We obtain the analytic solution of a system of three singular integrodifferential equations of the thermoelastic problem for the space containing a thin ellipsoidal elastic inclusion. It is assumed that a constant heat flux acts on the surfaces of the inclusion. We deduce the relations for the stress concentration in the vicinity of the inclusion and stresses inside the inclusion. Special cases of the problem for an elliptic crack and a platelike perfectly rigid elliptic inclusion are considered and the corresponding relations for the stress intensity factors are obtained.
Similar content being viewed by others
References
V. Z. Parton and E. M. Morozov, Mechanics of Elastoplastic Fracture [in Russian], Nauka, Moscow (1985).
A. H. Passos Morgado, Ya. Pivnik, and Yu. N. Podil’chuk, “Stress distribution in an infinite transversely isotropic body with rigid elliptic inclusion in a uniform heat flux,” Prikl. Mekh., No. 11, 3–10 (1995).
Yu. N. Podil’chuk and V. V. Dobrivecher, “On the thermal stressed state of a transversely isotropic body with rigid elliptic inclusion subjected to the action of a uniform heat flow in the plane of inclusion,” Prikl. Mekh., No. 8, 31–40 (1996).
M. M. Stadnyk, “Method for the solution of three-dimensional thermoelasticity problems for bodies with thin inclusions,” Fiz.-Khim. Mekh. Mater., 30, No. 6, 30–40 (1994); English translation: Mater. Sci., 30, No. 6, 643–653 (1994).
G. P. Cherepanov, Mechanics of Brittle Fracture [in Russian], Nauka, Moscow (1974).
M. M. Stadnyk, “Elastic ellipsoidal heat-conducting inclusion in a body under the action of a heat flux applied at infinity,” Fiz.-Khim. Mekh. Mater., 47, No. 3, 16–23 (2011); English translation: Mater. Sci., 47, No. 3, 284–293 (2011).
M. M. Stadnyk, “Thin heat-conducting inclusion in an elastic space under the action of a heat flux applied at infinity,” in: Scientific Bulletin of the Ukrainian National University of Forestry Engineering [in Ukrainian], Issue 22.4 (2012), pp. 332–339.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 48, No. 6, pp. 110–114, November–December, 2012.
Rights and permissions
About this article
Cite this article
Stadnyk, M.M. Ellipsoidal Elastic Inclusion in a Body Under the Action of a Constant Heat Flux on Its Surface. Mater Sci 48, 818–824 (2013). https://doi.org/10.1007/s11003-013-9574-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11003-013-9574-6