Solving of spatial problem of non-stationary heat conduction based on semi-analytical finite element method

Authors

DOI:

https://doi.org/10.15587/2312-8372.2015.42521

Keywords:

semi-analytical finite element method, non-stationary heat conductivity, curved coordinate system

Abstract

Based on the semi-analytical finite element method it is developed solution for solving of spatial problem of non-stationary heat conduction for prismatic bodies of complex shape cross-section. The basis of the initial equation is correlations of spatial unsteady heat conduction problem in curvilinear coordinates in differential and variational formulations. The formula for determining the matrix elements of thermal conductivity and heat capacity based on semi-analytical finite element method are obtained based on the presentation of temperature distribution along the coordinate by x3 Mikhlin polynomials allowing to use effective algorithm of the iterations block of upper relaxation systems for linear algebraic equations and implement efficient algorithm solution for solution system of differential equations in time. The value of semi-analytical finite element method and algorithms implemented in the form of problem-oriented subsystems for computer modeling of unsteady thermal processes are obtained. The reliability of results is substantiated by the interpretation of test cases with analytical and numerical results.

Author Biographies

Олександр Іванович Гуляр, Kyiv National University of Construction and Architecture, Str. Povitroflotsky 31, Kyiv, 03680

Doctor of Technical Sciences, Professor, Pensioner

Department of structural mechanics

Сергій Олегович Пискунов, Kyiv National University of Construction and Architecture, Str. Povitroflotsky 31, Kyiv, 03680

Doctor of Technical Sciences, Professor

Department of structural mechanics

Віктор Петрович Андрієвський, Kyiv National University of Construction and Architecture, Str. Povitroflotsky 31, Kyiv, 03680

Candidate of Technical Sciences, Associate Professor

Department of structural mechanics

Олексій Олександрович Шкриль, Kyiv National University of Construction and Architecture, Str. Povitroflotsky 31, Kyiv, 03680

Candidate of Technical Sciences, Associate Professor

Department of structural mechanics

References

  1. Zienkiewicz, O. C. (1971). The finite element method in engineering science. London: MCGRAW-HILL, 541.
  2. Lukanin, V. N., Shatrov, M. G., Kamfer, G. M. (1999). Teplotehnika. Moskow: Vysshaja shkola, 671.
  3. Concrete Suite – Theory Manual. Version 12. (2009). Canonsburg, PA, USA, Inc., 121.
  4. ABAQUS Theory Manual. (2000). USA, Hibbit, Karlsson & Sorensen Inc., 841.
  5. MSC/NASTRAN Quick Start Guide. Version 70.5. (2000). Los Angeles: The MacNeal-Schwendler Corporation, 211.
  6. Borhan, T. M. (2014). Prediction of the thermal conductivity of cocrete using ABAQUS model. Al-Qadisiya Journal For Engineering Sciences, 7 (1), 127-136.
  7. Piekarska, W. Kubiak, M., Saternus, Z. (2010). Application of ABAQUS to analysis of the temperature field in elements heated by moving heat sources. Archives of foundry engineering, 10 (4), 177-182.
  8. Lawrence, J., Li, L. (2000, January 1). Finite element analysis of temperature distribution using ABAQUS for a laser-based tile grout sealing process. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, Vol. 214, № 6, 451–461. doi:10.1243/0954405001517766
  9. Bazhenov, V. A., Guliar, A. I., Saharov, A. S., Topor, A. G. (1993). Poluanaliticheskii metod konechnyh elementov v mehanike deformiruemyh tel. K.: NIISM, 376.
  10. Bazhenov, V. A., Guliar, O. І., Piskunov, S. O., Saharov, O. S. (2014). Napivanalitychnyi metod skinchennykh elementiv v zadachakh kontynualnoho ruinuvannia prostorovykh til. K.: Karavela, 236.
  11. Kovalenko, A. D. (1970). Osnovy termouprugosti. K.: Nauk. dumka, 204.
  12. Shabrov, N. N. (1968). Metod konechnyh elementov v raschetah detalei teplovyh dvigatelei. L.: Mashinostroenie, 212.
  13. Dymnich, A. Kh., Troianskyi, O. A. (2003). Teploprovidnist. Donetsk, 370.
  14. Guliar, A. I., Kislookii, V. N., Saharov, A. S., Chornyi, S. M. (1974). Resheniia trehmernoi zadachi teploprovodnosti v krivolineinoi sisteme koordinat metodom konechnyh elementov. Soprotivlenie materialov i teoriia sooruzhenii, Vol. ХХІІ, 23-34.

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Published

2015-05-28

How to Cite

Гуляр, О. І., Пискунов, С. О., Андрієвський, В. П., & Шкриль, О. О. (2015). Solving of spatial problem of non-stationary heat conduction based on semi-analytical finite element method. Technology Audit and Production Reserves, 3(2(23), 61–67. https://doi.org/10.15587/2312-8372.2015.42521

Issue

Vol. 3 No. 2(23) (2015): Systems and control processes. Information technologies. Mathematical modeling. Information and control systems

Section

Mathematical Modeling: Original Research

License

Copyright (c) 2016 Олександр Іванович Гуляр, Сергій Олегович Пискунов, Віктор Петрович Андрієвський, Олексій Олександрович Шкриль

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