Journal of Mathematical Sciences

, Volume 208, Issue 4, pp 448–459

# Axisymmetric Contact Problem of Thermoelasticity for a Three-Layer Elastic Cylinder with Rigid Nonuniformly Heated Core

• O. O. BobylevJr.
• V. V. Loboda
Article

We consider an axisymmetric contact problem for a finite three-layer elastic cylinder with rigid nonuniformly heated core under the conditions of external convective heat transfer. The conditions of perfect unilateral mechanical contact and imperfect thermal contact are given on the surfaces of possible contact of the cylinder with the core and between the layers. The variational formulation of the problem is obtained. Finally, we propose an iterative numerical algorithm in each iteration of which it is necessary to solve the uncoupled elasticity and heat-conduction problems and the finite-element method is used for their discretization.

## Preview

### References

1. 1.
A. A. Bobylev, Jr., “Problem of contact interaction of an elastic body with a convex heated punch,” Visn. Dnipropetrovsk Univ., Ser. Mekh., Issue 14, 1, 192–198 (2010).Google Scholar
2. 2.
A. A. Bobylev, Jr., “Problem of compression of an elastic two-layer strip by rigid heated convex punches,” in: Visn. Dnipropetrovsk Univ., Ser. Mekh., Issue 14, 2, 15–22 (2010).Google Scholar
3. 3.
R. Glowinski, J.-L. Lions, and R. Trémolières, Analyse Numérique des Inéquations Variationnelles, Dunod, Paris (1976).
4. 4.
G. Duvaut and J.-L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris (1972).
5. 5.
V. S. Zarubin, Engineering Methods for the Solution of Heat-Conduction Problems [in Russian], Énergoatomizdat, Moscow (1983).Google Scholar
6. 6.
A. D. Kovalenko, Foundations of Thermoelasticity [in Russian], Naukova Dumka, Kiev (1970).Google Scholar
7. 7.
A. S. Kravchuk, “On the Hertz problem for linearly and nonlinearly elastic bodies of finite sizes,” Prikl. Mat. Mekh., 41, No. 2, 329–337 (1977).
8. 8.
I. I. Vorovich and V. M. Aleksandrov (editors), Mechanics of Contact Interactions, Collection of Papers [in Russian], Fizmatlit, Moscow (2001).Google Scholar
9. 9.
P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions, Birkhäuser, Boston (1985).
10. 10.
Ya. S. Podstrigach and Yu. M. Kolyano, Generalized Thermomechanics [in Russian], Naukova Dumka, Kiev (1976).Google Scholar
11. 11.
Yu. P. Shlykov, E. A. Ganin, and S. N. Tsarevskii, Contact Thermal Resistance [in Russian], Énergiya, Moscow (1977).Google Scholar
12. 12.
K. A. Chumak and R. M. Martynyak, “Periodic contact problem of thermoelasticity for bodies with rough surfaces in local regions,” Fiz.-Khim. Mekh. Mater., 48, No. 6, 92–97 (2012); English translation: Mater. Sci., 48, No. 6, 795–801 (2012).Google Scholar
13. 13.
G. E. Blandford and T. R. Tauchert, “Thermoelastic analysis of layered structures with imperfect layer contact,” Comput. & Struct., 21, No. 6, 1283–1291 (1985).
14. 14.
K. A. Chumak and R. M. Martynyak, “Thermal rectification between two thermoelastic solids with a periodic array of rough zones at the interface,” Int. J. Heat Mass Transfer, 55, No. 21–22, 5603–5608 (2012).
15. 15.
D. H. Liu, X. P. Zheng, and Y. H. Liu, “A discontinuous Galerkin finite element method for heat conduction problems with local high gradient and thermal contact resistance,” CMES — Comput. Model Eng. Sci., 39, No. 5, 263–299 (2009).
16. 16.
R. Martynyak and K. Chumak, “Effect of heat-conductive filler of interface gap on thermoelastic contact of solids,” Int. J. Heat Mass Transfer, 55, No. 4, 1170–1178 (2012).

## Authors and Affiliations

• O. O. BobylevJr.
• 1
• V. V. Loboda
• 1
1. 1.Honchar Dnipropetrovsk National UniversityDnipropetrovskUkraine