Istrazivanja i projektovanja za privreduJournal of Applied Engineering Science

NUMERICAL MODELing OF SCALE EFFECTS FOR CIRCULAR CYLINDER IN THE THEORY OF THERMOELASTIC MATERIALS WITH VOIDS


DOI: 10.5937/jaes0-28042 
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Creative Commons License

Volume 18 article 743 pages: 671 - 675

Yulong Li*
Northwestern Polytechnical University (NPU), School of Civil Aviation, Xi'an Shaanxi, Republic of China

Alexander V. Volkov
Institute of Applied Mechanics of Russian Academy of Sciences, Laboratory of Non-Classical Models of Composites Materials and Structures, Moscow, Russian Federation

Lev N. Rabinskiy
Moscow Aviation Institute (National Research University), Institute of General Engineering Education, Moscow, Russian Federation

Aleksandr O. Shemiakov
Moscow Aviation Institute (National Research University), Moscow, Russian Federation

This article is relevant, as changes during the external loading may affect the stress state of the materials. The aim of this paper is to consider the numerical modeling of heating for circular cylinders in the frame of the theory of elastic materials with voids. A numerical solution is build using COMSOL Multiphysics software, where the implementation of the considered theory is realized based on the direct equation-definition approach. Constitutive relations were written in General form partial differential equation module. A matrix form of the equations for the two-dimensional case was used. Scale effects arising in considered problems are discussed. The classical solution is the particular case of the considered theory, when the coupling number tends to asero, i.e. when the micro-dilatation effects are small and do not affect the material’s stress state. The limiting case in the case of the small value of the coupling number is the classical thermoelasticity solution.

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This work was supported by the RFBR grant 18-08- 00643-a, 20-01-00517-а and by the Grant of the President of the Russian Federation No MK-3869-2019.8.

1. Fialko, N.M., Prokopov, V.G., Meranova, N.O., Borisov, Yu.S., Korzhik, V.N., Sherenkovskaya, G.P. (1994). Heat transport processes in coating-substrate systems under gas-thermal deposition. Fizika i Khimiya Obrabotki Materialov, vol. 2, 68-75.

2. Blinov, D.G., Prokopov, V.G., Sherenkovskii, Yu.V., Fialko, N.M., Yurchuk, V.L. (2002). Simulation of natural convection problems based on low-dimensional model. International Communications in Heat and Mass Transfer, vol. 29, no. 6, 741-747.

3. Ryndin, V.V., Ivin, V.I. (1981). Investigation of multicylinder engine filling-up nonuniformity. Izvestia vyssihucebnyh zavedenij. Masinostroenie, vol. 10, 71-75.

4. Mindlin, R.D. (1964). Microstructure in linear elasticity. Archive for Rational Mechanics and Analysis, vol. 16, 51-78.

5. Cowin, S.C. (1984). The stresses around a hole in a linear elastic material with voids. Quarterly Journal of Mechanics and Applied Mathematics, vol. 37, 441-465, DOI: 10.1093/qjmam/37.3.441.

6. Khripach, N., Lezhnev, L., Tatarnikov, A., Stukolkin, R., Skvortsov, A. (2018). Turbo-generators in energy recovery systems. International Journal of Mechanical Engineering and Technology, vol. 9, no. 6, 1009- 1018.

7. Ryndin, V.V. (2020). Application of the postulate of nonequilibrium to calculate the nonequilibrium of systems of dissimilar gases and liquids. Periodico Tche Quimica, vol. 17, no. 34, 998-1011.

8. Lurie, S., Solyaev, Y., Volkov, A., Volkov-Bogorodskiy, D. (2017). Bending problems in the theory of elastic materials with voids and surface effects. Mathematic and Mechanics of Solids, vol. 23, no. 5, 787-804.

9. Lurie, S.A., Kalamkarov, A.L., Solyaev, Y.O., Ustenko, A.D. Volkov, A.V. (2018). Continuum micro-dilatation modeling of auxetic metamaterials. International Journal of Solids and Structures, vol. 3, 188-200.

10. Solyaev, Y., Lurie, S., Ustenko, A. (2019). Numerical modeling of a composite auxetic metamaterial using micro-dilatation theory. Continuum Mechanics and Thermodynamics, vol. 31, 1099-1107.

11. Skvortsov, A.A., Gnatyuk, E.O., Luk'Yanov, M.N., Khripach, N.A. (2018). Features of cracking of samples from titanium and iron-chromium-nickel alloys. Periodico Tche Quimica, vol. 15, no. 1, 166-173.

12. Sadd, H. (2005). Martin, elasticity: Theory, applications and numerics. Elsevier, Amsterdam. 13. Lakes, R.S. (2016). Physical meaning of elastic constants in Cosserat, void, and microstretch elasticity. Journal of Mechanics of Materials and Structures, vol. 1, no. 3, 217-229.

14. Ramezani, H., Steeb, H., Jeong, J. (2012). Analytical and numerical studies on Penalized Micro-Dilatation (PMD) theory: Macro-micro link concept. European Journal of Mechanics – A/Solids, vol. 34, 130-148.

15. Formalev, V.F., Kolesnik, S.A., Kuznetsova, E.L. (2019). Effect of components of the thermal conductivity tensor of heat-protection material on the value of heat fluxes from the gasdynamic boundary layer. High Temperature, vol. 57, no. 1, 58-62.

16. Formalev, V.F., Kolesnik, S.A., Kuznetsova, E.L. (2019). Approximate analytical solution of the problem of conjugate heat transfer between the boundary layer and the anisotropic strip. Periodico Tche Quimica, vol. 16, no. 32, 572-582.

17. Formalev, V.F., Kolesnik, S.A., Kuznetsova, E.L. (2019). Mathematical modeling of a new method of thermal protection based on the injection of special coolants. Periodico Tche Quimica, vol. 16, no. 32, 598-607.

18. Sultanov, K.S, Khusanov, B.E., Rikhsieva, B.B. (2020). Longitudinal waves in a cylinder with active external friction in a limited area. Journal of Physics: Conference Series, vol. 1546, no. 012140.