An axisymmetric stationary problem of thermoelasticity for a multilayer foundation with imperfect thermal contact between the layers is solved by the method of compliance functions along with the Hankel transform. The recurrence relations are constructed for the auxiliary functions and the compliance functions of neighboring layers of the foundation. We analyze the influence of the coefficient of thermal resistance on the distribution of normal and tangential stresses and temperature at the points of the bottom boundary of the top layer for a two-layer foundation subjected to the action of thermal loads.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. M. Antonenko, “Plane thermoelastic deformation of a multilayer plate elastically coupled with a rigid half plane,” Fiz.-Khim. Mekh. Mater., 53, No. 3, 105–111 (2017); English translation: Mater. Sci., 53, No. 3, 407–416 (2017); https://doi.org/10.1007/s11003-017-0089-4.
S. G. Blashevs'kiy, “Modeling of the process of thermal diffusion in two-layer symmetric space,” Visn. Kherson Nats. Tekh. Univ., Fundament. Nauk., 2, No. 3 (66), 29–33 (2018).
O. O. Bobylev, Jr., and V. V. Loboda, “Axisymmetric contact problem of thermoelasticity for a three-layer elastic cylinder with rigid nonuniformly heated core,” Mat. Metody Fiz.-Mekh. Polya, 56, No. 4, 149–157 (2013); English translation: J. Math. Sci., 208, No. 4, 448–459 (2015); https://doi.org/10.1007/s10958-015-2459-5.
I. G. Velychko and I. G. Tkachenko, “Axisymmetric mixed problem of thermoelasticity for a multilayer foundation,” Dynam. Syst., Issue 26, 3–12 (2009).
I. G. Velychko and I. G. Tkachenko, “ Plane thermoelastic deformation of multilayer foundation,” Visn. Dnipr. Univ., Ser. Mekh., Issue 8, 1, No. 6, 154–161 (2004).
I. G. Velychko and I. G. Tkachenko, “Space and axisymmetric thermoelastic deformations of multilayer foundations,” Visn. Dnipr. Univ., Ser. Mekh., Issue 8, 2, No. 6/2, 36–43 (2004).
S. М. Vereshchaka, А. V. Deineka, and V. V. Danil’tsev, “Thermoelastic stress state of a fiberglass hinged cylinder with regard for imperfect contact between the layers,” Visn. Zapor. Nats. Univ. Fiz.-Mat. Nauk., No. 3, 42–50 (2015).
B. Gera, “Mathematical modeling of the conditions of imperfect thermal contact of layers through a thin inclusion with heat sources,” Fiz.-Mat. Model. Inf. Tekhnol., Issue 18, 61–72 (2013).
B. Yu. Nemish, “Three-dimensional thermoelasticity problems for nonuniformly heated laminar transversally isotropic plates,” Prikl. Mekh., 35, No. 7, 95–103 (1999); English translation: Int. Appl. Mech., 35, No. 7, 732–740 (1999); https://doi.org/10.1007/BF02682211.
B. S. Okrepkyj and V. М. Nemish, “Axisymmetric thermal problem for the system of two contact layers with imperfect thermal contact,” Mizhvuz. Zbirn. “Nauk. Not.”, Issue 47, 131–136 (2014).
B. S. Okrepkyj and М. Ya. Shelestovs’ka, “Contact interaction of a circular stamp with a layer in the case of imperfect thermal contact,” Visn. Lazaryan Dnipr. Nats. Univ. Rail. Transp., Issue 39, 110–117 (2011).
B. Okrepkyj and F. Mygovych, “Axisymmetric thermal problem for a cylinder–half-space system of bodies in the case of imperfect thermal contact with regard for the anisotropy of materials,” Visn. Ternopil. Nats. Tekh. Univ., 14, No. 4, 188–192 (2009).
A. K. Privarnikov, Solution of Boundary Problems of the Theory of Elasticity for Multilayer Foundations. Method. Development [in Russian], Dnepr. Gos. Univ., Dnepropetrovsk (1976).
N. Antonenko and I. Tkachenko, “Plane thermoelastic deformation of a multilayer foundation with non-ideal thermal contact between its layers,” Mater. Sci. Forum, 968, 486–495 (2019); https://doi.org/10.4028/www.scientific.net/MSF.968.486.
B. V. Gera and V. A. Dmytruk, “Obtaining and investigation of the conditions of heat transfer through inhomogeneous inclusion with heat sources,” Math. Model. Comput., 2, No. 1, 33–47 (2015); https://doi.org/10.23939/mmc2015.01.033.
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 3, pp. 123–129, July–September, 2020.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Antonenko, N.M., Tkachenko, I.H. & Shupchynska, K.S. Axisymmetric Thermoelastic Deformation of a Multilayer Foundation with Imperfect Thermal Contact of the Layers. J Math Sci 273, 144–152 (2023). https://doi.org/10.1007/s10958-023-06490-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06490-2