Martynenko, MichailLebedeva, Irina2012-11-162012-11-162008Martynenko, M. The torsion of elastic medium with internal cylindrical crack / M. Martynenko, I. Lebedeva // Proceedings of 11th International Conference. Mechanika. – 2006. – P. 221–224.https://dspace.nuft.edu.ua/handle/123456789/3717A problem on torsion of an elastic medium weakened by mathematical cut on a part of the cylindrical surface is solved by exact methods of the linear theory of elasticity. The problem is reduced to a system of dual integral equations with respect to the trigonometric functions with one unknown density. Then the Fredholm integral-differential equation is examined. The analytical expressions for the stress intensity factor, the stress components on the cylinder surface outside the cut and difference between the displacements of the cut surfaces are obtained. Data obtained are applicable to the study of material damage.otherстрес-фактор інтенсивностістресс-фактор интенсивностиstress-intensity factorінтегральна неплоских тріщинматематичні вирізирозклад на власні функціїциліндричні поверхніинтегральная неплоских трещинматематические вырезыразложения по собственным функциямцилиндрические поверхностиintegral nonflat crackmathematical cuteigenfunction expansionscylindrical surfaceкафедра вищої математики імені проф. Можара В. І.Article