Skip to main content
Log in

Refinement of the Upper and Lower Bounds of Effective Heat Conductivity Coefficients of Rib-Reinforced Composite Media

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

We propose two refined structural models of the thermal behavior of a rib-reinforced composite medium at general anisotropy of the materials of compound components. For the criterion of equivalence of the rib-reinforced composite to the fictitious homogeneous anisotropic material, equality of the specific heat dissipation in them was used, which permits determining the upper and lower bounds of the effective heat conductivity coefficients of the composite material. The design values of the effective heat conductivity coefficients of a honeycomb structure with cavities filled and not filled with foam plastic have been determined. It has been shown that the refinement of certain thermal characteristics of 12%, and the refined "fork" of values of these quantities, does not exceed 2.5%. Indirect comparison has been made between the calculated and experimental values of the effective heat conductivity coefficients of such compounds, which has shown that the results obtained in the work are qualitatively reliable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. 1. A. Ya. Aleksandrov, L. É. Bryukker, L. M. Kurshin, and A. P. Prusakov, Calculation of Three-Layer Panels [in Russian], Oborongiz, Moscow (1960).

    Google Scholar 

  2. 2. A. Ya. Aleksandrov, M. Ya. Borodin, and V. V. Pavlov, Structures with Foam Plastic Fillers [in Russian], Mashinostroenie, Moscow (1972).

    Google Scholar 

  3. L. É. Bryukker and A. S. Rakin, Testing of three-layer rods at normal and high temperatures, in: Dynamics and Strength of Aviation Constructions, Mezhvuz. Sbornik Nauchn. Trudov, Izd. NGU, NÉTI, Novosibirsk (1978), Issue 4, pp. 73–79.

  4. A. K. Noor, W. S. Burton, and Ch. W. Bert, Computational models for sandwich panels and shells, Appl. Mech. Rev., 49, No. 3, 155–199 (1996).

    Article  Google Scholar 

  5. N. I. Akishev, I. I. Zakirov, V. N. Paimushin, and M. A. Shishov, A theoretical-and-experimental method of determining averaged elastic and spatial characteristics of a honeycomb filler for three-layer structures, Mekh. Kompozit. Mater., 47, No. 4, 543–556 (2011).

    Google Scholar 

  6. A. Wilbert, W.-Y. Jang, S. Kyriakides, and J. F. Floccari, Buckling and progressive crushing of laterally loaded honeycomb, Int. J. Solids Struct., No. 48, 803–816 (2011).

    Article  MATH  Google Scholar 

  7. B. V. Averin, V. A. Kudinov, E. V. Stefanyuk, and S. A. Nazarenko, Thermal and stressed-strained state of a three-layer panel with a lattice filler exposed to solar radiation, in: Mathematical Simulation and Boundary-Value Problems, Proc. All-Russia Sci. Conf., May 26–28, 2004, Samara, Izd. SamGTU, Samara (2004), Part 2, pp. 15–19.

  8. A. Vaziri, Z. Xue, and J. W. Hutchinson, Metal sandwich plates with polymer foam-filled cores, J. Mech. Mater. Struct., 1, No. 1, 97–127 (2006).

    Article  Google Scholar 

  9. 9. N. S. Bakhvalov and G. P. Panasenko, Averaging of the Processes in Periodic Media. Mathematical Problems of the Mechanics of Composite Materials [in Russian], Nauka, Moscow (1984).

    MATH  Google Scholar 

  10. A. G. Kolpakov, Composite Materials and Elements of Structures with Initial Stresses [in Russian], Izd. SO RAN, Novosibirsk (2007).

    Google Scholar 

  11. A. P. Yankovskii, Formulation of constitutive equations of the thermoelastic behavior of complexly reinforced foam plastics, Tekh. Mekh., No. 1, 71–82 (2010).

  12. A. P. Yankovskii, Determination of the effective heat conductivity coefficients of complexly reinforced foam plastics, Prikl. Fiz., No. 2, 5–10 (2010).

  13. G. L. Gorynin and Yu. V. Nemirovskii, Mathematical simulation of the process of heat conduction for 2D-periodic composite anisotropic materials, Mat. Metody Fiz.-Mekh. Polya, 57, No. 2, 142–151 (2014).

    MathSciNet  MATH  Google Scholar 

  14. V. M. Zhikov, S. M. Kozlov, and O. A. Oleinik, Averaging of Differential Operators [in Russian], Fizmatlit, Moscow (1993).

    Google Scholar 

  15. A. P. Yankovskii, Determination of the effective heat conductivity coefficients of fin-reinforced foam plastics on the basis of the energy equivalence criterion, Mat. Metody Fiz.-Mekh. Polya, 54, No. 1, 220–231 (2011).

    Google Scholar 

  16. A. P. Yankovskii, A revised structural model of the thermal conductivity of rib-reinforced foam plastics, Tepl. Prots. Tekh., 5, No. 4, 184–192 (2013).

    MathSciNet  Google Scholar 

  17. A. A. Berlin (Ed.), Polymer Composite Materials: Structure, Properties, Technology: Textbook [in Russian], revised edn., Professiya, St. Petersburg (2009).

  18. M. A. Biot, Variational Principles in Heat Transfer Theory [in Russian], Énergiya, Moscow (1975).

    Google Scholar 

  19. N. I. Bezukhov, V. L. Bazhanov, I. I. Gol′denblatt, N. A. Nikolaenko, and A. M. Sinyukov (I. I. Gol′denblatt Ed.), Calculations of the Strength, Stability, and Vibration under High-Temperature Conditions [in Russian], Mashinostroenie, Moscow (1965).

  20. V. V. Vasiliev, V. D. Protasov, V. V. Bolotin, et al. (V. V. Vasiliev and Yu. M. Tarnopol′skii Eds.), Composite Materials: Handbook [in Russian], Mashinostroenie, Moscow (1990).

  21. G. A. Vanin, Micromechanics of Composite Materials [in Russian], Naukova Dumka, Kiev (1985).

    MATH  Google Scholar 

  22. A. P. Yankovskii, Refinement of the upper and lower limits of effective rigidities of rib-reinforced composite media, Mekh. Kompozit. Mater. Konstruktsii, 21, No. 1, 114–134 (2015).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. P. Yankovskii.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 89, No. 4, pp. 1013–1023, July–August, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yankovskii, A.P. Refinement of the Upper and Lower Bounds of Effective Heat Conductivity Coefficients of Rib-Reinforced Composite Media. J Eng Phys Thermophy 89, 1014–1023 (2016). https://doi.org/10.1007/s10891-016-1463-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-016-1463-z

Keywords

Navigation