Analytical-Numerical Methods for Solving Heat Conduction Problems for Half-Spaces with Gradient Coating
References
- Miyamoto Y, Kaysser WA, Rabin BH, Kawasaki A, Ford RG. Functionally graded materials: design, processing and application. London: Kluwer Academic Publisher; 1999.
- Schulz U, Peters M, Bach FrW, Tegeder G. Graded coatings for thermal, wear and corrosion barriers. Mater Sci Eng. 2003; A 362: 61-80.
- Suresh S. Graded materials for resistance to contact deformation and damage. Sci. 2001; 292: 2447-2451.
- Birman V, Byrd LW. Modeling and analysis of functionally graded materials and structures. Appl Mech Rev. 2007; 60(5): 195-216.
- Gladwell GML. Contact problems in the classical theory of elasticity. Alpen an den Rein: Sitjhoff&Noordhoff; 1980.
- Wang CD, Tzeng CS, Pan E, Liao JJ. Displacements and stresses due to a vertical point load in an inhomogeneous transversely isotropic half-space. Int J Rock Mech Min Sci. 2003; 40: 667-685.
- Guler MA, Erdogan F. Contact mechanics of graded coatings, Int J Solids Struct. 2004; 41(14): 3865-3889.
- Ke LL, Wang YS. Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties. Int J Solids Struct. 2006; 43: 5779-5798.
- Ke LL, Wang YS. Two-dimensional sliding frictional contact of functionally graded materials. Eur J Mech A - Solids 2007; 26: 171-188.
- Ke LL, Wang YS. Fretting contact with finite friction of a functionally graded coating with arbitrarily varying elastic modulus. Part 1: Normal loading. J Strain Anal Eng. 2007; 42: 293-304.
- Ke LL, Wang YS. Fretting contact with finite friction of a functionally graded coating with arbitrarily varying elastic modulus. Part 2: Tangential loading. J Strain Anal Eng. 2007; 42: 305-313.
- Ke LL, Wang YS. Fretting contact of two dissimilar elastic bodies with functionally graded coatings. Mech Adv Mater Struct. 2010; 17: 433-447.
- Liu TJ, Wang YS, Zhang Ch. Axisymmetric contact problem of functionally graded materials. Arch Appl Mech. 2008; 78: 267-282.
- Liu TJ, Wang YS, Xing YM. The axisymmetric partial slip contact problem of a graded coating. Meccanica 2012; 47: 1673-1693.
- Liu TJ, Wang YS, Xing YM. Fretting contact of two elastic solids with graded coatings under torsion. Int J Solids Struct. 2012; 49: 1283-1293.
- Zhang Ch, Liu TJ, Wang YS, Xing YM. The axisymmetric stress analysis of double contact problem for functionally graded materials layer with arbitrary graded materials properties. Int J Solids Struct. 2016; 96: 229-239.
- Liu TJ, Wang YS. Reissner-Sagoci problem for functionally graded materials with arbitrary spatial variation of material properties. Mech Res Commun. 2009; 36: 322-329.
- Liu J, Ke LL, Wang YS. Two-dimensional thermoelastic contact problem of functionally graded materials involving frictional heating. Int J Solids Struct. 2011; 48 (18): 2536-2548.
- Liu J, Ke LL, Wang YS, Yang J. Thermoelastic frictional contact of functionally graded materials with arbitrarily varying properties. Int J Mech Sci. 2012; 63(1): 86-98.
- Mao JJ, Ke LL, Yang J, Kitipornchai S, Wang YS. Thermoelastic instability of functionally graded coating with arbitrarily varying properties considering contact resistance and frictional heat. Appl Math Model. 2016; 43(4-5): 1-12.
- Kulchytsky-Zhyhailo R, Bajkowski AS. Analytical and numerical methods of solution of three-dimensional problem of elasticity for functionally graded coated half-space. Int J Mech Sci. 2012; 54(1): 105-112.
- Wang Z, Yu C, Wang Q. An efficient method for solving three-dimensional fretting contact problems involving multilayered or functionally graded materials. Int J Solids Struct. 2015; 66: 46-61.
- Kulchytsky-Zhyhailo R, Bajkowski AS. Axisymmetrical problem of thermoelasticity for halfspace with gradient coating. Int J Mech Sci. 2016; 106: 62-71.
- Samarskii AA, Nikolaev ES, Numerical Method for Grid Equations. Vol. I: Direct Methods. Basel: Birkhauser Verlag; 1989.
- Krenev LI, Tokovyy YuV, Aizikovich SM, Seleznev NM, Gorokhov SV. A numerical-analytical solution to the mixed boundary-value problem of the heat-conduction theory for arbitrarily inhomogeneous coatings. Int J Thermal Sci. 2016; 107: 56-65.
- Sneddon IN. The use of integral transforms. New York: McGraw-Hill; 1972.
- Matysiak SJ, Kulchytsky-Zhyhailo R, Perkowski DM. Reissner-Sagoci problem for a homogeneous coating on a functionally graded half-space. Mech Res Commun. 2011; 38: 320-325.
- Conte SD, deBoor C, Elementary Numerical Analysis. New York: McGraw-Hill; 1972.
- Kulchytsky-Zhyhailo R, Matysiak SJ, Perkowski DM. On some thermo-elastic problem of a nonhomogeneous long pipe. IJHT 2021; 39 (5): 1430-1442.
- Kulchytsky-Zhyhailo R. Thermal stresses in a multi-layered spherical tank with a slowly graded structure. Acta Mechanica et Automatyka 2024; 18 (2): 274-281.
- Perkowski DM, Kulchytsky-Zhyhailo R, Matysiak SJ, Tokovyy YuV. Thermal surface deflection of a medium with multilayer coatings. Int J Mech Sci. 2025; 287 (1): 1-11.
Language: English
Page range: 271 - 279
Submitted on: Sep 18, 2025
Accepted on: Feb 28, 2026
Published on: Jul 16, 2026
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Keywords:
Related subjects:
© 2026 Roman Kulchytskyy-Zhyhailo, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.