Моделювання нестаціонарних процесів дифузії водню поблизу вершини тріщини в полі неоднорідних механічних напружень: Fìz.-mat. model. ìnf. tehnol. 2021, 33:93-98

• Date: 2021
• Main Authors: Pelekh, Yaroslav, Kunynets, Andrii, Mentynskyi, Serhii, Fil, Bohdan
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: математична модель; механічні напруження; дифузія водню; тріщини; ланцюгові дроби; двостороння апроксимація
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/209
• Journal Title: Physico-mathematical modeling and informational technologies

An elastic-plastic isotropic body is investigated, weakened by a rectilinear crack directed along the abscissa axis, under the action of stresses symmetric with respect to its plane. The hydrogen concentration near the crack tip is calculated. An approximate solution of this problem is constructed under the condition that the distribution of hydrostatic stresses along the crack extension is approximated by a parabola. For a numerical solution, a method of the third order of accuracy with a two-sided estimate of the main term of the local error is proposed. References Skorobogatko, V. Ya. (1983). The theory of branching chain fractions and its application in computational mathematics. M.: Nauka. (in Russian). Gorbunov, A. D., Shakhov, Yu. A. (1963). On the approximate solution of the Cauchy problem for ordinary differential equations with a predetermined number of correct signs. I. J. calculated. mat. and mathematics. phys., 3(2), 239-253. (in Russian). DOI https://doi.org/10.1016/0041-5553(63)90023-5 Dobronets, B. S., Shaidurov, V. V. (1990). Bilateral numerical methods. Novosibirsk: Science. (in Russian). Krylov, V. I., Bobkov, V. V., Monastyrny, P. I. (1977). Computational methods. Volume II. M.: Nauka. (in Russian