Mathematical problems of thermomechanics for deformable bodies under thermal irradiation

  • O. R. Hachkevych Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
  • R. M. Kushnir Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
  • R. F. Terletskii Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
Keywords: deformable body, electromagnetic field, thermal radiation, magnetization, polarization, radiation heat transfer, thermal stresses, mathematical problems

Abstract

UDC 535.51, 535.55, 539.3

It is a review of the results of researches in the field of mathematical problems of the thermomechanics of magnetizable and polarizable electroconductive deformable bodies under electromagnetic irradiation, which are carried out at Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine. In this paper, we formulate the problems of mathematical physics that describe the thermal and thermal stress state in such bodies taking into account the peculiarities of electromagnetic action in different frequency ranges and analyze the methods of study of the thermomechanical behavior of bodies (in particular, of different transparency, as semitransparent as well as opaque) in these ranges under thermal irradiation.

References

V. N. Koshlyakov, I. A. Lukovsky, Issledovany`e po mexany`ke v Insty`tute matematy`ky` AN USSR za 50 let, Ukr. mat. zhurn., 36, № 5, 576 – 583 (1984).

I. A. Lukovsky, O. G. Mazko, O. N. Timokha, , Doslidzhennya z matematy`chny`x problem mexaniky` v Insty`tuti matematy`ky` NAN Ukrayiny`, ,, Zb. pracz In-tu matematyki` NAN Ukrayiny,15, № 1, 247 – 283 (2018).

A. F. Ulitko, Vy`brani praci, Vy`d-o-poligraf. centr „Kyiv . un-t”, Kyiv (2004).

O. Hachkevych, R. Kushnir, Selected problems of the mechanics of coupled fields, J. Math. Sci., 220, № 2, 115 – 132 (2018), https://doi.org/10.1007/s10958-018-3666-7 DOI: https://doi.org/10.1007/s10958-018-3666-7

O. R. Hachkevych, R. F. Terletskii, Modeli termomexaniky` namagnetovny`x i polyary`zovny`x elektroprovidny`x deformivny`x tverdy`x til, Fiz.-xim. mexanika materialiv, 40, № 3, 19 – 37 (2004).

Ya. J. Burak, O. R. Hachkevych, R. F. Terletskii, Termomexanika bagatokomponentny`x til ny`z`koyi elektroprovidnosti, Modelyuvannya ta opty`mizaciya v termomexanici elektroprovidny`x neodnoridny`x til, t. 1, Spolom, L`viv (2006).

O. R. Hachkevych, B. D. Drobenko, Termomexanika namagnechuvany`x elektroprovidny`x termochutly`vy`x til, Modelyuvannya ta opty`mizaciya v termomexanici elektroprovidny`x neodnoridny`x til, t. 4, Spolom, L`viv (2010).

O. R. Hachkevych, R. F. Terletskii, R. O. Ivas`ko, Modelyuvannya elektromagnitny`x, teplovy`x i mexanichny`x procesiv u magnitny`x seredovy`shhax za vraxuvannya momentny`x chy`nny`kiv, Mat. metody` i fiz.-mex. polya, 61, № 4, 113 – 129 (2018). DOI: https://doi.org/10.5184/classicalj.113.2.0129

M. T. Solodyak, Termopruzhny`j stan magnetom'yakogo sharu u garmonijnomu za chasom magnetnomu poli z pidmagnechuvannyam, Fiz.-xim. mexanika materialiv, 40, № 2, 19 – 28 (2004).

O. R. Hachkevych, M. T. Solodyak, R. F. Terletskii, D. V. Tarlakovs`ky`j, Spivvidnoshennya elektrody`namiky`, energety`chni ta sy`lovi chy`nny`ky` diyi elektromagnetnogo polya dlya magnetny`x seredovy`shh, Fiz.-xim. mexanika materialiv, 50, № 4, 62 – 68 (2014).

A. D. Kovalenko, Osnovy termouprugosty`, Nauk. dumka, Kyiv (1970).

V. Novaczky, Teory`ya uprugosty`, My`r, Moskva (1975).

A. V. Lykov, Teory`ya teploprovodnosty`, Vyssh. shkola, Moskva (1967).

R. Zy`gel`, Dzh. Xauell, Teploobmen y`zlucheny`em, My`r, Moskva (1975).

N. A. Rubczov, Teploobmen y`zlucheny`em v sploshnyx sredax, Nauka, Novosy`by`rsk (1984).

O. R. Hachkevych, R. F. Terletskii, T. L. Kurniczkiy, Mexanotermody`fuziya v chastkovo prozory`x tilax, Modelyuvannya ta opty`mizaciya v termomexanici elektroprovidny`x neodnoridny`x til, t. 2, Spolom, L`viv (2007).

O. R. Hachkevych, R. F. Terletskii, M. B. Brukhal, Deyaki problemy` matematy`chnogo modelyuvannya v termomexanici til riznoyi prozorosti za teplovogo oprominennya, Mat. metody` i fiz.-mex. polya., 51, № 3, 202 – 219 (2008).

R. F. Terletskii, M. B. Brukhal, Yu. V. Nemy`rovs`ky`j, Modelyuvannya ta doslidzhennya termomexanichnoyi povedinky` termochutly`vy`x til za vraxuvannya vply`vu teplovogo vy`prominyuvannya, Mat. metody` ta fiz.-mex. polya, 56, № 2, 212 – 224 (2013).

M. Brukhal, R. Terletskii, O. Fundak, Metody`ka chy`slovogo rozv'yazuvannya nelinijny`x zadach teploperenesennya v tilax riznoyi prozorosti dlya teplovogo vy`prominyuvannya, Visn. L`viv. un-tu. Ser. Pry`kl. matematy`ka ta informaty`ka, vy`p. 13, 59 – 71 (2007).

O. R. Hachkevych, R. F. Terletskii, M. B. Brukhal, Modelyuvannya ta doslidzhennya teplovogo ta napruzhenogo staniv v oprominyuvanij sy`stemi z shariv riznoyi prozorosti, rozdileny`x nepogly`nayuchy`m seredovy`shhem, Mat. metody` i fiz.-mex. polya, 60, № 4, 124 – 136 (2017).

V. S. Popovych, G. T. Suly`m, Central`no-sy`metry`chna kvazistaty`chna zadacha termopruzhnosti termochutly`vogo tila, Fiz.-xim. mexanika materialiv, 40, № 3, 62 – 68 (2004).

V. S. Popovych, G. Yu. Garmatij, O. M. Vovk, Termopruzhny`j stan termochutly`voyi porozhny`stoyi kuli za umov konvekty`vno-promenevogo teploobminu z dovkillyam, Fiz.- xim. mexanika materialiv, 42, № 6, 39 – 48 (2006).

R. M. Kushnir, V. S. Popovych, O. M. Vovk, The thermoelastic state of a thermosensitive sphere and space with a spherical cavity subject to complex heat exchange, J. Engng. Math., 61, № 2-4, 357 – 369 (2008). DOI: https://doi.org/10.1007/s10665-008-9214-6

R. M. Kushnir, V. S. Popovych, Termopruzhnist` termochutly`vy`x til, Modelyuvannya ta opty`mizaciya v termomexanici elektroprovidny`x neodnoridny`x til, t. 3, Spolom, L`viv (2010).

V. S. Popovych, O. M. Vovk, G. Yu. Garmatij, Doslidzhennya staty`chnogo termopruzhnogo stanu termochutly`vogo porozhny`stogo cy`lindra za konvekty`vno-promenevogo teploobminu z dovkillyam, Mat. metody` ta fiz.-mex. polya, 54, № 4, 167 – 175 (2011).

R. M. Kushnir, V. S. Popovych, Heat Conduction problems of thermosensitive solids under complex heat exchange, Heat Conduction – Basic Research, Rijeka (Croatia) (2011), p. 131 – 154. DOI: https://doi.org/10.5772/27970

R. M. Kushnir, V. S. Popovych, V. V. Yanishevsky, Thermal and thermoelastic state of thin-walled thermosensitive structures subject to complex heat exchange, J. Thermal Stresses, 35, Issue 1–3, 91 – 102 (2012). DOI: https://doi.org/10.1080/01495739.2012.654747

V. Popovych, Methods for determination of the thermo-stressed state of thermosensitive solids under complex heat exchange conditions, Encyclopedia Thermal Stresses, Vol. 6, Springer, Dordrecht etc. (2014), p. 2997 – 3008. DOI: https://doi.org/10.1007/978-94-007-2739-7_617

Published
11.10.2021
How to Cite
Hachkevych , O. R., R. M. Kushnir, and R. F. Terletskii. “Mathematical Problems of Thermomechanics for Deformable Bodies under Thermal Irradiation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 10, Oct. 2021, pp. 1317-29, doi:10.37863/umzh.v73i10.6787.
Section
Research articles