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Quasistatic Thermoelastic Fields in a Half-Space Heated by a Circular Surface Heat Source
V. A. Pinsker
Open Joint-Stock Company "Drilling Techniques" of United Heavy Machinery, Moscow, Russia
An accurate analytical solution of a classical problem, related to unbound thermoelasticity in a homogeneous and isotropic linearly-elastic half-space has been obtained in a closed integral form. Important partial cases, when the expressions for temperature and stresses take a simpler form, have been analyzed. The asymptotics of the found solutions have been investigated at small and large values of dimensionless time near the heat source and at a distance from it. The fields of isotherms and isobars have been studied. Unapparent properties of spatial inversion of both temperature and thermal stresses have been found. Maximum values of all components of the thermoelastic field at different values of the Poisson ratio have been found. For steady-state heating, a general solution, expressed in terms of a set of elliptical integrals, has been constructed in an explicit form. It has been shown that only compression stresses are possible in a steady-state mode in a semibounded body. The deformation profile of a free boundary has been determined. Possibility of mechanical destructions in the heated half-space has been analyzed. The graphs illustrating the spatial distribution and the time evolution of thermoelastic fields are given. The constructed solution can serve as a Green function for a set of other problems, having similar geometrical and boundary conditions.
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