{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T18:07:15Z","timestamp":1775153235527,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T00:00:00Z","timestamp":1725580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>A spatial problem of elasticity theory is solved for a layer located on two bearings embedded in it. The bearings are represented as thick-walled pipes embedded in the layer parallel to its boundaries. The pipes are rigidly connected to the layer, and contact-type conditions (normal displacements and tangential stresses) are specified on the insides of the pipes. Stresses are set on the flat surfaces of the layer. The objective of this study is to obtain the stress\u2013strain state of the body of the layer under different geometric characteristics of the model. The solution to the problem is presented in the form of the Lam\u00e9 equation, whose terms are written in different coordinate systems. The generalized Fourier method is used to transfer the basic solutions between coordinate systems. By satisfying the boundary and conjugation conditions, the problem is reduced to a system of infinite linear algebraic equations of the second kind, to which the reduction method is applied. After finding the unknowns, using the generalized Fourier method, it is possible to find the stress\u2013strain state at any point of the body. The numerical study of the stress state showed high convergence of the approximate solutions to the exact one. The stress\u2013strain state of the composite body was analyzed for different geometric parameters and different pipe materials. The results obtained can be used for the preliminary determination of the geometric parameters of the model and the materials of the joints. The proposed solution method can be used not only to calculate the stress state of bearing joints, but also of bushings (under specified conditions of rigid contact without friction on the internal surfaces).<\/jats:p>","DOI":"10.3390\/computation12090182","type":"journal-article","created":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T10:29:45Z","timestamp":1725618585000},"page":"182","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Analysis of the Stress\u2013Strain State of a Layer on Two Cylindrical Bearings"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9491-0181","authenticated-orcid":false,"given":"Vitaly","family":"Miroshnikov","sequence":"first","affiliation":[{"name":"National Aerospace University \u201cKHAI\u201d, 61000 Kharkiv, Ukraine"}]},{"given":"Oleksandr","family":"Denshchykov","sequence":"additional","affiliation":[{"name":"National Aerospace University \u201cKHAI\u201d, 61000 Kharkiv, Ukraine"}]},{"given":"Iaroslav","family":"Grebeniuk","sequence":"additional","affiliation":[{"name":"National Aerospace University \u201cKHAI\u201d, 61000 Kharkiv, Ukraine"}]},{"given":"Oleksandr","family":"Savin","sequence":"additional","affiliation":[{"name":"National Aerospace University \u201cKHAI\u201d, 61000 Kharkiv, Ukraine"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,6]]},"reference":[{"key":"ref_1","unstructured":"Aitharaju, V., Aashat, S., Kia, H., Satyanarayana, A., and Bogert, P. (2024, June 16). Progressive Damage Modeling of Notched Composites. NASA Technical Reports Server, Available online: https:\/\/ntrs.nasa.gov\/archive\/nasa\/casi.ntrs.nasa.gov\/20160012242.pdf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s11029-019-09808-x","article-title":"Relationships Between the Ultimate Strengths of Polymer Composites in Static Bending, Compression, and Tension","volume":"55","author":"Kondratiev","year":"2019","journal-title":"Mech. Compos. Mater."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tekkaya, A.E., and Soyarslan, C. (2014). Finite Element Method. Encyclopedia of Production Engineering, Springer.","DOI":"10.1007\/978-3-642-20617-7_16699"},{"key":"ref_4","unstructured":"(2024, June 16). Static Structural Simulation Using Ansys Discovery. Available online: https:\/\/courses.ansys.com\/index.php\/courses\/structural-simulation."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"67","DOI":"10.15588\/1607-6885-2023-2-10","article-title":"Mathematical modeling of the dynamics of an elastic half-medium with a cylindrical cavity reinforced by a shell under axisymmetric loads","volume":"Volume 2","author":"Zasovenko","year":"2023","journal-title":"New Materials and Technologies in Metallurgy and Mechanical Engineering"},{"key":"ref_6","first-page":"5","article-title":"Comparative analysis of analytical and numerical methods for solving the plane problem of contact of elastic cylinders","volume":"1\u20132","author":"Azarov","year":"2015","journal-title":"Innov. Nauka"},{"key":"ref_7","unstructured":"Huz, A.N., Kubenko, V.D., and Cherevko, M.A. (1978). Dyfraktsyia Upruhykh Voln [Elastic Wave Diffraction], Naukova Dumka."},{"key":"ref_8","unstructured":"Grinchenko, V.T., and Meleshko, V.V. (1981). Garmonicheskiye Kolebaniya i volny v Uprugikh Telakh, Naukova Dumka."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/978-3-030-21894-2_51","article-title":"The Wave Field of a Layer with a Cylindrical Cavity","volume":"Volume 8","author":"Gdoutos","year":"2019","journal-title":"Proceedings of the Second International Conference on Theoretical, Applied and Experimental Mechanics, ICTAEM 2019"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.prostr.2021.10.058","article-title":"The dynamical problem for the infinite elastic layer with a cylindrical cavity","volume":"33","author":"Fesenko","year":"2021","journal-title":"Procedia Struct. Integr."},{"key":"ref_11","first-page":"234","article-title":"Analysis of Laminated Composites Subjected to Impact","volume":"Volume 188","author":"Ugrimov","year":"2021","journal-title":"Proceedings of the ICTM 2020: Integrated Computer Technologies in Mechanical Engineering-2020"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1007\/s11223-019-00033-4","article-title":"Stress-Strain Assessment for Laminated Aircraft Cockpit Windows at Static and Dynamic Load","volume":"50","author":"Rodichev","year":"2018","journal-title":"Strength Mater."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"116403","DOI":"10.1016\/j.compstruct.2022.116403","article-title":"Minimization of thermal stress in perforated composite plate using metaheuristic algorithms WOA, SCA and GA","volume":"304","author":"Jafari","year":"2022","journal-title":"Compos. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s00707-022-03413-1","article-title":"A general analytical solution of stresses around circular holes in functionally graded plates under various in-plane loading conditions","volume":"234","author":"Khechai","year":"2023","journal-title":"Acta Mech."},{"key":"ref_15","unstructured":"Nikolayev, A.G., and Protsenko, V.S. (2011). Obobshchennyy metod Fur\u02b9ye v Prostranstvennykh Zadachakh Teorii Uprugosti, Nats. Aerokosm. Universitet im. N.Ye. Zhukovskogo \u201cKHAI\u201d."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1134\/S1995423915020068","article-title":"The first boundary-value problem of the elasticity theory for a cylinder with N cylindrical cavities","volume":"8","author":"Nikolaev","year":"2015","journal-title":"Numer. Anal. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1134\/S0021894416060237","article-title":"Stresses in an elastic cylinder with cylindrical cavities forming a hexagonal structure","volume":"57","author":"Nikolaev","year":"2016","journal-title":"J. Appl. Mech. Tech. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s11029-016-9571-6","article-title":"Model of the Stress State of a Unidirectional Composite with Cylindrical Fibers Forming a Tetragonal Structure","volume":"52","author":"Nikolaev","year":"2016","journal-title":"Mech. Compos. Mater."},{"key":"ref_19","first-page":"48","article-title":"Solving a one mixed problem in elasticity theory for half-space with a cylindrical cavity by the generalized fourier method","volume":"2","author":"Ukrayinets","year":"2021","journal-title":"East.-Eur. J. Enterp. Technol."},{"key":"ref_20","first-page":"43","article-title":"Investigating a problem from the theory of elasticity for a half-space with cylindrical cavities for which boundary conditions of contact type are assigned","volume":"4","author":"Protsenko","year":"2018","journal-title":"East.-Eur. J. Enterp. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Miroshnikov, V., Younis, B., Savin, O., and Sobol, V. (2022). A Linear elasticity theory to analyze the stress state of an infinite layer with a cylindrical cavity under periodic loading. Computation, 10.","DOI":"10.3390\/computation10090160"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Miroshnikov, V., Savin, O., Sobol, V., and Nikichanov, V. (2023). Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports. Computation, 11.","DOI":"10.3390\/computation11090172"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"413","DOI":"10.4028\/www.scientific.net\/MSF.968.413","article-title":"Determination of the Stress State of the Layer with a Cylindrical Elastic Inclusion. 6th International Conference \u201cActual Problems of Engineering Mechanics\u201d (APEM 2019)","volume":"968","author":"Miroshnikov","year":"2019","journal-title":"Mater. Sci. Forum"},{"key":"ref_24","first-page":"23","article-title":"Solution of the Problem of the Theory of Elasticity and Analysis of the Stress State of a Fibrous Composite Layer Under the Action of Transverse Compressive Forces","volume":"4","author":"Miroshnikov","year":"2022","journal-title":"East.-Eur. J. Enterp. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Vitaly, M. (2023). Rotation of the Layer with the Cylindrical Pipe around the Rigid Cylinder. Advances in Mechanical and Power Engineering, Springer. CAMPE 2021; Lecture Notes in Mechanical Engineering.","DOI":"10.1007\/978-3-031-18487-1_32"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1109\/TSP.2022.3152607","article-title":"General Parameterized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and Z Transforms","volume":"70","author":"Singh","year":"2022","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/9\/182\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:49:58Z","timestamp":1760111398000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/9\/182"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,6]]},"references-count":26,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["computation12090182"],"URL":"https:\/\/doi.org\/10.3390\/computation12090182","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,6]]}}}