Under the action of a stationary heat source, we construct the Boussinesq functions of the problem of thermoelasticity under the conditions of plane deformation of a semiinfinite body with free, rigidly, smoothly, or flexibly fastened boundary either kept at zero temperature or thermally insulated. The problem of construction of Boussinesq functions is reduced to solving boundary-value problems for harmonic functions in the half space. Relations for displacements and stresses are obtained. These relations are the corresponding Green functions and can be used to determine the thermoelastic state of the half space under the conditions of heat release in a ribbon-like domain.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 4, pp. 73–80, October–December, 2020.
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Kit, H.S., Ivas’ko, N.M. Two-Dimensional Problem of Thermoelasticity for a Half Space with Free, Rigidly, Smoothly, or Flexibly Fastened Boundary Subjected to the Action of Heat Sources. J Math Sci 273, 972–981 (2023). https://doi.org/10.1007/s10958-023-06558-z
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DOI: https://doi.org/10.1007/s10958-023-06558-z