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This article examines the performance of shallow reinforced concrete shells with hinged supports along their perimeter. The relevance of this topic stems from the widespread use of such structures in modern construction for covering large buildings, as well as the insufficient understanding of their behavior under non-ideal boundary conditions. The aim of the study is to evaluate the stress-strain state and stability of the shells, taking into account geometric and physical nonlinearity, as well as the effect of long-term loads (concrete creep). The modeling was performed using the finite element method in the Pascal programming language based on DELPHI-7. The calculations take into account the rheological properties of concrete, nonlinear stress-strain relationships, and various loading schemes. Linear and nonlinear stability analyses were performed, including those involving the possible failure of supporting elements. The results showed that, when supported by a hinge, the shell loses stability under loads significantly lower than the design value, especially under long-term loads. The formation of characteristic localized dents and a loss of overall spatial performance of the structure were also detected. These data highlight the need for more accurate consideration of boundary conditions and nonlinear effects in the design of shallow shells. Recommendations are proposed for optimizing the shell shape and reinforcing the contour to improve its stability. The obtained results can be used in engineering practice for the analysis, design, inspection and safety of similar structures.
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27. Peleshko V. Applied creep theory for bodies with anisotropy due to plastic prestrain. Mechanics of Solids. 2007. 42 (2). P. 307 – 320. https://doi.org/10.3103/S002565440702015X
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30. Duissenbekov B., Tokmuratov A., Zhangabay N., Orazbayev Zh., Yerimbetov B., Aldiyarov Zh. Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting. Curved and Layered Structures. 2020. 7 (1). P. 48 – 55. https://doi.org/10.1515/cls-2020-0005
2. Karpov V., Semenov A. Strength and Stability of Orthotropic Shells. World Applied Sciences Journal. 2014. 30 (5). P. 617 – 623. https://doi.org/10.5829/idosi.wasj.2014.30.05.14064
3. Volokitin A., Volokitina I., Gelmanova Z., Denissova A. Thermomechanical treatment influence on the copper wire microstructure evolution. Theoretical and Applied Mechanics Letters. 2026. 16 (2). P. 100650. https://doi.org/10.1016/j.taml.2025.100650
4. Mityakina N.A. Experimental and theoretical studies of composite coatings from shell panels [Eksperimental'no-teoreticheskiye issledovaniya sostavnykh pokrytiy iz paneley-obolochek]. Belgorod: BSTU Publishing House, 2014. 112 p.
5. Zhangabay N., Tagybayev A., Utelbayeva A., Buganova S., Tolganbayev A., Tulesheva G., Jumabayev A., Kolesnikov A., Kambarov M., Imanaliyev K., Kozlov P. Analysis of the influence of thermal insulation material on the thermal resistance of new facade structures with horizontal air channels. Case Studies in Construction Materials. 2023. 18. P. e02026. https://doi.org/10.1016/j.cscm.2023.e02026
6. Krivoshein I.V. Iterative methods for calculating nonlinearly deformable shallow shells and plates [Iteratsionnyye metody rascheta nelineyno deformiruyemykh pologikh obolochek i plastinok]. Saratov: Saratov State Technical University, 2014. 168 p.
7. Varlamova T.V., Ksenofontova T.K., Verkhoglyadova A.S., Mareeva O.V. Accounting for dynamic effects in the design of cantilever structures. Construction Materials and Products. 2022. 5 (6). P. 54 – 63. https://doi.org/10.58224/2618-7183-2022-5-6-54-63
8. Nayzabekov A.B., Volokitina I.E. Effect of the Initial Structural State of Cr–Mo High-Temperature Steel on Mechanical Properties after Equal-Channel Angular Pressing. Physics of Metals and Metallography. 2019. 120 (2). P. 177 – 183. https://doi.org/10.1134/S0031918X19020133
9. Krivoshapko S.N. Hanging cable structures and roofs of structures. Construction of Unique Buildings and Structures. 2015. 7(34). P. 51–70.
10. Tursunkululy T., Zhangabay N., Suleimenov U., Abshenov K., Utelbayeva A., Moldagaliyev A., Kolesnikov A., Turashova Zh., Karshyga G., Kozlov P. Analysis of strength and eigenfrequencies of a steel vertical cylindrical tank without liquid, reinforced by a plain composite thread. Case Studies in Construction Materials. 2023. 18. P. e02019. https://doi.org/10.1016/j.cscm.2023.e02019
11. Qu Y., Wu S., Chen Y., Hua H. Vibration analysis of ring-stiffened conical–cylindrical–spherical shells based on a modified variational approach. International Journal of Mechanical Sciences. 2013. 69. P. 72 – 84. https://doi.org/10.1016/j.ijmecsci.2013.01.026
12. Volokitina I.E. Effect of Cryogenic Cooling After ECAP on Mechanical Properties of Aluminum Alloy D16. Metal Science and Heat Treatment. 2019. 61(3-4). P. 234–238. https://doi.org/10.1007/s11041-019-00406-1
13. Sanzharovsky R.S., Manchenko M.M., Gadzhiev M.A., Musabayev T.T., Ter-Emmanuilyan T.N., Varenik K.A. The system of insolvency of the modern theory of long-term resistance of reinforced concrete and warnings for. Structural Mechanics of Engineering Constructions and Buildings. 2019. 15(1). P. 4 – 24.
14. Rabotnov Yu.N. Creep of structural elements [Polzuchest' elementov konstruktsiy]. Moscow: Nauka, 2014. 752 p.
15. Mussabayev T.T., Nuguzhinov Z.S., Nemova D., Kayupov T., Tolkynbaev T.A., Akmakanova A.Z., Khafizova G.S. Creep of Concrete in Shell Structures: Nonlinear Theory. Materials. 2023. 16 (16). P. 5587. https://doi.org/10.3390/ma16165587
16. Karpov V., Semenov A. Dimensionless parameters in the theory of reinforced shells. PNRPU Mechanics Bulletin. 2015. 3. P. 74 – 94. https://doi.org/10.15593/perm.mech/2015.3.07
17. Lazouski D., Glukhov D., Khatkevich A., Hil A., Chaparanganda E. Nonlinear calculation of bent steel-reinforced concrete elements. Vestnik of Polotsk State University. Part F. Constructions. Applied Sciences. 2024. 37 (2). P. 9 – 23. https://doi.org/10.52928/2070-1683-2024-37-2-9-23
18. Tokmuratov A., Sanzharovskiy R., Duissenbekov B., Zhanabay N., Utelbayeva A. Example of calculation of flat reinforced concrete shells short-term effects of loads. Herald of the Kazakh-British Technical University. 2020. 17 (2). P. 201 – 204.
19. Shishov I.I., Lukin M.V. Calculation and design of a biconvex shell and an underground reservoir [Raschet i konstruirovaniye dvoyakovypukloy obolochki i podzemnogo rezervuara]. Vladimir: Publishing house of VlSU, 2016. 84 p.
20. Nurseitov Sh., Yerimbetov B., Duissenbekov B., Chalabayev B., Kolesnikov A., Dossaliyev K., Kunanbayeva Ya., Aubakirova F. Capabilities of existing frame buildings with shear diaphragms to resist seismic effects of destructive earthquakes. Construction Materials and Products. 2025. 8 (2). P. 10. https://doi.org/10.58224/2618-7183-2025-8-2-10
21. Mitrofanov O.V., Kaikov K.V. Stability and bearing capacity of cylindrical panels and shells made of composite materials [Ustoychivost' i nesushchaya sposobnost' tsilindricheskikh paneley i obolochek iz kompozitnykh materialov]. Moscow: Publishing house "Sputnik +", 2017. 64 p.
22. Kopzhassarov B., Mominova S., Kim K.D., Kopzhassarov A., Kolesnikov A., Dyussembayev I., Baisarova G., Zhaiylkhan N. The challenges of reusing thermal power plant wastes to produce cellular concrete modified with wollastonite. Construction Materials and Products. 2025. 8 (3). P. 10. https://doi.org/10.58224/2618-7183-2025-8-3-10
23. Chepurnenko A., Saibel A.V., Yazyev B.M. Determination of the Breaking Load for Concrete Slabs Based on the Deformation Theory of Plasticity. Procedia Engineering. 2016. 150. P. 1694 К 1700. https://doi.org/10.1016/j.proeng.2016.07.157
24. Musabayev T.T., Kayupov T. Computer Program for Calculating Creep of Cylindrical Heterogeneous Bodies Taking into Account Temperature. Certificate No. 433 dated November 7, 2018 on State Registration of Rights to a Copyright Object, Computer Program.
25. Sanzharovskiy R., Sieber F., Ter-Emmanuilyan T. The theory of calculation of reinforced concrete structures and the principles of the Eurocode. Structural Mechanics of Engineering Constructions and Buildings. 2021. 17 (5). P. 455 – 465. https://doi.org/10.22363/1815-5235-2021-17-5-455-465
26. Balamirzoev A.G., Murtuzov M.M., Selimkhanov D.N., Dibirova Z.G., Abdullaev A.R. Nonlinear transverse vibrations of composite rods under a statically applied transverse load. Construction Materials and Products. 2021. 4 (2). P. 29 – 37. https://doi.org/10.34031/2618-7183-2021-4-2-29-37
27. Peleshko V. Applied creep theory for bodies with anisotropy due to plastic prestrain. Mechanics of Solids. 2007. 42 (2). P. 307 – 320. https://doi.org/10.3103/S002565440702015X
28. Pikul V.V. Stability of Shells [Ustoychivost' obolochek]. Vladivostok: FEFU Engineering School, Far Eastern Federal University, 2016. 340 p.
29. Mikhailova E.Yu., Tarlakovsky D.V., Fedotenkov G.V. Elastic Plates and Shallow Shells [Uprugiye plastiny i pologiye obolochki]. Moscow: Publishing House MAI, 2018. 92 p.
30. Duissenbekov B., Tokmuratov A., Zhangabay N., Orazbayev Zh., Yerimbetov B., Aldiyarov Zh. Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting. Curved and Layered Structures. 2020. 7 (1). P. 48 – 55. https://doi.org/10.1515/cls-2020-0005
Duissenbekov B.K., Yerimbetov B.T., Dossaliyev K.S., Chalabayev B.M., Bychkov A.Yu., Botabayev N.E., Kunanbayeva Ya.B., Aubakirova F.Kh. Stress-strain state and stability of hinged-supported constructions along the boundary of shallow reinforced concrete shells. Construction Materials and Products. 2026. 9 (1). 7. https://doi.org/10.58224/2618-7183-2026-9-1-7