Stationary problem of heat conductivity for complex-shape multilayer plates

doi:10.26565/2304-6201-2019-41-05

Alyona Igorevna Malykhina https://orcid.org/0000-0001-9659-2562
Dmytro Oleksandrovych Merkulov https://orcid.org/0000-0001-5697-200X
Oleksii Vitaliiovych Postnyi https://orcid.org/0000-0002-3151-3891
Natalia Volodymyrivna Smetankina https://orcid.org/0000-0001-9528-3741

DOI: https://doi.org/10.26565/2304-6201-2019-41-05

Keywords: multilayer plate, complex form, stationary thermal conductivity, film heat source

Abstract

A method for calculating stationary temperature fields in a complex-shape multilayer plate when it is heated with film heat sources is proposed. Convective heat exchange takes place on the outer surfaces of the plate. The solution of the stationary heat conduction problem is obtained for a three-dimensional formulation based on the immersion method. A comparative analysis of the temperature distribution along the thickness of a square plate with the results obtained by finite element method has been carried out. As an example, the problem of stationary thermal conductivity for a five-layer glazing element of a vehicle when heated with a film heat source has been solved.

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References

Kantor B.Ya., Smetankina N.V., Shupikov A.N. Analysis of non-stationary temperature fields in laminated strips and plates// Int. J. Solids and Structures. 2001. Vol. 38. P. 8673 – 8684.

Болотин В.В., Новичков Ю.Н. Механика многослойных конструкций. М.: Машиностроение, 1980. 375 с., ил.

Сахаров А.С. Метод конечных элементов в механике твердых тел / Под общ. редакцией А.С. Сахарова и И. Альтенбаха //Киев: Вища школа. Головное изд-во, 1982. 480 с.

Рвачев В.Л., Слесаренко А.П., Литвин М.М. Расчет температурного поля кусочно-однородных тел сложной формы // Теплофизика и теплотехника. 1977. Вып. 32. С. 18–22.

Сметанкіна Н.В., Свєт Є.В. Розрахунок температурних полів у багатошарових пластинах складної форми // Машинознавство. 2003. № 4. С. 8–12.

Сметанкина Н.В., Свєт Є.В., Шупиков А.Н. Задача стационарной теплопроводности многослойных пластин сложной формы в плане // Пробл. машиностроения. 2004. Т. 7, № 3. С. 25–31.

Smetankina N.V., Shupikov A.N., Svet Ye.V. Nonstationary heat conduction in complex-shape laminated plates // Trans. ASME. J. of Heat Transfer. March, 2007. Vol. 129. P. 335–341.

Бахвалов Н.С. Численные методы. – М.: Наука, 1975. – 632 с.

Smetankina N. V., Shupikov A. N., Sotrikhin S. Yu., Yareschenko V. G. Dynamic response of an elliptic plate to impact loading. Theory and experiment// Int. J. of Impact Engng. 2007. Vol. 34 № 2 P. 264-276.

Zielinski A.P. On curvilinear distribution expressed by double Fourier series // J. Appl. Math. and Phys. 1980. Vol. 31. P. 717–729.

Zielinski A.P. Metoda trygonometrycznych szeregow okreslonych na konture w zastosowaniu do plyt o brzegu swobodnym i swobodnie podpartym // Rozpr. inz. 1982. Vol. 30, № 2. P. 151–165.

Zielinski A.P. A contour series method applied to shells // Thin–Walled Struct. 1985. N 3. P. 217–229.

B. Ya. Kantor, N. V. Smetankina, A. N. Shupikov “Analysis of non-stationary temperature fields in laminated strips and plates” Int. J. Solids and Structures. vol. 38. pp. 8673 – 8684. 2001.

V. V. Bolotin, Iu. N. Novichkov. “Mechanics of multilayer structures” Moskva: Mashinostroenie, 1980. 375 p.

A. S. Sakharov “The finite element method in solid mechanics” Kyiv: Vyshcha shkola, 1982. 480 p.

V. L. Rvachev, A. P. Slesarenko, M. M. Litvin “Calculation of the temperature field of piecewise homogeneous bodies of complex shape” Teplofizika i teplotehnika. no. 32. pp.18–22. 1977.

N. V. Smetankina, Ye. V. Svєt “Calculation of temperature fields in multilayer plates of complex shape” Mashinoznavstvo. vol. 4. pp.8–12. 2003.

N. V. Smetankina “Modeling of non-stationary heat condition in laminated strips” Seventeenth International Scientific Mykhailo Kravchuk Conference (May 19–20, 2016, Kyiv): Conference materials. vol. 1. Differential and integral equations and its applications. Кyiv: NTUU «KPI», pp. 35-38. 2016.

N. V. Smetankina, A. N. Shupikov, Ye. V. Svєt “Nonstationary heat conduction in complex-shape laminated plates” Trans. ASME. J. of Heat Transfer. vol. 129. pp. 335–341. March, 2007.

N. S. Bakhvalov Numerical methods. Nauka, pp. 632. 1975.

N. V. Smetankina, A. N. Shupikov, S. Yu. Sotrikhin, V. G. Yareschenko “Dynamic response of an elliptic plate to impact loading. Theory and experiment” Int. J. of Impact Engng. vol. 34 no. 2 pp. 264-276. 2007.

A. P. Zielinski “On curvilinear distribution expressed by double Fourier series” J. Appl. Math. and Phys. vol. 31. pp. 717–729. 1980.

A. P. Zielinski “Metoda trygonometrycznych szeregow okreslonych na konture w zastosowaniu do plyt o brzegu swobodnym i swobodnie podpartym” Rozpr. inz. vol. 30, no. 2. pp. 151–165. 1982.

A. P. Zielinski “A contour series method applied to shells” Thin–Walled Struct. no. 3. pp. 217–229. 1985.