To the Study of the State of the System of Multiple Galleries under the Effect of Normal and Shear Stresses
UDC
539.3EDN
FYGEFADOI:
10.31429/vestnik-17-1-1-42-48Abstract
The method for studying the boundary value problems modeling multilayer structures with multiple interlayer bulkheads, developed in the works of scientists of the SSC RAS and KubSU, is generalized in this paper to the vector case of a general spatial problem.A complementary approach is presented, allowing analyzing the result of vertical and shearing effectson partitionsof ore formation. As a substrate and a coating layer, we consider homogeneous elastic layers that possess the same physical and mechanical properties but have different thicknesses.The boundary of the coating layer is considered free of stress. Linear static equations for the Kirchhoff plate system are used to describethe state of the ore formation. The block element method used in the work allowed us to reduce the boundary value problem for two elastic layers separated by a plate with a set of parallel linear holes to a system of integral equations of the Fredholm type solvableby the integral factorization method. The described approach can be applied to the study of different-sized block structures on other scales.
Keywords:
multilayer structure, Kirchhoff plates, normal and shear stresses, block element method, system of integral equations, integral factorization methodFunding information
Отдельные фрагменты работы выполнены в рамках ГЗ ЮНЦ РАН, проект № 01201354241 и при частичной поддержке РФФИ (проекты 18-05-80008, 18-01-00124).
References
- Насонов Л.Н. Механика горных пород и крепление горных выработок. М.: Недра, 1969. 328 с. [Nasonov, L.N. Mekhanika gornykh porod i kreplenie gornykh vyrabotok [Rock mechanics and mine fastening]. Nedra, Moscow, 1969. (In Russian)]
- Баренблатт Г.И., Христианович С.А. Об обрушении кровли при горных выработках // Известия АН СССР. Отделение технических наук. 1955. № 11. С. 73–82. [Barenblatt, G.I., Khristianovich, S.A. Ob obrushenii krovli pri gornykh vyrabotkakh [On the collapse of the roof during mining]. Izvestiya AN SSSR. Otdelenie tekhnicheskikh nauk [Proceedings of the USSR Academy of Sciences. Department of Technical Sciences], 1955, no. 11, pp. 73–82. (In Russian)]
- Булычев Н.С. Механика подземных сооружений. М.: Недра, 1982. 337 с. [Bulychev, N.S. Mekhanika podzemnykh sooruzheniy [The mechanics of underground structures]. Nedra, Moscow, 1982. (In Russian)]
- Половов Б.Д. Геомеханический анализ протяженных горных выработок. Екатеринбург: УГГУ, 2005. 169 с. [Polovov, B.D. Geomekhanicheskiy analiz protyazhennykh gornykh vyrabotok [Geomechanical analysis of long mine workings]. UGGU, Ekaterinburg, 2005. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. К теории влияния глобального фактора на прочность совокупности параллельных соединений // Вычислительная механика сплошных сред. 2016. Т. 9, № 4. С. 412–419. [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M. K teorii vliyaniya global'nogo faktora na prochnost' sovokupnosti parallel'nykh soedineniy [On the theory of the influence of the global factor on the strength of a set of parallel compounds]. Vychislitel'naya mekhanika sploshnykh sred [Computational mechanics of continuous media], 2016, vol. 9, no. 4, pp. 412–419. (In Russian)]
- Babeshko V.A., Evdokimova O.V., Babeshko O.M., Pavlova A.B., Telatnikov I.S., Fedorenko A.G. The theory of block structures in problems on the strength of galleries and constructions with multiple connections // Doklady Physics. 2019. Vol. 64. No. 1. С. 4–8.
- Бабешко В.А., Бабешко О.М., Евдокимова О.В. К проблеме мониторинга напряженности зон параллельных штолен // МТТ. 2016. № 5. С. 6–14. [Babeshko, V.A., Babeshko, O.M., Evdokimova, O.V. K probleme monitoringa napryazhennosti zon parallel'nykh shtolen [On the problem of monitoring the tension of zones of parallel tunnels]. Mekhanika tverdogo tela [Solid Mechanics], 2016, no. 5, pp. 6–14. (In Russian)]
- Телятников И.С. Об одном обобщенном подходе в проблеме оценки прочности подземных сооружений, параллельных штолен // Экологический вестник научных центров Черноморского экономического сотрудничества. 2019. № 4. С. 6–12. [Telyatnikov, I.S. Ob odnom obobshchennom podkhode v probleme otsenki prochnosti podzemnykh sooruzheniy, parallel'nykh shtolen [About one generalized approach to the problem of assessing the strength of underground structures parallel to adits]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of Scientific Centers of the Black Sea Economic Cooperation], 2019, no. 4, pp. 6–12. (In Russian)]
- Вольмир А.С. Гибкие пластинки и оболочки. М.: Государственное издательство технико-теоретической литературы, 1956. 422 с. [Vol'mir, A.S. Gibkie plastinki i obolochki [Flexible plates and shells]. Gosudarstvennoe izdatel'stvo tekhniko-teoreticheskoy literatury, Moscow, 1956. (In Russian)]
- Гольденвейзер А.Л. Теория упругих тонких оболочек. М.: Наука, 1976. 512 с. [Gol'denveyzer, A.L. Teoriya uprugikh tonkikh obolochek [Theory of elastic thin shells]. Nauka, Moscow, 1976. (In Russian)]
- Ворович И.И., Бабешко В.А. Динамические смешанные задачи теории упругости для неклассических областей. М.: Наука, 1979. 319 с. [Vorovich, I.I., Babeshko, V.A. Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastey [Dynamic mixed problems of elasticity theory for non-classical domains]. Nauka, Moscow, 1979. (In Russian)]
- Бабешко В.А. Обобщенный метод факторизации в пространственных динамических смешанных задачах теории упругости. М.: Наука, 1984. 265 с. [Babeshko, V.A. Obobshchennyy metod faktorizatsii v prostranstvennykh dinamicheskikh smeshannykh zadachakh teorii uprugosti Generalized factorization method in spatial dynamic mixed problems of elasticity theory. Nauka, Moscow, 1984. (In Russian)]
- Бабешко В.А., Бабешко О.М. Формулы факторизации некоторых мероморфных матриц-функций // ДАН. 2004. Т. 399, № 1. С. 163–167. [Babeshko, V.A., Babeshko, O.M. Formuly faktorizatsii nekotorykh meromorfnykh matrits-funktsiy [Factorization formulas for some meromorphic matrix functions]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2004, vol. 399, no 1, pp. 163–167. (In Russian)]
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Dates
Submitted
March 18, 2020
Accepted
March 24, 2020
Published
March 31, 2020
How to Cite
[1]
Telyatnikov, I.S., To the Study of the State of the System of Multiple Galleries under the Effect of Normal and Shear Stresses. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, т. 17, № 1, pp. 42–48. DOI: 10.31429/vestnik-17-1-1-42-48
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Copyright (c) 2020 Телятников И.С.
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