Termostressed state of a three-layer rectangular plate under non-stationary convective heating conditions

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dc.citation.epage420
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та обчислення
dc.citation.spage413
dc.citation.volume11
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorЖидик, У. В.
dc.contributor.authorКлапчук, М. І.
dc.contributor.authorБаглай, О. І.
dc.contributor.authorВолошин, М. М.
dc.contributor.authorІвасик, Г. В.
dc.contributor.authorМорська, М. О.
dc.contributor.authorZhydyk, U. V.
dc.contributor.authorKlapchuk, M. I.
dc.contributor.authorBahlai, O. I.
dc.contributor.authorVoloshyn, M. M.
dc.contributor.authorIvasyk, H. V.
dc.contributor.authorMorska, N. O.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-10-20T08:10:32Z
dc.date.created2024-02-27
dc.date.issued2024-02-27
dc.description.abstractРозглядається прямокутна ізотропна пластина шаруватої нерегулярної структури. Вона конвективно нестаціонарно нагрівається зовнішнім середовищем. Для визначення її термонапруженого стану записано вихідні співвідношення нестаціонарної задачі теплопровідності та термопружності з використанням п’ятимодальної математичної моделі зсувної теорії термопружності. З використанням методів інтегральних перетворень Фур’є і Лапласа знайдено загальні розв’язки нестаціонарної задачі теплопровідності та квазістатичної задачі термопружності для шарнірно опертої на краях розглядуваної пластини. Числовий аналіз температурного поля, радіальних прогинів, нормальних зусиль, згинних моментів і нормальних напружень залежно від геометричних параметрів та критерію Біо виконано для тришарової пластини. Матеріали її шарів виготовлені з кераміки і металу. Проаналізовано температуру і механічні параметри для структури шарів пластини — “метал–кераміка–метал”.
dc.description.abstractThe study considers a rectangular isotropic plate with a layered irregular structure. It is convectively non-stationarily heated by an external environment. The initial relationships of the non-stationary heat conduction and thermoelasticity problem are formulated using a five-mode mathematical model based on the shear deformation theory of thermoelasticity. Using the methods of Fourier and Laplace integral transforms, general solutions have been obtained for the non-stationary heat conduction problem and the quasi-static thermoelasticity problem for a hinge-supported plate along its edges. A numerical analysis of the temperature field, radial deflections, normal forces, bending moments, and normal stresses, depending on geometric parameters and the Bi criterion, has been performed for a three-layer plate. The materials of its layers are made of ceramics and metal. The temperature and mechanical parameters have been analyzed for the layering configuration of the plate: metal-ceramic-metal.
dc.format.extent413-420
dc.format.pages8
dc.identifier.citationTermostressed state of a three-layer rectangular plate under non-stationary convective heating conditions / U. V. Zhydyk, M. I. Klapchuk, O. I. Bahlai, M. M. Voloshyn, H. V. Ivasyk, N. O. Morska // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 413–420.
dc.identifier.citationenTermostressed state of a three-layer rectangular plate under non-stationary convective heating conditions / U. V. Zhydyk, M. I. Klapchuk, O. I. Bahlai, M. M. Voloshyn, H. V. Ivasyk, N. O. Morska // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 413–420.
dc.identifier.doidoi.org/10.23939/mmc2024.02.413
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/113825
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та обчислення, 2 (11), 2024
dc.relation.ispartofMathematical Modeling and Computing, 2 (11), 2024
dc.relation.references[1] Hetnarski R. Encyclopedia of Thermal Stresses. 11, 5835–6643 (2014).
dc.relation.references[2] Reddy J. N. Mechanics of Laminated Composite Plates and Shells. Theory and Analysis. New York, CRC Press (2004).
dc.relation.references[3] Koliano Yu. Metody teploprovidnosti ta termopruzhnosti neodnoridnykh til. Naukova dumka (1992), (in Ukrainian).
dc.relation.references[4] Qjuhua L., Hou P., Shang S. Three-dimensional exact analytical solutions of transversely isotropic plate under heat sources. Journal of Thermal Stresses. 44 (11), 1324–1348 (2021).
dc.relation.references[5] Vel S. S., Batra R. C. Three-dimensional analysis of transient thermal stresses in functionally graded plates. International Journal of Solids and Structures. 40 (25), 7181–7196. (2003).
dc.relation.references[6] Zenkour A. M. Generalized shear deformation theory for bending analysis of functionally graded plates. Applied Mathematical Modelling. 30 (1), 67–84 (2006).
dc.relation.references[7] Zhydyk U. V., Fliachok V. M. Termopruzhnyi analiz neodnoridnykh anizotropnykh plastyn. Naukovi notatky. 33, 281–287 (2011), (in Ukrainian).
dc.relation.references[8] Houari M. S. A., Benyoucef S., Mechab I., Tounsi A., Bedia E. A. A. Two-variable refined plate theory for thermoelastic bending analysis of FG sandwich plates. Journal of Thermal Stresses. 34 (4), 315–334. (2011).
dc.relation.references[9] Zhydyk U. V., Fliachok V. M. Termopruzhnyi zghyn sharuvatykh anizotropnykh plastyn symetrychnoi struktury. Kvalilohiia knyhy. 2 (32), 77–81 (2017), (in Ukrainian).
dc.relation.references[10] Naik State N. S., Sayyad A. S. An accurate computational model for thermal analysis of laminated composite and sandwich plates. Journal of Thermal Stresses. 42 (5), 559–579 (2019).
dc.relation.references[11] Manthena V. R., Kedar G. D. On thermoelastic problem of a thermosensitive functionally graded rectangular plate with instantaneous point heat source. Journal of Thermal Stresses. 42 (7), 849–862 (2019).
dc.relation.references[12] Manthena V. R., Lamba N. K., Kedar G. D. Transient thermoelastic problem of a nonhomogeneous rectangular plate. Journal of Thermal Stresses. 40 (5), 627–640 (2017).
dc.relation.references[13] Zenkour A. M., Alghamdi N. A. Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads. Mechanics of Advanced Materials and Structures. 17 (6), 419–432 (2010).
dc.relation.references[14] Varelis D., Saravanos D. A. A coupled nonlinear plate finite element for thermal buckling and postbuckling of piezoelectric composite plates including thermomechanical effects. Journal of Thermal Stresses. 45 (1), 30–50 (2022).
dc.relation.references[15] Zghal S., Trabelsi S., Frikha A., Dammak F. Thermal free vibration analysis of FG plates and panels with an improved finite shell element. Journal of Thermal Stresses. 44 (3), 315–341 (2021).
dc.relation.references[16] Hachkevych O. R., Musij R. S., Melnyk N. B., Dmytruk V. A. Dynamic thermoelastic processes in conductive plate under the action of electromagnetic pulses of microsecond and nanosecond durations. Journal of Thermal Stresses. 42 (9), 1110–1122 (2019).
dc.relation.references[17] Javaheri R., Eslami M. R. Thermal buckling of functionally graded plates. AIAA Journal. 40 (1), 162–169 (2002).
dc.relation.references[18] Thai H.-T., Kim S.-E. A review of theories for the modeling and analysis of functionally graded plates and shells. Composite Structures. 128 (1), 70–86 (2015).
dc.relation.references[19] Swaminathan K., Sangeetha D. M. Thermal analysis of FGM plates – a critical review of various modeling techniques and solution methods. Composite Structures. 160 (1), 43–60 (2017).
dc.relation.references[20] Musii R., Zhydyk U., Svidrak I., Shynder V., Morska N. Determination and analysis of the thermoelastic state of layered orthotropic cylindrical shells. Mathematical Modeling and Computing. 10 (3), 918–926 (2023).
dc.relation.references[21] Mirsky S. I. Vibrations of orthotropic thick cylindrical shells. Journal of the Acoustical Society of America. 36 (1), 41–51 (1964).
dc.relation.referencesen[1] Hetnarski R. Encyclopedia of Thermal Stresses. 11, 5835–6643 (2014).
dc.relation.referencesen[2] Reddy J. N. Mechanics of Laminated Composite Plates and Shells. Theory and Analysis. New York, CRC Press (2004).
dc.relation.referencesen[3] Koliano Yu. Metody teploprovidnosti ta termopruzhnosti neodnoridnykh til. Naukova dumka (1992), (in Ukrainian).
dc.relation.referencesen[4] Qjuhua L., Hou P., Shang S. Three-dimensional exact analytical solutions of transversely isotropic plate under heat sources. Journal of Thermal Stresses. 44 (11), 1324–1348 (2021).
dc.relation.referencesen[5] Vel S. S., Batra R. C. Three-dimensional analysis of transient thermal stresses in functionally graded plates. International Journal of Solids and Structures. 40 (25), 7181–7196. (2003).
dc.relation.referencesen[6] Zenkour A. M. Generalized shear deformation theory for bending analysis of functionally graded plates. Applied Mathematical Modelling. 30 (1), 67–84 (2006).
dc.relation.referencesen[7] Zhydyk U. V., Fliachok V. M. Termopruzhnyi analiz neodnoridnykh anizotropnykh plastyn. Naukovi notatky. 33, 281–287 (2011), (in Ukrainian).
dc.relation.referencesen[8] Houari M. S. A., Benyoucef S., Mechab I., Tounsi A., Bedia E. A. A. Two-variable refined plate theory for thermoelastic bending analysis of FG sandwich plates. Journal of Thermal Stresses. 34 (4), 315–334. (2011).
dc.relation.referencesen[9] Zhydyk U. V., Fliachok V. M. Termopruzhnyi zghyn sharuvatykh anizotropnykh plastyn symetrychnoi struktury. Kvalilohiia knyhy. 2 (32), 77–81 (2017), (in Ukrainian).
dc.relation.referencesen[10] Naik State N. S., Sayyad A. S. An accurate computational model for thermal analysis of laminated composite and sandwich plates. Journal of Thermal Stresses. 42 (5), 559–579 (2019).
dc.relation.referencesen[11] Manthena V. R., Kedar G. D. On thermoelastic problem of a thermosensitive functionally graded rectangular plate with instantaneous point heat source. Journal of Thermal Stresses. 42 (7), 849–862 (2019).
dc.relation.referencesen[12] Manthena V. R., Lamba N. K., Kedar G. D. Transient thermoelastic problem of a nonhomogeneous rectangular plate. Journal of Thermal Stresses. 40 (5), 627–640 (2017).
dc.relation.referencesen[13] Zenkour A. M., Alghamdi N. A. Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads. Mechanics of Advanced Materials and Structures. 17 (6), 419–432 (2010).
dc.relation.referencesen[14] Varelis D., Saravanos D. A. A coupled nonlinear plate finite element for thermal buckling and postbuckling of piezoelectric composite plates including thermomechanical effects. Journal of Thermal Stresses. 45 (1), 30–50 (2022).
dc.relation.referencesen[15] Zghal S., Trabelsi S., Frikha A., Dammak F. Thermal free vibration analysis of FG plates and panels with an improved finite shell element. Journal of Thermal Stresses. 44 (3), 315–341 (2021).
dc.relation.referencesen[16] Hachkevych O. R., Musij R. S., Melnyk N. B., Dmytruk V. A. Dynamic thermoelastic processes in conductive plate under the action of electromagnetic pulses of microsecond and nanosecond durations. Journal of Thermal Stresses. 42 (9), 1110–1122 (2019).
dc.relation.referencesen[17] Javaheri R., Eslami M. R. Thermal buckling of functionally graded plates. AIAA Journal. 40 (1), 162–169 (2002).
dc.relation.referencesen[18] Thai H.-T., Kim S.-E. A review of theories for the modeling and analysis of functionally graded plates and shells. Composite Structures. 128 (1), 70–86 (2015).
dc.relation.referencesen[19] Swaminathan K., Sangeetha D. M. Thermal analysis of FGM plates – a critical review of various modeling techniques and solution methods. Composite Structures. 160 (1), 43–60 (2017).
dc.relation.referencesen[20] Musii R., Zhydyk U., Svidrak I., Shynder V., Morska N. Determination and analysis of the thermoelastic state of layered orthotropic cylindrical shells. Mathematical Modeling and Computing. 10 (3), 918–926 (2023).
dc.relation.referencesen[21] Mirsky S. I. Vibrations of orthotropic thick cylindrical shells. Journal of the Acoustical Society of America. 36 (1), 41–51 (1964).
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.subjectтришарова пластина
dc.subjectконвективний теплообмін
dc.subjectнестаціонарний нагрів
dc.subjectтемпература
dc.subjectтермонапружений стан
dc.subjectthree-layer plate
dc.subjectconvective heat transfer
dc.subjectnon-stationary heating
dc.subjecttemperature
dc.subjectthermoelastic state
dc.titleTermostressed state of a three-layer rectangular plate under non-stationary convective heating conditions
dc.title.alternativeТермонапружений стан тришарової прямокутної пластини за умов нестаціонарного конвективного нагрівання
dc.typeArticle

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Mathematical Modeling And Computing. – 2024. – Vol. 11, No. 2