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Generalized Boundary Conditions to Solving Thermal Stress Problems for Bodies with Thin Coatings

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Encyclopedia of Thermal Stresses

Synonyms

Approximate boundary conditions; Effective boundary conditions

Overview

The generalized boundary conditions (GBCs) are used to develop a technique for solving thermal stress problems for bodies with thin coatings. Different methods for deriving GBCs for heat transfer are illustrated for the cases of planar and nonplanar coatings. GBCs of mechanical conjugation of a body with environment through a thin coating, taking into account of thermal strains in the coating, are derived based on the application of the thermoelastic theory of thin shells. They are written for the case of isotropic and transversely isotropic one- and multilayer coatings. Then the technique of approximate computation of heat conduction and corresponding thermal stress state in bodies with thin coatings under transient thermal loads is presented, which is based on the solution of nonclassical boundary-value problems of heat conduction and thermoelasticity with GBCs followed by determination of the...

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References

  1. Podstrigach Ya S, Shvets RN (1978) Thermoelasticity of thin shells. Naukova Dumka, Kiev (in Russian)

    MATH  Google Scholar 

  2. Lukasiewicz SA (1989) Thermal stresses in shells. In: Hetnarski RB (ed) Thermal stresses III. Elsevier, North Holland, pp 355–553

    Google Scholar 

  3. Shevchuk VA (2002) Calculation of thermal state in solids with multilayer coatings. Lect Notes Comput Sci 2330:500–509

    Google Scholar 

  4. Al Nimr MA, Alcam MK (1997) A generalized boundary condition. Int J Heat and Mass Transfer 33(1–2):157–161

    Google Scholar 

  5. Attetkov AV, Belyakov NS (2006) The temperature field of an infinite solid containing a cylindrical channel with a thermally thin surface coating. High Temp 44(1):139–143

    Google Scholar 

  6. Podstrigach YS, Shevchuk PR, Onufrik TM, Povstenko Yu Z (1975) Surface phenomena in solids taking into account physico-mechanical processes. Mater Sci 11(2):162–167

    Google Scholar 

  7. Shevchuk VA (2000) Analysis of the stressed state of bodies with multilayer thin coatings. Strength Mater 32:92–102

    Google Scholar 

  8. Shevchuk VA, Silberschmidt VV (2005) Semi-analytical analysis of thermally induced damage in thin ceramic coatings. Int J Solids Struct 42:4738–4757

    MATH  Google Scholar 

  9. Pelekh BL, Fleishman FN (1988) Approximate method for the solution of problems in the theory of elasticity for bodies with thin curvilinear coatings. Izv Akad Nauk SSSR, Mekh Tverd Tela 5:36–41 (In Russian)

    Google Scholar 

  10. Moulton D, Pelesko JA (2008) Thermal boundary conditions: an asymptotic analysis. Heat Mass Transfer 44:795–803

    Google Scholar 

  11. Shevchuk VA (2006) Modeling and computation of heat transfer in a system “body-multilayer coating”. Heat Transfer Research 37(5):412–423

    Google Scholar 

  12. Ting TCT (2007) Mechanics of a thin anisotropic elastic layer and a layer that is bonded to an anisotropic elastic body or bodies. Proc R Soc A 463:2223–2239

    MATH  MathSciNet  Google Scholar 

  13. Rahmani L (2008) The effect of a thin layer on a nonlinear thermoelastic plate. Appl Math Sciences 2(50):2489–2499

    MATH  MathSciNet  Google Scholar 

  14. Ozisik MN (1993) Heat сonduction. John Wiley, New York, NY, USA

    Google Scholar 

  15. Ambartsumian SA (1991) Fragments of the theory of anisotropic shells. Series in Theor and Appl Mech, 10, World Scientific, Singapore

    MATH  Google Scholar 

  16. Lekhnitskii SG (1981) Theory of elasticity of an anisotropic body (Translated from the revised 1977 Russian edition). Mir, Moscow

    Google Scholar 

  17. Shevchuk VA, Silberschmidt VV (2005) Analysis of damage evolution in thin multi-layer coatings under thermal loading. Proceedings of the 6th International Congress on Thermal Stresses, Vienna University of Technology, vol 1. pp 313-316

    Google Scholar 

  18. Boley BA, Weiner JH (1997) Theory of thermal stresses. Dover Publications Inc, Mineola, NY, USA Reprint

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 79060, Lviv, Ukraine

    Victor A. Shevchuk

Authors
  1. Victor A. Shevchuk
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Corresponding author

Correspondence to Victor A. Shevchuk .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY, USA

    Richard B. Hetnarski

  2. Naples, FL, USA

    Richard B. Hetnarski

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Shevchuk, V.A. (2014). Generalized Boundary Conditions to Solving Thermal Stress Problems for Bodies with Thin Coatings. In: Hetnarski, R.B. (eds) Encyclopedia of Thermal Stresses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2739-7_601

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