Precise heating of an unlimited plate with constraints on thermal stresses

Title	Precise heating of an unlimited plate with constraints on thermal stresses
Authors	N. D. Morozkin¹, N. N. Morozkin¹, M. F. Sadrislamov¹ ¹Ufa University of Science and Technology
Annotation	The problem of determining the time-varying temperature of the heating medium is investigated, which allows obtaining, over a fixed time, a final temperature distribution in the body as close as possible to the desired one. It is required that the tensile and compressive thermal stresses arising due to non-uniform heating do not lead to the failure of the heated product. Materials are considered in which the ultimate strengths under compression and tension depend significantly on temperature, while the thermophysical coefficients and other mechanical characteristics can be assumed constant. An algorithm for finding the optimal control is proposed for the case of heating a one-dimensional infinite plate. The results of calculations are presented in the absence of phase constraints.
Keywords	optimal control, thermal conductivity, thermal stresses, Fourier method, conditional gradient method.
Citation	Morozkin N. D., Morozkin N. N., Sadrislamov M. F. ''Precise heating of an unlimited plate with constraints on thermal stresses'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 164-168. Available at: https://conf.svmo.ru/files/2026/papers/paper96.pdf. - Date of access: 25.09.2026.

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Precise heating of an unlimited plate with constraints on thermal stresses

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