ANALYSIS OF THE STRESS STATE OF A LAYER WITH TWO CYLINDRICAL EMBEDDED SUPPORTS AND CYLINDRICAL BUSHINGS

В. Ю. Мірошніков, О. Б. Савін, М. Л. Косенко, О. О. Ільїн

Abstract


The spatial problem of the theory of elasticity for a layer on cylindrical embedded supports with cylindrical sleeves (thick-walled pipes) located between each support and the layer is solved. Smooth contact conditions are set at the interface between the layer and the pipes. Stresses are specified on the surfaces of the layer, and displacements are specified on the inner surface of the pipe (rigidly conjugated to the support). The analytical and numerical solution of the problem is based on the Lamé equations written for the layer and each pipe. When the boundary conditions and the conditions of conjugation of the layer with the pipes are met, a system of integro-algebraic equations is created, which reduces to a system of linear algebraic equations. Each equation is written in its local coordinate system. For this purpose, the transition formulas of the generalized Fourier method are applied to the basic solutions of the Lamé equation. After solving the system of equations and finding the unknowns, the stress-strain state in the body of the layer and pipes was obtained.  The reduction method was used to obtain numerical results. Fulfillment of the boundary conditions showed high convergence of the results, the accuracy of which depends on the order of the system of equations. The analysis of the stress-strain state of the layer and the pipe was carried out for different sleeve materials in places of stress concentration. The results indicate an increase in the stresses sφ and sz on cylindrical surfaces in the case of using polyamide bushings. The proposed method makes it possible to analyze the stress-strain state of a wide range of pipe structures. It also provides an opportunity to assess how changes in material and geometric parameters affect the stress distribution in such systems, which allows optimizing structures and ensuring their reliability. In the further development of this research topic, it is necessary to consider models where bushings are combined with other types of inhomogeneities (cavities, reinforcement) and other boundary conditions.


Keywords


fiber composite; layer with cylindrical sleeves; generalized Fourier method; Lamé equation

References


Tekkaya, A. E., Soyarslan, C. (2014). Finite Element Method in CIRP Encyclopedia of Production Engineering (р. 508–514). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-20617-7_16699

Static Structural Simulation Using Ansys Discovery. Available online: https://courses.ansys.com/index.php/courses/structural-simulation (accessed on 16.04.2024).

Zasovenko, А., & Fasoliak, А. (2023). Mathematical modeling of the dynamics of an elastic half-medium with a cylindrical cavity reinforced by a shell under axisymmetric loads. New Materials and Technologies in Metallurgy and Mechanical Engineering, 2, 67–73. https://doi.org/10.15588/1607-6885-2023-2-10

Huz, A. N., Kubenko, V. D., Cherevko M. A (1978). Difraktsia upruhykh voln. Kyiv: Nauk. Dumka. 307 s.

Hrynchenko, V. T., Meleshko, V. V. (1981). Harmonycheskie kolebania i volny v upruhykh telakh. Kyiv: Nauk. Dumka. 284 s.

Fesenko, A., & Vaysfel’d, N. (2019). The Wave Field of a Layer with a Cylindrical Cavity in Structural Integrity. Springer International Publishing. pp. 277–282. https://doi.org/10.1007/978-3-030-21894-2_51.

Fesenko, A., & Vaysfel’d, N. (2021). The dynamical problem for the infinite elastic layer with a cylindrical cavity. Procedia Structural Integrity, 33, 509–527. https://doi.org/10.1016/j.prostr.2021.10.058.

Malits, P. (2021). Torsion of an elastic half-space with a cylindrical cavity by a punch. European Journal of Mechanics - A/Solids, 89, 104308. https://doi.org/10.1016/j.euromechsol.2021.104308.

Khechai, A., Belarbi, M.O., Bouaziz, A. et al. (2023). A general analytical solution of stresses around circular holes in functionally graded plates under various in-plane loading conditions. Acta Mech, vol. 234, pp. 671–691. https://doi.org/10.1007/s00707-022-03413-1.

Snitser, A. R. (1996). The reissner-sagoci problem for a multilayer base with a cylindrical cavity. Journal of Mathematical Sciences, 82(3), 3439–3443. https://doi.org/10.1007/bf02362661.

Nikolaev, A. G., Protsenko, V. S. (2011). Obobshchennyy metod Fur'e v prostranstvennykh zadachakh teorii uprugosti. Khar'kov: Nats. aerokosm inniversitet im. N.Ye. Zhukovskogo «KHAI». 344 s.

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, 8(2), 148–158. https://doi.org/10.1134/s1995423915020068

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, 57(6), 1141–1149. https://doi.org/10.1134/s0021894416060237

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, 52(2), 177–188. https://doi.org/10.1007/s11029-016-9571-6.

Nikolaev, A. G., Orlov, Ye. M. (2012). Reshenie pervoy osesimmetrichnoy termouprugoy krayevoy zadachi dlya transversal'no-izotropnogo poluprostranstva so sferoidal'noy polost'yu. Problemi obchisl. mekhaníki í mítsností konstruktsíy. Vol.20. pp. 253 – 259.

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, 2(7 (110)), 48–57. https://doi.org/10.15587/1729-4061.2021.229428.

Miroshnikov, V., Denysova, T., & Protsenko, V. (2019). The study of the first main problem of the theory of elasticity for a layer with a cylindrical cavity. Strength of Materials and Theory of Structures, 103, 208–218. https://doi.org/10.32347/2410-2547.2019.103.208-218.

Miroshnikov, V. Y., Medvedeva, A. V., & Oleshkevich, S. V. (2019). Determination of the Stress State of the Layer with a Cylindrical Elastic Inclusion. Materials Science Forum, 968, 413–420. https://doi.org/10.4028/www.scientific.net/

msf.968.413.

Miroshnikov, V. Y. (2019). Investigation of the Stress State of a Composite in the Form of a Layer and a Half Space with a Longitudinal Cylindrical Cavity at Stresses Given on Boundary Surfaces. Journal of Mechanical Engineering, 22(4), 24 31. https://doi.org/10.15407/pmach2019.04.024.

Vitaly, M. (2023). Rotation of the Layer with the Cylindrical Pipe Around the Rigid Cylinder. Advances in Mechanical and Power Engineering . CAMPE 2021. Lecture Notes in Mechanical Engineering. Springer, Cham, pp 314–322. https://doi.org/10.1007/978-3-031-18487-1_32.

Miroshnikov, V. Y., 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, 26(1), 15–22. https://doi.org/10.15407/

pmach2023.01.015.

Miroshnikov, V. Y., 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, 25(1), 22–29. https://doi.org/10.15407/pmach2022.02.022.




DOI: https://doi.org/10.32620/oikit.2024.101.08

Refbacks

  • There are currently no refbacks.