Abstract:
An efficient method for the analytical-numerical solution to the non-axyally symmetric boundary value problem of elasticity theory for a multiconnected body in the form of a cylinder with N cylindrical cavities is proposed. The solution is constructed as superposition of the exact basis solutions of the Lame equation for a cylinder in the coordinate systems assigned to the centers of the boundary surfaces of the body. The boundary conditions are exactly satisfied with the help of the apparatus of the generalized Fourier method. As a result, the original problem reduces to an infinite system of linear algebraic equations, which has a Fredholm operator in the Hilbert space l2. The resolving system is numerically solved by the reduction. The rate of convergence of the reduction is investigated. The numerical analysis of stresses in the areas of their greatest concentration is carried out. The reliability of the results obtained is confirmed by comparing them for the two cases: a cylinder with sixteen and a cylinder with four cylindrical cavities.
Citation:
A. G. Nikolaev, E. A. Tanchik, “The first boundary value problem of elasticity theory for a cylinder with N cylindrical cavities”, Sib. Zh. Vychisl. Mat., 18:2 (2015), 177–189; Num. Anal. Appl., 8:2 (2015), 148–158
\Bibitem{NikTan15}
\by A.~G.~Nikolaev, E.~A.~Tanchik
\paper The first boundary value problem of elasticity theory for a~cylinder with $N$~cylindrical cavities
\jour Sib. Zh. Vychisl. Mat.
\yr 2015
\vol 18
\issue 2
\pages 177--189
\mathnet{http://mi.mathnet.ru/sjvm575}
\crossref{https://doi.org/10.15372/SJNM20150206}
\elib{https://elibrary.ru/item.asp?id=23463696}
\transl
\jour Num. Anal. Appl.
\yr 2015
\vol 8
\issue 2
\pages 148--158
\crossref{https://doi.org/10.1134/S1995423915020068}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84930644009}
Linking options:
https://www.mathnet.ru/eng/sjvm575
https://www.mathnet.ru/eng/sjvm/v18/i2/p177
This publication is cited in the following 10 articles:
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Vitaly Miroshnikov, Oleksandr Denshchykov, Iaroslav Grebeniuk, Oleksandr Savin, “An Analysis of the Stress–Strain State of a Layer on Two Cylindrical Bearings”, Computation, 12:9 (2024), 182
Oleksandr Yu. Denshchykov, Valentyn P. Pelykh, Yaroslav V. Hrebeniuk, Vitalii Yu. Miroshnikov, “First Basic Problem of Elasticity Theory for a Composite Layer with Two Thick-Walled Tubes”, J. of Mech. Eng., 27:4 (2024), 40
Vitalii Yu. Miroshnikov, Oleksandr B. Savin, Mykhailo M. Hrebennikov, Vladyslav F. Demenko, “Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports”, J. of Mech. Eng., 26:1 (2023), 15
Vitaly Miroshnikov, Oleksandr Savin, Vladimir Sobol, Vyacheslav Nikichanov, “Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports”, Computation, 11:9 (2023), 172
Miroshnikov Vitaly, Lecture Notes in Mechanical Engineering, Advances in Mechanical and Power Engineering, 2023, 314
Vitalii Yu. Miroshnikov, Oleksandr B. Savin, Mykhailo M. Hrebennikov, Oleksandr A. Pohrebniak, “Analysis of the Stress State of a Layer with Two Cylindrical Elastic Inclusions and Mixed Boundary Conditions”, J. of Mech. Eng., 25:1 (2022), 22
Vitaly Miroshnikov, Basheer Younis, Oleksandr Savin, Vladimir Sobol, “A Linear Elasticity Theory to Analyze the Stress State of an Infinite Layer with a Cylindrical Cavity under Periodic Load”, Computation, 10:9 (2022), 160
Miroshnikov V.Yu., Denysova V T., “Investigation of the Second Main Problem of Elasticity For a Layer With N Cylindrical Inclusions”, Opir Materialiv Teor. Sporud, 2021, no. 106, 156–166
A. G. Nikolaev, E. A. Tanchik, “Model of the stress state of a unidirectional composite with cylindrical fibers forming a tetragonal structure”, Mech. Compos. Mater., 52:2 (2016), 177–188
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