By using the Laguerre and Hankel integral transformations, we construct the solution of an axisymmetric quasistatic problem of thermoelasticity for a half space with coating. We present some results of the numerical analysis of thermal stressed state depending on the relative geometric and thermomechanical properties of the coating and the half space. We also clarify the possibility of application of the proposed method to the analysis of the effect of nanocoatings.
Similar content being viewed by others
References
V. A. Halazyuk, “Method of the Chebyshev–Laguerre polynomials in a mixed problem for a second-order linear differential equation with constant coefficients,” Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 1, 3–7 (1981).
O. V. Halazyuk and I. M. Turchyn, “Quasistatic plane nonaxisymmetric thermoelasticity problem for a radially layered cylindrical body,” Byul. Dnipropetrovs’k Univ., Ser. Mekh., Issue 11, Vol. 2 (No. 2/2), 58–65 (2007).
Yu. M. Kolyano, Methods of Heat Conduction and Thermoelasticity for an Inhomogeneous Body [in Russian], Naukova Dumka, Kiev (1992).
Ya. S. Podstrigach, V. A. Lomakin, and Yu. M. Kolyano, Thermoelasticity of Bodies with Inhomogeneous Structures [in Russian], Nauka, Moscow (1984).
B. V. Protsyuk, “Static and quasistatic axially symmetric problems of thermoelasticity for layered bodies with plane-parallel boundaries,” Mat. Metody Fiz.-Mekh. Polya, 44, No. 4, 103–112 (2001).
I. Sneddon, Fourier Transforms, McGraw-Hill, New York (1951).
M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York (1972).
H. Sulym, Foundations of the Mathematical Theory of Thermoelastic Equilibrium of Deformed Bodies with Thin Inclusions [in Ukrainian], Doslid.-Vydavnych. Tsentr NTSh, Lviv (2007).
O. Turchyn and I. Turchyn, “Nonstationary axisymmetric temperature field induced by pulsed heating in a layered half space,” in: Byul. Lviv Univ., Ser. Mekh.-Math., Issue 69, 256–261 (2008).
H. Belghazi, M. El Ganaoui, and J. C. Labbe, “Analytical solution of unsteady heat conduction in a two-layered material in imperfect contact subjected to a moving heat source,” Int. J. Therm. Sci., 49, No. 2, 311–318 (2010).
R. M. Kushnir, “Generalized conjugation problems in mechanics of piecewise–homogeneous elements of structures,” Z. Angew. Math. Mech., 76, No. S5, 283–284 (1996).
R. M. Kushnir, “Thermal stresses – Advanced theory and applications,” J. Тherm. Stresses, 33, No. 1, 76–78 (2010).
Y. Sugano, “An expression for transient thermal stress in an nonhomogeneous plate with temperature variation through thickness,” Ing. Arch., 57, 147–156 (1987).
Y. Tanigawa, “Some basic thermoelastic problems for nonhomogeneous structural materials,” Appl. Mech. Rev., 48, No. 6, 287–300 (1995).
Y. Tanigawa, T. Akai, R. Kawamura, and N. Oka, “Transient heat conduction and thermal stress problems of a nonhomogeneous plate with temperature-dependent material properties,” J. Therm. Stresses, 19, No. 1, 77–102 (1996).
I. Timar, I. Turcsin, G. Szulim, and V. Scsukin, “Quasistatic thermal elastic task for layer elastic half space system with local pulsed heating,” GÉP, 58, No. 12, 39–42 (2007).
B. L. Wang, J. C. Han, and S. Y. Du, “Thermoelastic fracture mechanics for nonhomogeneous material subjected to unsteady thermal load,” Trans. ASME, J. Appl. Mech., 67, No. 1, 87–95 (2000).
X. Yangjian, T. Daihui, and D. Haiyang, “Convective heat transfer, steady heat conduction, and thermal stress in a ceramic/FGM/metal composite EFBF plate,” J. Software, 6, No. 2, 201–208 (2011).
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 4, pp. 85–95, October–December, 2012.
Rights and permissions
About this article
Cite this article
Sulym, H.T., Turchyn, І.M. Axisymmetric Quasistatic Thermal Stressed State in a Half Space With Coating. J Math Sci 198, 103–117 (2014). https://doi.org/10.1007/s10958-014-1776-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-014-1776-4