# On the distribution of stresses near the crack in a toroidal shell with a flexible coating

## Authors

• M. V. Makoviichuk Ivano-Frankivsk Branch of Pidstryhach-Institute for Applied Problems in Mechanics and Mathematics, NAS of Ukraine, 76002, Ivano-Frankivsk, Mykytynetska str., 3
• I. P. Shatskyi Ivano-Frankivsk Branch of Pidstryhach-Institute for Applied Problems in Mechanics and Mathematics, NAS of Ukraine, 76002, Ivano-Frankivsk, Mykytynetska str., 3
• A. B. Shcherbii Ivano-Frankivsk Branch of Pidstryhach-Institute for Applied Problems in Mechanics and Mathematics, NAS of Ukraine, 76002, Ivano-Frankivsk, Mykytynetska str., 3

## Keywords:

toroidal shell, crack, flexible coating, elastic equilibrium

## Abstract

Elastic equilibrium of shallow toroidal shell loaded by internal pressure and containing the cross-cutting crack located along equator or throat of the shell has been studied in the two-dimensional formulation. The shell is reinforced by coating on one of the face surfaces. The crack in the shell with a flexible coating is simulated by a cuts with eccentrically hinge joint edges. The boundary problem for equations of classical shell theory with interrelated conditions of tension and bending along the cutting line is formulated within the framework of such model. Singular integral equation for the unknown jump of normal displacement on the crack edges has been elaborated. Based on asymptotical solutions of integral equation obtained using the small parameter method forces and moments intensity factors in the vicinity of the defect tips are defined. Their dependences of on the parameters of shell curvature and form parameter are investigated. It is established that the reinforcement of the shell leads to a decrease in the force intensity factor and to the appearance of a non-zero moment intensity factor.

Pages of the article in the issue: 67 - 70

Language of the article: Ukrainian

## References

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SHATS’KY, I. P. MAKOVIICHUK, M. V. & SHCHERBII, А. B. (2019) Influence of a flexible сoating on the strength of a shallow сylindrical shell with longitudinal crack. Journal of Mathematical Sciences, 238 (2), pp. 165–173.

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2021-12-07

## How to Cite

Makoviichuk, M. V., Shatskyi, I. P., & Shcherbii, A. B. (2021). On the distribution of stresses near the crack in a toroidal shell with a flexible coating. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (3), 67–70. https://doi.org/10.17721/1812-5409.2021/3.11

## Section

Differential equations, mathematical physics and mechanics