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Reconstruction of the Thermal Load of a Functionally Graded Hollow Sphere by Surface Displacements

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We formulate and solve a problem of reconstruction of the unknown time-dependent temperature distribution on one boundary surface of a functionally graded hollow sphere according to the temperature and radial displacements on the other boundary surface. We suggest a procedure reducing the formulated problem to the inverse thermoelasticity problem. By applying the finite-difference method, we construct a numerical algorithm aimed at solving the obtained inverse problem. By using the solution of the direct thermoelasticity problem, we analyze the stability of the obtained solution of the inverse problem and the distributions of displacements and stresses obtained on the basis of this solution against the errors of the input data.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

    R. M. Kushnir, A. V. Yasinskyy & Yu. V. Tokovyy

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  1. R. M. Kushnir
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  2. A. V. Yasinskyy
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  3. Yu. V. Tokovyy
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Correspondence to A. V. Yasinskyy.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 1, pp. 149–160, January–March, 2020.

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Kushnir, R.M., Yasinskyy, A.V. & Tokovyy, Y.V. Reconstruction of the Thermal Load of a Functionally Graded Hollow Sphere by Surface Displacements. J Math Sci 270, 176–190 (2023). https://doi.org/10.1007/s10958-023-06339-8

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  • DOI: https://doi.org/10.1007/s10958-023-06339-8

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