# Analysis of the Stress State of a Layer with Two Cylindrical Swivel Joints and a Cylindrical Cavity

 DOI https://doi.org/10.15407/pmach2024.02.025 Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia Publisher Anatolii Pidhornyi Institute for Mechanical Engineering Problems National Academy of Science of Ukraine ISSN 2709-2984 (Print), 2709-2992 (Online) Issue Vol. 27, no. 2, 2024 (June) Pages 25-35 Cited by J. of Mech. Eng., 2024, vol. 27, no. 2, pp. 25-35

Authors

Vitalii Yu. Miroshnikov, National Aerospace University “Kharkiv Aviation Institute” (17, Vadyma Manka str., Kharkiv, 61070, Ukraine), e-mail: v.miroshnikov@khai.edu, ORCID: 0000-0002-9491-0181

Valentyn P. Pelykh, National Aerospace University “Kharkiv Aviation Institute” (17, Vadyma Manka str., Kharkiv, 61070, Ukraine), e-mail: venator.verba@gmail.com, ORCID: 0009-0007-5301-6697

Oleksandr Yu. Denshchykov, National Aerospace University “Kharkiv Aviation Institute” (17, Vadyma Manka str., Kharkiv, 61070, Ukraine), e-mail: Alex_day@ukr.net, ORCID: 0009-0008-2385-5841

Abstract

In practice, connections in the form of cylindrical swivel joints are often encountered. However, exact methods for calculating such models are absent. Therefore, the development of algorithms to solve such problems is relevant. In this study, a spatial elasticity problem is solved for an infinite layer with two cylindrical swivel joints and a cylindrical cavity positioned parallel to each other and parallel to the layer surfaces. The embedded cylindrical swivel joints are represented as cavity with given contact-type conditions (normal displacements and tangential stresses). Stresses are specified on the layer surfaces and the cavity surface. The layer is considered in a Cartesian coordinate system, while the cylindrical cavities are considered in local cylindrical coordinates. The spatial elasticity problem is solved using the generalized Fourier method applied to the Lamé equations. Satisfying the boundary conditions results in a system of infinite linear algebraic equations, which undergo reduction methods. In the numerical study, the accuracy of boundary condition fulfillment reached 10-3 for stress values ranging from 0 to 1, with the equation system (Fourier series members) order of m=4. As the order of the system equations increases, the accuracy of calculations increases. Stress state analysis was conducted at varying distances between supports. The obtained results indicate that with an increased distance between supports, stresses on the supporting cylindrical surfaces of the layer and the cylindrical cavity surface decrease. These stresses are redistributed to the upper and lower surfaces of the layer, where the stresses increase and exceed the specified ones. The numerical outcomes can be applied to predict geometric parameters during design processes.

Keywords: layer with cylindrical cavities, generalized Fourier method, contact-type conditions.

References

1. Tekkaya, A. E. & Soyarslan, C. (2014). Finite Element Method. In: Laperrière, L. & Reinhart, G. (eds) CIRP Encyclopedia of Production Engineering. Berlin, Heidelberg: Springer, pp. 508–514. https://doi.org/10.1007/978-3-642-20617-7_16699.
2. Karvatskyi, A. Ya. (2018). Metod skinchennykh elementiv u zadachakh mekhaniky sutsilnykh seredovyshch [Finite element method in problems of continuum mechanics]: Laboratory workshop on the academic discipline: textbook. Kyiv: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, 391 p. (in Ukrainian).
3. Zasovenko, A. V. & Fasoliak, A. V. (2023). Matematychne modeliuvannia dynamiky pruzhnoho pivprostoru z tsylindrychnoiu porozhnynoiu, yaka pidkriplena obolonkoiu, pry osesymetrychnykh navantazhenniakh [Mathematical modeling of the dynamics of an elastic half-medium with a cylindrical cavity reinforced by a shell under axisymmetric loads]. Novi materialy i tekhnolohii v metalurhii ta mashynobuduvanni – New materials and technologies in metallurgy and mechanical engineering, no. 2, pp. 67–73. https://doi.org/10.15588/1607-6885-2023-2-10 (in Ukrainian).
4. Azarov, A. D., Zhuravlev, G. A., & Piskunov, A. S. (2015). Sravnitelnyy analiz analiticheskogo i chislennogo metodov resheniya ploskoy zadachi o kontakte uprugikh tsilindrov [Comparative analysis of analytical and numerical methods for solving the plane problem of contact of elastic cylinders]. Innovatsionnaya naukaInnovative science, no. 1–2, pp. 5–13 (in Russian).
5. Guz, A. N., Kubenko, V. D., & Cherevko, M. A. (1978). Difraktsiya uprugikh voln [Elastic wave diffraction]. Kyiv: Naukova dumka, 307 p. (in Russian).
6. Grinchenko, V. T. & Meleshko, V. V. (1981). Garmonicheskiye kolebaniya i volny v uprugikh telakh [Harmonic vibrations and waves in elastic bodies]. Kyiv: Naukova dumka, 284 p. (in Russian).
7. Fesenko, A. & Vaysfel’d, N. (2019). The wave field of a layer with a cylindrical cavity. In: Gdoutos, E. (eds) Proceedings of the Second International Conference on Theoretical, Applied and Experimental Mechanics. ICTAEM 2019. Structural Integrity, vol. 8. Cham: Springer, pp. 277–282. https://doi.org/10.1007/978-3-030-21894-2_51.
8. Fesenko, A. & Vaysfel’d, N. (2021). The dynamical problem for the infinite elastic layer with a cylindrical cavity. Procedia Structural Integrity, vol. 33, pp. 509–527. https://doi.org/10.1016/j.prostr.2021.10.058.
9. Jafari, M., Chaleshtari, M. H. B., Khoramishad, H., & Altenbach H. (2022). Minimization of thermal stress in perforated composite plate using metaheuristic algorithms WOA, SCA and GA. Composite Structures, vol. 304, part 2, article 116403. https://doi.org/10.1016/j.compstruct.2022.116403.
10. Malits, P. (2021). Torsion of an elastic half-space with a cylindrical cavity by a punch. European Journal of Mechanics – A/Solids, vol. 89, article 104308. https://doi.org/10.1016/j.euromechsol.2021.104308.
11. Khechai, A., Belarbi, M.-O., Bouaziz, A., & Rekbi, F. M. L. (2023). A general analytical solution of stresses around circular holes in functionally graded plates under various in-plane loading conditions. Acta Mechanica, vol. 234, pp. 671–691. https://doi.org/10.1007/s00707-022-03413-1.
12. Smetankina, N., Kurennov, S., & Barakhov, K. (2023). Dynamic stresses in the adhesive joint. The Goland-Reissner model. In: Cioboată D. D. (eds) International Conference on Reliable Systems Engineering (ICoRSE) – 2023. ICoRSE 2023. Lecture Notes in Networks and Systems. Cham: Springer, vol. 762, pp. 456–468. https://doi.org/10.1007/978-3-031-40628-7_38.
13. Ugrimov, S., Smetankina, N., Kravchenko, O., Yareshchenko, V., & Kruszka, L. (2023). A study of the dynamic response of materials and multilayer structures to shock loads. In: Altenbach H., et al. Advances in Mechanical and Power Engineering. CAMPE 2021. Lecture Notes in Mechanical Engineering. Cham: Springer, pp. 304–313. https://doi.org/10.1007/978-3-031-18487-1_31.
14. Smetankina, N., Merkulova, A., Merkulov, D., Misura, S., & Misiura, Ie. (2023). Modelling thermal stresses in laminated aircraft elements of a complex form with account of heat sources. In: Cioboată D. D. (eds) International Conference on Reliable Systems Engineering (ICoRSE) – 2022. ICoRSE 2022. Lecture Notes in Networks and Systems. Cham: Springer, vol. 534, pp. 233–246. https://doi.org/10.1007/978-3-031-15944-2_22.
15. Smetankina, N., Kravchenko, I., Merculov, V., Ivchenko, D., & Malykhina, A. (2020). Modelling of bird strike on an aircraft glazing. In book: Nechyporuk M., Pavlikov V., Kritskiy D. (eds) Integrated Computer Technologies in Mechanical Engineering. Advances in Intelligent Systems and Computing. Cham: Springer, vol. 1113, pp. 289–297. https://doi.org/10.1007/978-3-030-37618-5_25.
16. Nikolayev, A. G. & Protsenko, V. S. (2011). Obobshchennyy metod Furye v prostranstvennykh zadachakh teorii uprugosti [Generalized Fourier method in spatial problems of the theory of elasticity]. Kharkiv: National Aerospace University “Kharkiv Aviation Institute”, 344 p. (in Russian).
17. Nikolaev, A. G. & Tanchik, E. A. (2015). The first boundary-value problem of the elasticity theory for a cylinder with N cylindrical cavities. Numerical Analysis and Applications, vol. 8, pp. 148–158. https://doi.org/10.1134/S1995423915020068.
18. Nikolaev, A. G. & Tanchik, E. A. (2016). Stresses in an elastic cylinder with cylindrical cavities forming a hexagonal structure. Journal of Applied Mechanics and Technical Physics, vol. 57, pp. 1141–1149. https://doi.org/10.1134/S0021894416060237.
19. Nikolaev, A. G. & Tanchik, E. A. (2016). Model of the stress state of a unidirectional composite with cylindrical fibers forming a tetragonal structure. Mechanics of Composite Materials, vol. 52, pp. 177–188. https://doi.org/10.1007/s11029-016-9571-6.
20. Nikolayev, A. G. & Orlov, Ye. M. (2012). Resheniye pervoy osesimmetrichnoy termouprugoy krayevoy zadachi dlya transversalno-izotropnogo poluprostranstva so sferoidalnoy polostyu [Solution of the first axisymmetric thermoelastic boundary value problem for a transversally isotropic half-space with a spheroidal cavity]. Problemy vychislitelnoy mekhaniki i prochnosti konstruktsiy – Problems of Computational Mechanics and Strength of Structures, iss. 20, pp. 253–259 (in Russian).
21. Ukrayinets, N., Murahovska, O., & Prokhorova, O. (2021). Solving a one mixed problem in elasticity theory for half-space with a cylindrical cavity by the generalized Fourier method. Eastern-European Journal of Enterprise Technologies, vol. 2, no. 7 (110), pp. 48–57. https://doi.org/10.15587/1729-4061.2021.229428.
22. Miroshnikov, V. Yu. (2020). Stress state of an elastic layer with a cylindrical cavity on a rigid foundation. International Applied Mechanics, vol. 56, iss. 3, pp. 372–381. https://doi.org/10.1007/s10778-020-01021-x.
23. Miroshnikov, V. (2023). Rotation of the layer with the cylindrical pipe around the rigid cylinder. In: Altenbach H., et al. Advances in Mechanical and Power Engineering. CAMPE 2021. Lecture Notes in Mechanical Engineering. Cham: Springer, pp. 314–322. https://doi.org/10.1007/978-3-031-18487-1_32.
24. Miroshnikov, V. Yu., Medvedeva, A. V., & Oleshkevich, S. V. (2019). Determination of the stress state of the layer with a cylindrical elastic inclusion. Materials Science Forum, vol. 968, pp. 413–420. https://doi.org/10.4028/www.scientific.net/MSF.968.413.
25. Miroshnikov, V. Yu. (2019). Investigation of the stress strain state of the layer with a longitudinal cylindrical thick-walled tube and the displacements given at the boundaries of the layer. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, vol. 22, no. 2, pp. 44–52. https://doi.org/10.15407/pmach2019.02.044.
26. Miroshnikov, V. Yu., Savin, O. B., Hrebennikov, M. M., & Pohrebniak, O. A. (2022). Analysis of the stress state of a layer with two cylindrical elastic inclusions and mixed boundary conditions. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, vol. 25, no. 2, pp. 22–29. https://doi.org/10.15407/pmach2022.02.022.
27. Miroshnikov, V. Yu., Savin, O. B., Hrebennikov, M. M., & Demenko, V. F. (2023). Analysis of the stress state for a layer with two incut cylindrical supports. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, vol. 26, no. 1, pp. 15–22. https://doi.org/10.15407/pmach2023.01.015.
28. Miroshnikov, V., Savin, O., Sobol, V., & Nikichanov, V. (2023). Solving the problem of elasticity for a layer with N cylindrical embedded supports. Computation, vol. 11, article 172, 11 p. https://doi.org/10.3390/computation11090172.

Received 23 December 2023

Published 30 June 2024