We propose a generalization of the method of direct integration of the original equations of two-dimensional problems of thermoelasticity for solids with corner points (i.e., the plane problems for a rectangular domain and an annular sector and the axisymmetric problem for a cylinder of finite length). In this way, the problems are reduced to a governing integrodifferential equation for the key function, which is unique for each problem. By using the equilibrium equations, the expressions for the components of the stress tensor are deduced in terms of the key function, whereas the sets of boundary conditions are equivalently reduced to the corresponding sets of integral conditions for the key function. We also propose the algorithms aimed at the separation of variables in the deduced governing equations by using the complete sets of specially constructed eigen- and associated functions, as well as at the construction of solutions to the formulated problems in the form of explicit dependences on thermal loading with regard for the boundary conditions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 10, pp. 1355–1367, October, 2021. Ukrainian DOI: https://doi.org/10.37863/umzh.v73i10.6784.
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Kushnir, R.M., Tokovyi, Y.V., Yuzvyak, M.Y. et al. Reduction of the Two-Dimensional Thermoelasticity Problems for Solids with Corner Points to Key Integrodifferential Equations. Ukr Math J 73, 1566–1579 (2022). https://doi.org/10.1007/s11253-022-02014-4
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DOI: https://doi.org/10.1007/s11253-022-02014-4