# Analysis of the limit equilibrium of a bent spherical shell with collinear cracks according to local and integral failure criteria

## Authors

• M. V. Makoviichuk Laboratory of Modeling of Damping Systems, Pidstryhach-Institute for Applied Problems in Mechanics and Mathematics, NAS of Ukraine, Ivano-Frankivsk https://orcid.org/0000-0003-4202-1953
• І. P. Shatskyi Laboratory of Modeling of Damping Systems, Pidstryhach-Institute for Applied Problems in Mechanics and Mathematics, NAS of Ukraine, Ivano-Frankivsk

## Keywords:

spherical shell, collinear cracks, crack closure, bending, limit load, failure criteria

## Abstract

The stressed-strain state and limit equilibrium of shallow spherical shell weakened by two cross-cutting meridional collinear cracks is studied in the two-dimensional formulation. The crack closure caused by bending deformation was taken into account based on the model of the crack edges contact along a line in one of the face surfaces of the shell. The boundary problem for equations of classical shell theory with interrelated conditions along the line of the cracks is formulated within the framework of such model. Singular integral equation for the unknown jump of normal rotation angle on the cracks edges has been elaborated.

Based on numerical solutions of singular integral equation the stressed-strain state and limit equilibrium of the spherical shell depending on the parameters of shell curvature and distance between cracks are investigated. Using the local and integral through-the-thickness energy failure criteria of linear mechanics of fracture, the upper and lower values of limit load were established. It was found that the upper estimate of the limit load according to the integral criterion is approximately twice the magnitude of the lower estimate according to the local criterion.

Pages of the article in the issue: 132 - 135

Language of the article: Ukrainian

## References

SHATS'KYI, I. P. (1991) Integral equations of the problem of bending of a shallow shell weakened by a cut whose edges are in contact. Dop. Akad. Nauk Ukr RSR. Ser. A. (2). p. 26–29.

SHATSKY, I., MAKOVIYCHUK, M. (2010) An equilibrium of bending spherical shell with taking into account the closure of collinear cracks. Physico-mathematical modelling and informational technologies. (12). p. 189–195.

PANASYUK, V. V., SAVRUK, M. P. & DATSYSHYN, A. P. (1976) Raspredelenie napryazheniy okolo treshchin v plastinach i obolochkach, Kiev: Naukova dumka.

OSADCHUK, V. A. (1985) Napriazhenno-deformirovannoe sostoianie i predel’noe ravnovesie obolochek s razrezami. Kiev: Naukova dumka.

SHATSKYI, І. (2014) Two-side estimates of limiting bending load for plate with rectlinear crack. In: 5th Int. Conf. “Fracture mechanics of materials and structural integrity.” Karpenko Physico-Mechanical Institute, NASU, Lviv. p. 425–430.

2023-12-23

## How to Cite

Makoviichuk, M. V., & Shatskyi І. P. (2023). Analysis of the limit equilibrium of a bent spherical shell with collinear cracks according to local and integral failure criteria. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (2), 132–135. https://doi.org/10.17721/1812-5409.2023/2.21

## Section

Differential equations, mathematical physics and mechanics