Summary
Plane temperature and thermoelastic problems of discs and holes or inclusions in an infinite elastic matrix are considered, when the boundary of the problems is mapped on the unit circle by a known conformal mapping. By application of complex variables for curvilinear coordinate systems the temperature and thermoelastic problem is expressed in terms of the holomorphic functions. Using the method of continuation of the complex function for curvilinear boundaries, the problem is reduced to a Hilbert problem, whose solution gives the heat flow, temperature, stresses and the displacements. The analysis is applied to two particular cases (hypotrochoidal hole and hypotrochoidal rigid inclusion) and the results obtained are successfully compared with those existing in the literature.
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Kattis, M.A. Thermoelastic plane problems with curvilinear boundaries. Acta Mechanica 87, 93–103 (1991). https://doi.org/10.1007/BF01177175
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DOI: https://doi.org/10.1007/BF01177175