title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð·Ð°Ð´Ð°Ñ Ð³Ð¸Ð¿ÐµÑÐ±Ð¾Ð»Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐµÑÐ¼Ð¾ÑÐ¿ÑÑÐ³Ð¾ÑÑÐ¸ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼ÐµÑÐ¾Ð´Ð° ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ°Ð·Ð½Ð¾ÑÑÐµÐ¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Numerical modeling of hyperbolic thermoelasticity problems using the finite-difference method
Creators: name: ÐÑÑÐ¸Ð½ÑÐºÐ°Ñ, ÐÐ»Ð¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð¢ÐµÐ¿Ð»Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¾ÑÑÑ
ÐÐµÐ½ÐµÑÐ°ÑÐ¾ÑÑ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÐµ
ÐÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ñ
ÑÐµÑÐ¼Ð¾ÑÐ¿ÑÑÐ³Ð¾ÑÑÑ
Ð³Ð¸Ð¿ÐµÑÐ±Ð¾Ð»Ð¸ÑÐµÑÐºÐ¾Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ
Ð¼ÐµÑÐ¾Ð´ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ°Ð·Ð½Ð¾ÑÑÐµÐ¹
Ð½ÐµÑÐ²Ð½Ð°Ñ ÑÑ ÐµÐ¼Ð°
thermoelasticity
hyperbolic equation
finite-difference method
implicit scheme

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description: The subject of the graduate qualification work is Â«Numerical modeling of hyperbolic thermoelasticity problems using the finite-difference methodÂ». This paper devotes to studying the behavior of a sample under a short-term laser perturbation created at the initial moment of time near one of its boundaries. During the study, the following tasks were solved: Two-dimensional hyperbolic heat conductivity problem using the implicit scheme of the finite-difference method. Two-dimensional hyperbolic Lord-Schulmanâs thermoelasticity problem for a plane-strain medium using the implicit scheme of the finite-difference method. Comparison of the obtained results with the one-dimensional analytical solution and the solution obtained using the explicit scheme. Error estimation of the implicit numerical methodFor the conductivity problem, the temperature field was obtained. For the thermoelasticity problem, the field of temperatures and deformations. After comparing the obtained solution with the known ones, it was found that the implicit scheme, in contrast to the explicit one, does not lead to the appearance of significant oscillations in the region of a sharp change in the function and, thereby, more accurately predicts the behavior of the sought values ââin the entire region. However, the implicit method predicts smaller peak quantities. However, the implicit method predicts smaller peaks. This is due to possible damping that occurs when solving an implicit pooling scheme. Implicit exclusion scheme error when decreasing space step.