Abstract
A contact problem of two elastic convex and axially symmetric solids heated (or cooled) to temperatures of different values is considered. Pertinent formulae have been derived for relations between the contact pressure, geometrical characteristics of the solids and distributions of heat flux over the contacting region. We have analysed: 1. The problem of the loss of the contact between two solids pressed together with active heat fluxes. We discuss the cases for which the contact of the axially symmetric solids can take the form of a circle, or an annulus. 2. The problem of a paradox when the mathematically well posed contact problem of thermoelasticity leads to a physically unacceptable solution with a region of overlapping materials. Here we discuss a generalization of the “cooled sphere” paradox. The heat flux functions are continuously differentiable, of constant sign. The conditions have been derived for the cases when the paradox can be avoided.
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REFERENCES
J.R. Barber, Indentation of the semi-infinite elastic solid by a hot sphere. Internat. J. Mech. Sci. 15(1973) 813–819.
J.R. Barber, The effect of heat flow on the contact area between a continuous rigid punch and a frictionless elastic half-space. J. Appl. Math. Phys. (ZAMP) 27(1976) 439–445.
J.R. Barber, Contact problems involving a cooled punch. J. Elasticity 8(1978) 409–423.
J.R. Barber and M. Comninou, Thermoelastic contact problems. In: R.B. Hetnarski (ed), Thermal Stresses. Elsevier Science, Amsterdam (1989) pp. 1–105.
N.M. Borodachev, On solution of contact problem of thermoelasticity in a case of axial symmetry. Izv. Acad. Nauk SSSR, Techn. Mekh. Mashinstr. 5(1962) 86–90 (in Russian).
M. Comninou and J.R. Barber, The thermoelastic Hertz problem with pressure dependent contact resistance. Internat. J. Mech. Sci. 26(11/12) (1984) 549–554.
M. Comninou and J. Dundurs, On the Barber boundary conditions for thermoelastic contact. J. Appl. Mech. 46(1979) 1–5.
M.B. Generalov, B.A. Kudryavtsev and V.Z. Parton, Contact problem of thermoelasticity for rotating bodies. Izv. Ac. Nauk SSSR, MTT (Mechanics of Solid Body) 3(1976) 46–52 (in Russian).
D.L. George and I.N. Sneddon, The axisymmetric Boussinesq problem for a heated punch. J. Math. Phys. 11(1963) 665–689.
G.M.L. Gladwell, J.R. Barber and Z.S. Olesiak, Thermal problems with radiation boundary conditions. Quart. J. Mech. Appl. Math. 36(1983) 387–401.
W. Nowacki, Thermoelasticity, 2nd edn. PWN (Polish Scientific Editors)/Pergamon Press (1986), (1st edn, Addison Wesley/Pergamon Press/PWN (1962)).
W. Nowacki and Z.S. Olesiak, Termodyfuzja w Ciałach Stałych. PWN (Polish Scientific Editors) (1991), (in Polish).
Z.S. Olesiak, O.O. Yevtushenko and R.D. Kulchytsky-Zhyhailo, On contact of two heated solids. Physico-chemical Mechanics of Materials 31(5) (1995) 32–39 (in Ukrainian, translated into English).
Z. Olesiak, On certain properties of thermal stresses. Mech. Teoret. i Stos. 5(5) (1967) 181–191 (in Polish).
Z.S. Olesiak, On problems in which the stresses depend essentially on the direction of heat flux. Problems of Fluid-flow Machines, I.M.P., Pol. Acad. Sci., Gdańsk (1993) 545–557 (in Polish).
Z. Olesiak, Some remarks on the contact problem of thermoelasticity for a semi-space. Bull Acad. Polon. Sci. Ser. Sci. Techniques 13(8) (1965) 339–344.
I.N. Sneddon, The use of transform methods in elasticity, Technical Report, North Carolina State College (1964) pp. 132–144.
I.N. Sneddon, Mixed Boundary Value Problems in Potential Theory. North-Holland, Amsterdam (1966).
I.N. Sneddon, The Use of Integral Transforms. McGraw-Hill, New York (1972) p. 539.
Yu. P. Shlykov and E.A. Galin, Contact Heat Exchange. Gosenergo, Moscow (1963) p. 144 (in Russian).
Yu.P. Shlykov, E.A. Galin and S.I. Tsarevski, Contact Thermal Resistance. Energia, Moscow (1977) p. 328 (in Russian).
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Kulchytsky-Zhyhailo, R., Olesiak, Z. & Yevtushenko, O. On Thermal Contact of Two Axially Symmetric Elastic Solids. Journal of Elasticity 63, 1–17 (2001). https://doi.org/10.1023/A:1013039522807
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DOI: https://doi.org/10.1023/A:1013039522807