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Optimization of Nonstationary Thermal Displacements in a Given Cross Section of a Half Space in the Plane Strain State

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We construct the solution of the problem of optimal control over the distribution of nonstationary vertical thermal displacements of a half space in the plane strain state. The power of internal heat sources concentrated in a plane parallel to the boundary is chosen as the control function. Under the assumption of existence of the control function guaranteeing the attainment of the greatest lower bound of the uniform deviation of the controlled distribution of vertical displacements from the given distribution, we reduce the problem of optimization to the inverse problem of thermoelasticity. The solution of the obtained inverse problem is constructed and analyzed.

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Authors and Affiliations

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

    A. V. Yasinskyy & O. V. Ierokhova

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  1. A. V. Yasinskyy
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  2. O. V. Ierokhova
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 2, pp. 140–147, April–June, 2015.

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Yasinskyy, A.V., Ierokhova, O.V. Optimization of Nonstationary Thermal Displacements in a Given Cross Section of a Half Space in the Plane Strain State. J Math Sci 223, 173–183 (2017). https://doi.org/10.1007/s10958-017-3346-z

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  • DOI: https://doi.org/10.1007/s10958-017-3346-z

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