thermal stresses is revealed; the properties of Maxwell and Kelvin viscoelastic media are described.

About the authors

E. M. Kartashov

Federal State Budgetary Educational Institution of Higher Education “MIREA – Russian Technological University” (Lomonosov Institute of Fine Chemical Technology), Department of Higher and Applied Mathematics

Email: professor.kartashov@gmail.com
ORCID iD: 0000-0002-7808-4246
Scopus Author ID: 7004134344
ResearcherId: Q-9572-2016
Dr. Sci. (Phys.-Math.), Honored Scientist of the Russian Federation, Honorary Worker of Higher Professional Education of the Russian Federation, Honorary Worker of Science and Technology of the Russian Federation, Honorary Professor of the Lomonosov Moscow State University of Fine Chemical Technology, Laureate of the Golden Medal of the Academy of Sciences of Belarus in Thermophysics Moscow, 119571

E. V. Solomonova

Federal State Budgetary Educational Institution of Higher Education “MIREA – Russian Technological University” (Lomonosov Institute of Fine Chemical Technology), Department of Higher and Applied Mathematics

Email: katrin-vaso@yandex.ru
Lecturer Moscow, 119571

I. R. Tishaeva

Federal State Budgetary Educational Institution of Higher Education “MIREA – Russian Technological University” (Lomonosov Institute of Fine Chemical Technology), Department of Higher and Applied Mathematics

Email: irina.tishaeva@rambler.ru
ORCID iD: 0000-0003-1866-6866
Candidate of Technical Sciences, Associate Professor Moscow, 119571

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