Надіслати цю статтю Методологія дослідження термонапруженого стану тіл із тонкими багатошаровими покриттями
Анотація
Зразок для цитування: В. А. Шевчук, “Методологія дослідження термонапруженого стану тіл із тонкими багатошаровими покриттями,” Мат. методи та фіз.-мех. поля, 64, No. 3, 41–54 (2021), https://doi.org/10.15407/mmpmf2021.64.3.41-54
Translation: V. A. Shevchuk, “Methodology of investigations of the thermal stressed state of bodies with thin multilayer coatings,” J. Math. Sci., 278, No. 5, 780–794 (2024), https://doi.org/10.1007/s10958-024-06961-0
Ключові слова
Посилання
A. V. Attetkov, N. S. Belyakov, “The temperature field of an infinite solid containing a cylindrical channel with a thermally thin surface coating,” Teplofiz. Vysok. Temp., 44, No. 1, 136–140 (2006); English translation: High Temp., 44, No. 1, 139–143 (2006), https://doi.org/10.1007/s10740-006-0016-0
R. E. Bellman, R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, Elsevier, New York (1965), https://doi.org/10.1109/TAC.1965.1098135
Yu. N. Belyaev, “Methods of calculations of transfer matrices of elastic strains,” Vestn. Permsk. Nats. Issled. Politekhn. Univ. Ser. Mekhanika, No. 3, 63–109 (2013).
A. A. Berezovskii, R. A, Shuvar, “Plane nonstationary temperature field of a circular cylinder with a thermally thin coating,” in: Problems of Nonstationary Heat Conduction [in Russian], Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, Kiev (1984), pp. 97–104.
A. T. Vasilenko, “Main relationships of some versions of refined models of shells,” in: A. N. Guz (editor), Mechanics of Composites, Vol. 8: Ya. M. Grigorenko, A. T. Vasilenko, I. G. Emel’yanov, N. N. Kryukov, N. D. Pankratova, B. L. Pelekh, G. G Vlaikov, A. V. Maksimuk, and G. P. Urusova, Statics of Structural Elements [in Russian], A.S.K., Kiev (1999), pp. 78–91.
A. P. Gavris’, P. R. Shevchuk, “Mathematical modeling of the processes occurring during high-temperature spray coating,” Mat. Met. Fiz.-Mekh. Polya, Issue 33, 13–18 (1991); English translation: J. Sov. Math., 65, No. 5, 1818–1822 (1993), https://doi.org/10.1007/BF01097295
N. Hembara, Yo. Luchko, “Modeling of the thermal conductivity of shells with a bilateral multilayer coating,” Visn. Ternop. Nats. Tekhn. Univ., 69, No. 1, 222–230 (2013).
A. D. Gorbunov, “Analytic calculation of heating (cooling) of simple bodies coated with a thin shell,” Metallurg. Teprotekh., Issue 2 (17), 56–62 (2010).
Ya. M. Grigorenko, A. T. Vasilenko, Theory of Shells of Variable Rigidity, in: A. N. Guz (editor), Methods for Calculation of Shells [in Russian], Vol. 4, Naukova Dumka, Kiev (1981).
A. I. Zhornik, V. A. Kirichek, “Approximate solution of the problem of heat conduction for a solid cylinder with a thin coating,” Nauchn. Diskuss.: Vopr. Tekh. Nauk, Nos. 9-10 (28), 21–29 (2015).
D. D. Zakharov, “Effective high-order approximations of layered coatings and linings of anisotropic elastic, viscoelastic and nematic materials,” Prikl. Mat. Mekh., 74, No. 3, 403–418 (2010); English translation: J. Appl. Math. Mech., 74, No. 3, 286–296 (2010), https://doi.org/10.1016/j.jappmathmech.2010.07.004
D. V. Ivashchuk, Investigation of Thermodiffusion Processes and the Stressed State in Bodies with Coatings [in Russian], Author’s Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Lviv (1978).
Yu. M. Kolyano, M. E. Khomyakevich, “Generalized heat conduction in coated bodies that accounts for the coating curvature,” Inzh.-Fiz. Zh., 65, No. 6, 745–749 (1993); English translation: J. Eng. Phys. Thermophys., 65, No. 6, 1251–1256 (1993), https://doi.org/10.1007/BF00861951
G. M. Komarov, “Conditions of conjugation through a thermally thin layer in problems of heat conduction,” Dop. Nats. Akad. Nauk Ukr., No. 7, 26–32 (1996).
L. B. Lerman, “Layered inhomogeneous objects with interfaces. Application of translation matrices in some applied problems,” Khim. Fiz Tekhnol. Poverkhn., 7, No. 3, 255–284 (2016), https://doi.org/10.15407/hftp07.03.255
Yo. Yo. Luchko, “Calculation of the thermal conductivity of concrete plates with multilayer coatings,” Nauk. Visn. Mukachiv. Tekhnol. Inst., Issue 2, 40–46 (2006).
Ya. S. Pidstryhach, Selected Works [in Ukrainian], Naukova Dumka, Kyiv (1995).
Ya. S. Podstrigach, “On the application of the operator method to the derivation of the main relations of the theory of heat conduction of thin-walled elements and composite structures,” Tepl. Napryazh. Élem. Konstruk., Issue 5, 24–35 (1965).
Ya. S. Podstrigach., Yu. M. Kolyano, M. M. Semerak, Temperature Fields and Stresses in Elements of Electrovacuum Devices [in Russian], Naukova Dumka, Kiev (1981).
Ya. S. Podstrigach, R. N. Shvets, Thermoelasticity of Thin Shells [in Russian], Naukova Dumka, Kiev (1978).
Ya. S. Podstrigach, P R. Shevchuk, “Effect of surface layers on diffusion processes and the resulting stress state in solids,” Fiz.-Khim. Mekh. Mater., 3, No. 5, 575–583 (1967); English translation: Sov. Mater. Sci., 3, No. 5, 420–426 (1968), https://doi.org/10.1007/BF00716058
Ya. S. Podstrigach, P. R. Shevchuk, “Temperature fields and stresses in bodies with thin coatings,” Tepl. Napryazh. Élem. Konstruk., Issue 7, 227–233 (1967).
R. F. Terlets’kyi, O. P. Turii, “Modeling and investigation of heat transfer in plates with thin coatings with regard for the influence of radiation,” Mat. Met. Fiz.-Mekh. Polya, 55, No. 2, 186–201 (2012); English translation: J. Math. Sci., 192, No. 6, 703–722 (2013), https://doi.org/10.1007/s10958-013-1427-1
N. P. Fleishman, “Mathematical models of thermal conjugation of media with thin foreign interlayers or coatings,” Visn. L’viv. Univ. Ser. Mekh.-Mat., Issue 39, 30–34 (1993).
V. A. Shevchuk, “Analytical solution of nonstationary heat conduction problem for a half-space with a multilayer coating,” Inzh.-Fiz. Zh., 86, No. 2, 423–431 (2013); English translation: J. Eng. Phys. Thermophys., 86, No. 2, 450–459 (2013), https://doi.org/10.1007/s10891-013-0854-7
V. A. Shevchuk, “Determination of residual stresses in a cylinder with a thin multilayer coating,” Prykl. Probl. Mekh. Mat., Issue 10, 159–167 (2012).
V. A. Shevchuk, “On the construction of generalized boundary conditions of convective heat exchange of bodies with a medium through thin nonplane coatings,” Dop. Nats. Akad. Nauk Ukr., No. 7, 76–82 (2011).
V. A. Shevchuk, “Problem of thermoelasticity for a half-space with a multilayer coating,” Prykl. Probl. Mekh. Mat., Issue 11, 157–163 (2013).
V. A. Shevchuk, “Problem of thermoelasticity for a cylinder with thin multilayer coating,” Mat. Met. Fiz.-Mekh. Polya, 60, No. 2, 117–129. (2017); English translation: J. Math. Sci., 243, No. 1, 145–161 (2019), https://doi.org/10.1007/s10958-019-04532-2.
V. A. Shevchuk, “Nonstationary one-dimensional problem of heat conduction for a cylinder with a thin multilayer coating,” Mat. Met. Fiz.-Mekh. Polya, 54, No. 2, 179–185 (2011); English translation: J. Math. Sci., 184, No. 2, 215–223 (2012), https://doi.org/10.1007/s10958-012-0865-5
V. A. Shevchuk, “Generalized boundary conditions for heat transfer between a body and the surrounding medium through a multilayer thin covering,” Mat. Met. Fiz.-Mekh. Polya, Issue 38, 116–120 (1995); English translation: J. Math. Sci., 81, No. 6, 3099–3102 (1996), https://doi.org/10.1007/BF02362603.
V. A. Shevchuk, “Analysis of the stressed state of bodies with multilayer thin coatings,” Probl. Prochn., No. 1, 136–150 (2000); English translation: Strength Mater., 32, No. 1, 92–102 (2000), https://doi.org/10.1007/BF02511512
V. A. Shevchuk, “Calculation of temperature stresses in bodies with thin multilayer coatings,” Visn. Dnipropetrovs’k. Univ. Ser. Mekhanika, 19, Issue 15(1), 129–139 (2011).
V. A. Shevchuk, “Heat conduction in plates with thin two-sided multilayer coatings under the conditions of nonstationary heating,” Mat. Met. Fiz.-Mekh. Polya, 58, No. 2, 148–157 (2015); English translation: J. Math. Sci., 223, No. 2, 184–197 (2017), https://doi.org/10.1007/s10958-017-3347-y
V. A. Shevchuk, “Thermostressed state of plate with a thin bilateral multilayer coating under conditions of nonstationary heat exchange,” Prykl. Probl. Mekh. Mat., Issue 14, 113–122 (2016).
V. A. Shevchuk, “Generalized boundary conditions of radiant-convection heat exchange of bodies with ambient medium through multilayer nonplanar coatings,” Mat. Met. Fiz.-Mekh. Polya, 62, No. 2, 82–97 (2019); English translation: J. Math. Sci., 261, No. 1, 95–114 (2022), https://doi.org/10.1007/s10958-022-05741-y
V. A. Shevchuk, A. P. Gavris’, “Nonstationary heat-conduction problem for a half-space with a multilayer coating upon cyclic change in the ambient temperature,” Inzh.-Fiz. Zh., 93, No. 6, 1543–1551 (2020); English translation: J. Eng. Phys. Thermophys., 93, No. 6, 1489–1497 (2020), https://doi.org/10.1007/s10891-020-02254-w.
V. A. Shevchuk, O. P. Havrys’, “Choice of the iterative method for solving a nonlinear nonstationary problem of heat conduction for a half-space in radiative cooling,” Mat. Met. Fiz.-Mekh. Polya, 57, No. 4, 179–185 (2014); English translation: J. Math. Sci., 220, 226–234 (2017), https://doi.org/10.1007/s10958-016-3179-1
V. A. Shevchuk, O. P. Havrys’, “Thermostressed state of a half-space with a multilayer coating under radiative-convective heat exchange,” Prykl. Probl. Mekh. Mat., Issue 15, 171–179 (2017).
V. A. Shevchuk, B. M. Kalynyak, “Stressed state of cylindrical bodies with multilayer inhomogeneous coatings,” Fiz.-Khim. Mekh. Mater., 46, No. 6, 35–41 (2010); English translation: Mater Sci., 46, No. 6, 747–756 (2011), https://doi.org/10.1007/s11003-011-9348-y
V. Shevchuk, O. Havrys’, “Analytic solution of the boundary-value problem of heat conduction for a half-space–multilayer coating system with an inhomogeneous initial condition under convective heat exchange with a medium,” Fiz.-Mat. Model. Inform. Tekhnol., Issue 24, 130–140 (2016).
V. Shevchuk, O. Havrys’, “Investigation of the temperature field of a half-space with a multilayer coating under radiativeconvective heat exchange,” Fiz.-Mat. Model. Inform. Tekhnol., Issue 20, 229–240 (2014).
V. Shevchuk, O. Havrys’, “Problem of thermoelasticity for a half-space with a multilayer coating under thermocyclic treatment,” in: R. M. Kushnir and H. S. Kit (editors), Mathematical Problems of Mechanics of Inhomogeneous Structures: Collection of Scientific Works of the 10th International Scientific Conference [in Ukrainian], Issue 5, Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of the National Academy of Sciences of Ukraine, Lviv (2019), pp. 129–130.
V. Shevchuk, O. Havrys’, P. Shevchuk, “Nonlinear boundary-value problem of radiative-convective heat exchange of bodies with multilayer coatings,” Mashynoznavstvo, No. 5 (155), 21–25 (2010).
P. R. Shevchuk, A. P. Gavris’, “The influence of radiant heating on temperature schemes and residual stresses under hightemperature spray coating,” Mat. Met. Fiz.-Mekh. Polya, Issue 30, 69–73 (1989); English translation: J. Sov. Math., 63, No. 3, 371–374 (1993), https://doi.org/10.1007/BF01255745
M. A. Al-Nimr, M. K. Alkam, “A generalized thermal boundary condition,” Heat Mass Transf., 33, Nos. 1-2, 157–161 (1997), https://doi.org/10.1007/s002310050173
A. Auvray, G. Vial, “Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers,” ESAIM Proc. Surv., 61, 38–54 (2018), https://doi.org/10.1051/proc/201861038
L. Y. Bahar, “Transfer matrix approach to layered systems,” J. Eng. Mech. Div., 98, No. 5, 1159–1172 (1972), https://doi.org/10.1061/JMCEA3.0001660
L. Y. Bahar, R. B. Hetnarski, “Coupled thermoelasticity of a layered medium,” J. Therm. Stresses, 3, No. 1, 141–152 (1980), https://doi.org/10.1080/01495738008926958
A. Campo, “A quasilinearization approach for the transient response of bodies with surface radiation,” Lett. Heat Mass Transf., 4, No. 4, 291–298 (1977), https://doi.org/10.1016/0094-4548(77)90118-7
J.-L. Chen, N. O. Hembara, M. M. Hvozdyuk, “Nonstationary temperature problem for a cylindrical shell with multilayer thin coatings,” Fiz.-Khim. Mekh. Mater., 54, No. 3, 49–57 (2018); English translation: Mater. Sci., 54, No. 3, 339–348 (2018), https://doi.org/10.1007/s11003-018-0190-3
Y. Z. Chen, “Study of multiply-layered cylinders made of functionally graded materials using the transfer matrix method,” J. Mech. Mater. Struct., 6, No. 5, 641–657 (2011), https://doi.org/10.2140/jomms.2011.6.641
H. J. Choi, T. E. Jin, K. Y. Lee, “Transient thermal stresses in a cladded semi-infinite medium containing an underclad crack,” J. Therm. Stresses, 18, No. 3, 269–290 (1995), https://doi.org/10.1080/01495739508946303
F. Du, M. R. Lovell, T. W. Wu, “Boundary element method analysis of temperature fields in coated cutting tools,” Int. J. Solids Struct., 38, Nos. 26-27, 4557–4570 (2001), https://doi.org/10.1016/S0020-7683(00)00291-2
X. Hou, Z. Deng, G. Yin, “Application of transfer matrix method in heat transfer performance analysis of multi-re-entrant honeycomb structures,” Heat Mass Transf., 50, No. 12, 1765–1782 (2014), https://doi.org/10.1007/s00231-014-1352-y
S. A. Lukasiewicz, “Thermal stresses in shells,” in: R. B. Hetnarski (editor), Thermal Stresses III, North Holland, Amsterdam (1989), pp. 355–553.
D. Moulton, J. A. Pelesko, “Thermal boundary conditions: an asymptotic analysis,” Heat Mass Transf., 44, No. 7, 795–803 (2008), https://doi.org/10.1007/s00231-007-0277-0
L. A. Pipes, “Matrix analysis of heat transfer problems,” J. Franklin Inst., 263, No. 3, 195–206 (1957), https://doi.org/10.1016/0016-0032(57)90927-4
L. Rahmani, G. Vial, “Reinforcement of a thin plate by a thin layer,” Math. Meth. Appl. Sci., 31, No. 3, 315–338 (2008), https://doi.org/10.1002/mma.910
A. A. Rizk, F. Erdogan, “Cracking of coated materials under transient thermal stresses,” J. Therm. Stresses, 12, No. 2, 125–168 (1989), https://doi.org/10.1080/01495738908961959
A. E.-F. A. Rizk, S. F. Radwan, “Transient thermal stress problem for a cracked semi-infinite medium,” J. Therm. Stresses, 15, No. 4, 451–468 (1992), https://doi.org/10.1080/01495739208946150
V. A. Shevchuk, “Calculation of thermal state of bodies with multilayer coatings,” in: Proc. of the Int. Conf. “Computational Science – ICCS 2002” (April 21–24, 2002, Netherlands), Ser.: P. M. A. Sloot, A. G. Hoekstra, C. J. K. Tan, and J. J. Dongarra (editors), Lecture Notes in Computer Science, Vol. 2330, Springer, Berlin (2002), pp. 500–509, https://doi.org/10.1007/3-540-46080-2_52
V. A. Shevchuk, “Generalized boundary conditions to solving thermal stress problems for bodies with thin coatings,” in: R. B. Hetnarski (editor), Encyclopedia of Thermal Stresses, Vol. 4, Springer, Dordrecht (2014), pp. 1942–1953, https://doi.org/10.1007/978-94-007-2739-7_601
V. A. Shevchuk, “Modeling and computation of heat transfer in a system “body–multilayer coating,” Heat Transf. Res., 37, No. 5, 421–433 (2006), https://doi.org/10.1615/HeatTransRes.v37.i5.50
V. A. Shevchuk, “Thermoelasticity problem for a multilayer coating/half-space assembly with undercoat crack subjected to convective thermal loading,” J. Therm. Stresses, 40, No. 10, 1215–1230 (2017), https://doi.org/10.1080/01495739.2017.1301788
V. A. Shevchuk, V. V. Silberschmidt, “Analysis of damage evolution in thick ceramic coatings,” Mater. Sci. Eng. A, 426, Nos. 1-2, 121–127 (2006), https://doi.org/10.1016/j.msea.2006.03.080
V. A. Shevchuk, V. V. Silberschmidt, “Analysis of damage evolution in thin multi-layer coatings under thermal loading,” in: F. Ziegler, R. Heuer, and C. Adam (editors), Proc. of the 6th Int. Congr. on Thermal Stresses (May 26–29, 2005, Vienna, Austria), Vol. 2, Vienna University of Technology, Vienna (2005), pp. 313–316.
V. A. Shevchuk, V. V. Silberschmidt, “Semi-analytical analysis of thermally induced damage in thin ceramic coatings,” Int. J. Solids Struct., 42, Nos. 16-17, 4738–4757 (2005), https://doi.org/10.1016/j.ijsolstr.2005.02.002
T. C. T. Ting, “Mechanics of a thin anisotropic elastic layer and a layer that is bonded to an anisotropic elastic body or bodies,” Proc. Roy. Soc. A, 463, Issue 2085, 2223–2239 (2007), https://doi.org/10.1098/rspa.2007.1875
H. Wang, Q. Qin, “Thermal analysis of a functionally graded coating/substrate system using the approximated transfer approach,” Coatings, 9, No. 1, Article No. 51 (2019), https://doi.org/10.3390/coatings9010051
X. Wang, L. J. Sudak, “Three-dimensional analysis of multi-layered functionally graded anisotropic cylindrical panel under thermomechanical loading,” Mech. Mater., 40, Nos. 4-5, 235–254 (2008), https://doi.org/10.1016/j.mechmat.2007.06.008
W. Wunderlich, W. D. Pilkey, Mechanics of Structures: Variational and Computational Methods, CRC Press Inc., Boca Raton (2002), https://doi.org/10.1201/9781420041835
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