https://oldena.lpnu.ua/handle/ntb/41469| Title: | The formulation and development of methods of solving thermomechanics problems for irradiated layered solids |
| Other Titles: | Формулювання і розроблення методів розв’язку задач термомеханіки шаруватих опромінюваних тіл |
| Authors: | Гачкевич, О. Терлецький, Р. Турій, О. Hachkevych, O. Terlets’kyi, R. Turii, O. |
| Affiliation: | Інститут прикладних проблем механіки i математики ім. Я. С. Пiдстригача НАН України Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine |
| Bibliographic description (Ukraine): | Hachkevych O. The formulation and development of methods of solving thermomechanics problems for irradiated layered solids / O. Hachkevych, R. Terlets’kyi, O. Turii // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 4. — No 1. — P. 21–36. |
| Bibliographic description (International): | Hachkevych O. The formulation and development of methods of solving thermomechanics problems for irradiated layered solids / O. Hachkevych, R. Terlets’kyi, O. Turii // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 4. — No 1. — P. 21–36. |
| Is part of: | Mathematical Modeling and Computing, 1 (4), 2017 |
| Issue: | 1 |
| Volume: | 4 |
| Issue Date: | 15-Jun-2017 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Lviv |
| UDC: | 539.3 |
| Keywords: | моделювання термонапружений стан теплове опромінення теплоперенос багатошарові пластини частково-прозорі та непрозорі шари modeling thermal and stressed states thermal irradiation heat transfer multilayered plates semi-transparent and opaque layers |
| Number of pages: | 16 |
| Page range: | 21-36 |
| Start page: | 21 |
| End page: | 36 |
| Abstract: | Запропоновано математичну модель, що описує на основi феноменологiчної теорiї ви-
промiнювання та теорiї квазiстатичної термопружностi термонапружений стан опро-
мiнюваних плоско-шаруватих тiл (пластин) зi складниками рiзної прозоростi з ураху-
ванням впливу теплового випромiнювання на поверхнях, у частково прозорих обла-
стях i на межах контакту. Записано вихiднi спiввiдношення моделi для нескiнченних
двошарових пластин за рiзних комбiнацiй радiацiйних властивостей складникiв. За-
пропоновано методи розв’язку нових нелiнiйних задач. Виявлено, на основi аналiзу
знайдених розв’язкiв, ряд нових закономiрностей у розподiлах температури та ком-
понент тензора напружень в опромiнюваних шаруватих пластинах залежно вiд умов
закрiплення, радiацiйних властивостей складникiв A mathematical model to describe a thermoelastic state of plane-parallel plates (plate composites) subjected to a thermal radiation is developed. The model is grounded on phenomenological theory of radiation and quasistatic thermoelasticity. It takes into account an effect of radiation on plate surfaces, contact boundaries, and in semi-transparent areas. It is assumed a perfect contact between the constituents of layers that boundary contact is modeled on the plane surface defined on both sides of its radiation characteristics of the material layers and the conditions of heat and mechanical contacts are ideal. The methods to solve new nonlinear contact-boundaries problems of thermoelasticity are proposed. On analysing the posed problems solutions, the new features of temperature and stresses distributions in plates are established, dependent on radiative properties of layers, layer’s thickness and on source temperature. |
| URI: | https://ena.lpnu.ua/handle/ntb/41469 |
| ISSN: | 2312-9794 |
| Copyright owner: | © 2017 Lviv Polytechnic National University CMM IAPMM NASU |
| References (Ukraine): | [1] HachkevychO.R., Terlets’kyiR. F., Kournyts’kyiT. L. Mechanothermodiffusion in semi-transparent solids. Lviv, SPOLOM, (2007), (in Ukrainian). [2] AdrianovV.N. Fundamentals of Radiation and Complex Heat Transfer. Moscow, Energija, 464 p. (1972), (in Russian). [3] GrigorjevB.A. Pulse heating radiations. Moscow, Nauka, Vol.1, 320 p. (1974), (in Russian). [4] RubtsovN.A. Radiation heat transfer in continuous media. Novosibirsk, Nauka, 277 p. (1984), (in Russian). [5] SiegelR, Howell J. Thermal radiation heat transfer. Moscow, Mir, 935 p. (1975), (in Russian). [6] AndersonE.E., ViskantaR. Effective Thermal Conductivity for Heat Transfer Through Semitransparent Solids. J. Am. Ceram. Soc. 56, n.10, 541–546 (1973). [7] HachkevychO.R., Terlets’kyiR. F. Models of thermomechanics of magnetized and polarized electrically conductive deformable solids. Phys.-Chem. Mechanics ofMaterials. 40, n.3, 19–37. (2004), (in Ukrainian). [8] HachkevychO.R., MusijR. S., MelnikN.B. Thermomechanical behavior of electrically conductive hollow cylinder with pulsed electromagnetic action. Math. Methods and Phys.-Mech. Fields. 44, n.1, 146–154 (2001), (in Ukrainian). [9] Postol’nykY. S., OgurtsovA.P. Applied Nonlinear thermomechanics. Kyiv. 280 p. (2000), (in Ukrainian). [10] HoC.-H., ¨Ozi¸sikM.N. Combined conduction and radiation in a two-layer planar medium with flux boundary condition. Num. Heat Transfer. 11, n.3, 321–340 (1987). [11] HoC.-H., ¨Ozi¸sikM.N. Simultaneous conduction and radiation in a two-layer planar medium. J. Thermophys. Heat Transfer. 1, n.2, 154–161 (1987). [12] SiegelR. Two flux Green’s function analysis for transient spectral radiation in a composite. J. Thermophys. Heat Transfer. 10, n.4, 681–688 (1996). [13] TanH.-P., Wang P.-Y., XiaX.-L. Transient coupled radiation and conduction in an absorbing and scattering composite layer. J. Thermophys. Heat Transfer. 14, n.1, 77–87 (2000). [14] TimoshenkoV.P., TrenerM.G. A method for evaluting heat transfer in multilayer semi-transparent materials. Heat Transfer-Soviet Research. 18, 321–340 (1986). [15] TsaiC.-F., NixonG. Transient temperature distribution of a multilayer composite wall with effects of internal thermal radiation and conduction. Num. Heat Transfer. 10, n.1, 95–101 (1986). [16] Wang P.-Y., ChengH.-E., TanH.-P. Transient thermal analysis of semitransparent composite layer with an opaque boundary. Int. J. Heat Mass Transfer. 45, n.2, 425–440 (2002). [17] PopovychV. S. Models and methods of calculation thermostressed state of thermo sensitive structural elements under complex conditions of heat transfer: Dis. . .Doctor. Sc. Science. Luts’k, 312 p. (2005), (in Ukrainian). [18] PopovychV. S. Construction of the solutions of the problems of thermoelasticity thermosensitive solids under the conditions of convective-radiant heat exchange. Reports of National Academy of Sciences of Ukraine. 11, 69–73 (1997), (in Ukrainian). [19] PopovychV. S., HarmatijH.Y., VovkO.M. Thermoelastic state of a thermosensitive hollow sphere under the conditions of convective-radiant heat exchange with the environment. Phys.-Chem. Mechanics of Materials. 42, n.6, 39–48 (2006), (in Ukrainian). [PopovychV. S., HarmatijH.Y., VovkO.M. Thermoelastic state of a thermosensitive hollow sphere under the conditions of convective-radiant heat exchange with the environment. Materials Science. 42, n.6, 756–770 (2006)]. [20] BruchalM.B., Terlets’kyiR. F., TuriiO.P. Thermomechanics problems for irradiated solids. Theoretical and Applied Mechanics. 4, n.50, 30–37 (2012), (in Russian). [21] Terlets’kyiR. F., TuriiO.P. Modeling and investigation of heat transfer in plates with thin coatings with regard for the influence of radiation. J. of Mathematical Sciences. 192, n.6, 703–722 (2013). [22] TuriiO.P. Nonlinear contact boundary problem of thermomechanics for the irradiated two-layer plate connected by an intermediate layer. Physico-Mathematical Modelling And Informational Technologies. 9, 118–132 (2009), (in Ukrainian). [23] KushnirR.M., PopovychV. S., VovkO.M. The thermoelastic state of a thermosensitive sphere and space with spherical cavity subject to complex heat exchange. J. Eng. Math. 61, n.2, 357–369 (2008). [24] PopovychV. S., VovkO.M. The method of solving convective-radiant heat exchange between the cylindrical and N-corner prismatic shells. Math. Methods and Phys.-Mech. Fields. 47, n.1, 158–168 (2004), (in Ukrainian). [25] HachkevychO.R., BojchukV.Y. Thermal stress of a long cylinder when heated by thermal radiation. Applied Mechanics. 23, n.4, 16–23 (1987), (in Russian). [26] HachkevychO.R., BojchukV.Y. Thermomechanical behavior of nonmetallic electrically conductive bodies under high-temperature treatment. Math. Methods and Phys.-Mech. Fields. 39, n.1, 74–79 (1996), (in Russian). [27] KoljanoY.M., KulykA.N. Temperature stresses from volumetric sources. Kyiv, Naukova Dumka, 288 p. (1983), (in Russian). [28] PljackoG.V., PodstryhachYa. S. On the state of stress caused by a laser beam in the process of destruction of transparent polymers. Phys.-Chem. Mechanics of Materials. 6, n.3, 93–97 (1970), (in Russian). [29] HetnarskiR.B., DeBolt F.C. Thermal stresses due to laser radiation. Part 1: Heat conduction. J. Thermal Stresses. 15, n.2, 331 (1992). [30] HetnarskiR.B., Hector L.G., Hosseini TehraniP., EslamiM.R. Thermal stresses due to a laser pulse train: Coupled solution. Proc. 3rd Int. Congress on Thermal Stresses. Cracow (Poland), 61–64 (1999). [31] UglovA.A., KoljanoY.M., KulykA.N., Stookuj F. I. Stresses in planar solids with absorption under the action of a local heat source. Physics And Chemistry Of Material Processing. 6, 117–120 (1976), (in Russian). [32] KoljanoY.M., Bernar I. I. Temperature stresses in the plate with two-sided laser treatment. Strength Problems. 5, 36–48 (1983), (in Russian). [33] MuresanCr., VaillonR., MenezoC., MorlotR. Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation. Journal of Quantitative Spectroscopy and Radiative Transfer. 84, n.4, 551–562 (2004). [34] Michael F.Modest. Radiative heat transfer. The Pennsylvania State University, 822 p. (2003). [35] IljushinА.А. Continuum mechanics. Moscow. Publ. Mosc. University, 287 p. (1978), (in Russian). [36] BerezovskyjА. Nonlinear boundary value problems of a heat-radiating solids. Kyiv, Naukova Dumka, 176 p. (1968), (in Russian). [37] KushnirR., ProtsyukB. A Method of the Green’s Functions for Quasistatic Thermoelasticity Problems in Layer Themosensitive Bodies under Complex Heat Exchange. Operator Theory: Advances and Applications. 191, 143–154 (2009). [38] MamedovYa.D., Ashyrov S.A. Nonlinear Volterra equations. Ashgabat, Ylym, 176 p. (1977), (in Russian). [39] Thermal engineering reference book. Under. Ed. V.N.Yurneva and others. Moscow, Energija. Vol.1, 744 p. (1975), (in Russian). [40] Radiative properties of solid materials: Reference Book. Ed. A.E. Sheydlin. Moscow, Energija, 471 p. (1974), (in Russian). [41] Machine-building materials. Quick reference. Under. Ed. V.M.Raskatova. Moscow, Mashynostrojenije, Vol.1, 511 p. (1980), (in Russian). [42] Volkov E.A. Numerical methods. Moscow, Nauka, 256 p.(1982), (in Russian). [43] SamarskyjА.А. Theory of difference schemes. Moscow, Nauka, 616 p. (1989), (in Russian). [44] BellmanR., KalabaR. Quasilinearization and nonlinear boundary value problems. Moscow, Mir, 223 p. (1968), (in Russian). |
| References (International): | [1] HachkevychO.R., Terlets’kyiR. F., Kournyts’kyiT. L. Mechanothermodiffusion in semi-transparent solids. Lviv, SPOLOM, (2007), (in Ukrainian). [2] AdrianovV.N. Fundamentals of Radiation and Complex Heat Transfer. Moscow, Energija, 464 p. (1972), (in Russian). [3] GrigorjevB.A. Pulse heating radiations. Moscow, Nauka, Vol.1, 320 p. (1974), (in Russian). [4] RubtsovN.A. Radiation heat transfer in continuous media. Novosibirsk, Nauka, 277 p. (1984), (in Russian). [5] SiegelR, Howell J. Thermal radiation heat transfer. Moscow, Mir, 935 p. (1975), (in Russian). [6] AndersonE.E., ViskantaR. Effective Thermal Conductivity for Heat Transfer Through Semitransparent Solids. J. Am. Ceram. Soc. 56, n.10, 541–546 (1973). [7] HachkevychO.R., Terlets’kyiR. F. Models of thermomechanics of magnetized and polarized electrically conductive deformable solids. Phys.-Chem. Mechanics ofMaterials. 40, n.3, 19–37. (2004), (in Ukrainian). [8] HachkevychO.R., MusijR. S., MelnikN.B. Thermomechanical behavior of electrically conductive hollow cylinder with pulsed electromagnetic action. Math. Methods and Phys.-Mech. Fields. 44, n.1, 146–154 (2001), (in Ukrainian). [9] Postol’nykY. S., OgurtsovA.P. Applied Nonlinear thermomechanics. Kyiv. 280 p. (2000), (in Ukrainian). [10] HoC.-H., ¨Ozi¸sikM.N. Combined conduction and radiation in a two-layer planar medium with flux boundary condition. Num. Heat Transfer. 11, n.3, 321–340 (1987). [11] HoC.-H., ¨Ozi¸sikM.N. Simultaneous conduction and radiation in a two-layer planar medium. J. Thermophys. Heat Transfer. 1, n.2, 154–161 (1987). [12] SiegelR. Two flux Green’s function analysis for transient spectral radiation in a composite. J. Thermophys. Heat Transfer. 10, n.4, 681–688 (1996). [13] TanH.-P., Wang P.-Y., XiaX.-L. Transient coupled radiation and conduction in an absorbing and scattering composite layer. J. Thermophys. Heat Transfer. 14, n.1, 77–87 (2000). [14] TimoshenkoV.P., TrenerM.G. A method for evaluting heat transfer in multilayer semi-transparent materials. Heat Transfer-Soviet Research. 18, 321–340 (1986). [15] TsaiC.-F., NixonG. Transient temperature distribution of a multilayer composite wall with effects of internal thermal radiation and conduction. Num. Heat Transfer. 10, n.1, 95–101 (1986). [16] Wang P.-Y., ChengH.-E., TanH.-P. Transient thermal analysis of semitransparent composite layer with an opaque boundary. Int. J. Heat Mass Transfer. 45, n.2, 425–440 (2002). [17] PopovychV. S. Models and methods of calculation thermostressed state of thermo sensitive structural elements under complex conditions of heat transfer: Dis. . .Doctor. Sc. Science. Luts’k, 312 p. (2005), (in Ukrainian). [18] PopovychV. S. Construction of the solutions of the problems of thermoelasticity thermosensitive solids under the conditions of convective-radiant heat exchange. Reports of National Academy of Sciences of Ukraine. 11, 69–73 (1997), (in Ukrainian). [19] PopovychV. S., HarmatijH.Y., VovkO.M. Thermoelastic state of a thermosensitive hollow sphere under the conditions of convective-radiant heat exchange with the environment. Phys.-Chem. Mechanics of Materials. 42, n.6, 39–48 (2006), (in Ukrainian). [PopovychV. S., HarmatijH.Y., VovkO.M. Thermoelastic state of a thermosensitive hollow sphere under the conditions of convective-radiant heat exchange with the environment. Materials Science. 42, n.6, 756–770 (2006)]. [20] BruchalM.B., Terlets’kyiR. F., TuriiO.P. Thermomechanics problems for irradiated solids. Theoretical and Applied Mechanics. 4, n.50, 30–37 (2012), (in Russian). [21] Terlets’kyiR. F., TuriiO.P. Modeling and investigation of heat transfer in plates with thin coatings with regard for the influence of radiation. J. of Mathematical Sciences. 192, n.6, 703–722 (2013). [22] TuriiO.P. Nonlinear contact boundary problem of thermomechanics for the irradiated two-layer plate connected by an intermediate layer. Physico-Mathematical Modelling And Informational Technologies. 9, 118–132 (2009), (in Ukrainian). [23] KushnirR.M., PopovychV. S., VovkO.M. The thermoelastic state of a thermosensitive sphere and space with spherical cavity subject to complex heat exchange. J. Eng. Math. 61, n.2, 357–369 (2008). [24] PopovychV. S., VovkO.M. The method of solving convective-radiant heat exchange between the cylindrical and N-corner prismatic shells. Math. Methods and Phys.-Mech. Fields. 47, n.1, 158–168 (2004), (in Ukrainian). [25] HachkevychO.R., BojchukV.Y. Thermal stress of a long cylinder when heated by thermal radiation. Applied Mechanics. 23, n.4, 16–23 (1987), (in Russian). [26] HachkevychO.R., BojchukV.Y. Thermomechanical behavior of nonmetallic electrically conductive bodies under high-temperature treatment. Math. Methods and Phys.-Mech. Fields. 39, n.1, 74–79 (1996), (in Russian). [27] KoljanoY.M., KulykA.N. Temperature stresses from volumetric sources. Kyiv, Naukova Dumka, 288 p. (1983), (in Russian). [28] PljackoG.V., PodstryhachYa. S. On the state of stress caused by a laser beam in the process of destruction of transparent polymers. Phys.-Chem. Mechanics of Materials. 6, n.3, 93–97 (1970), (in Russian). [29] HetnarskiR.B., DeBolt F.C. Thermal stresses due to laser radiation. Part 1: Heat conduction. J. Thermal Stresses. 15, n.2, 331 (1992). [30] HetnarskiR.B., Hector L.G., Hosseini TehraniP., EslamiM.R. Thermal stresses due to a laser pulse train: Coupled solution. Proc. 3rd Int. Congress on Thermal Stresses. Cracow (Poland), 61–64 (1999). [31] UglovA.A., KoljanoY.M., KulykA.N., Stookuj F. I. Stresses in planar solids with absorption under the action of a local heat source. Physics And Chemistry Of Material Processing. 6, 117–120 (1976), (in Russian). [32] KoljanoY.M., Bernar I. I. Temperature stresses in the plate with two-sided laser treatment. Strength Problems. 5, 36–48 (1983), (in Russian). [33] MuresanCr., VaillonR., MenezoC., MorlotR. Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation. Journal of Quantitative Spectroscopy and Radiative Transfer. 84, n.4, 551–562 (2004). [34] Michael F.Modest. Radiative heat transfer. The Pennsylvania State University, 822 p. (2003). [35] IljushinA.A. Continuum mechanics. Moscow. Publ. Mosc. University, 287 p. (1978), (in Russian). [36] BerezovskyjA. Nonlinear boundary value problems of a heat-radiating solids. Kyiv, Naukova Dumka, 176 p. (1968), (in Russian). [37] KushnirR., ProtsyukB. A Method of the Green’s Functions for Quasistatic Thermoelasticity Problems in Layer Themosensitive Bodies under Complex Heat Exchange. Operator Theory: Advances and Applications. 191, 143–154 (2009). [38] MamedovYa.D., Ashyrov S.A. Nonlinear Volterra equations. Ashgabat, Ylym, 176 p. (1977), (in Russian). [39] Thermal engineering reference book. Under. Ed. V.N.Yurneva and others. Moscow, Energija. Vol.1, 744 p. (1975), (in Russian). [40] Radiative properties of solid materials: Reference Book. Ed. A.E. Sheydlin. Moscow, Energija, 471 p. (1974), (in Russian). [41] Machine-building materials. Quick reference. Under. Ed. V.M.Raskatova. Moscow, Mashynostrojenije, Vol.1, 511 p. (1980), (in Russian). [42] Volkov E.A. Numerical methods. Moscow, Nauka, 256 p.(1982), (in Russian). [43] SamarskyjA.A. Theory of difference schemes. Moscow, Nauka, 616 p. (1989), (in Russian). [44] BellmanR., KalabaR. Quasilinearization and nonlinear boundary value problems. Moscow, Mir, 223 p. (1968), (in Russian). |
| Content type: | Article |
| Appears in Collections: | Mathematical Modeling And Computing. – 2017. – Vol. 4, No. 1 |
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