Abstract
We study the contact problem of thermoelasticity for a half plane. The function that describes the profile of the stamp is represented in the form of a series in Jacobi polynomials. Heat is produced as a result of the work of friction forces in the region of contact. We assume that the surface of the stamp is heat-insulated and that the heat generated propagates inside the half plane. The solution of the contact problem of thermoelasticity is obtained in two steps: First, the problem is reduced to the integral equation, which is solved analytically. Then we determine the values of contact pressure and heat flow inside the half plane and evaluate the stressed state of the body. Numerical analysis demonstrates that thermal stresses are small as compared to those induced by mechanical loading. By analyzing the components of the stress tensor, we conclude that only one of them (σ xx ) is compressive and relatively large. It was discovered that the effect of stress concentrations is more pronounced if the profile of the stamp is more flat than the profile of a circular cylinder.
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Franko L'viv State University, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 2, pp. 14–22, March – April, 1995.
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Hrylits'kyi, D.V., Evtushenko, O.O. & Pauk, V.I. Investigation of thermomechanical processes in the course of polishing. Mater Sci 31, 160–169 (1996). https://doi.org/10.1007/BF00558635
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DOI: https://doi.org/10.1007/BF00558635