Determination of the contact stresses in the materials and underground constructions with parallel and crosses inclusions
UDC
539.3Abstract
It is very important to estimate the contact stresses in the elastic materials with parallel and cross inclusions because it has applications in building, engineering, electronics, mine engineering. Traditionally the studies are carried out for an individual fixture, and then found parameters are accepted for all other facilities. At the same time a plurality of such facilities may lead to the occurrence of another factor badly affecting the strength. This factor is connected with the capability to localize the state of strain in one of the structure's zones, which results an exceeding of the planned strength parameters. The calculating theory of strength properties of these objects in the present scientific work is based on the example of the underground structures. The investigation use the block element method, which is based on the factorization approaches. The problem comes to the Fredholm's system of the integral equations of the second kind. It is succeeded to turn integral equation to the system of the algebraic equations, which are accessible to the analytical analysis, allowing finding out the strain and shift by means of the calculation of the integrals, describing the kernels of these equations by the theory of residue. The algorithm of realizing this investigation is presented. The possibility of the factorization methods for the such problems are discussed.
Keywords:
stress-strain state, drifts, factorization, deformable layers, interface layer, Kirchhoff plates, block elements, differential and integral equationsFunding information
Отдельные фрагменты работы выполнены в рамках реализации Госзадания на 2016 г. проект (0256-2014-0006), Программы президиума РАН 1-33П, проекты с (0256-2015-0088) по (0256-2015-0093) и при поддержке грантов РФФИ (14-08-00404, 15-01-01379, 15-08-01377, 16-41-230214, 16-41-230218, 16-48-230216).
References
- Бабешко В.А., Бабешко О.М., Евдокимова О.В, Федоренко А.Г., Шестопалов В.Л. К проблеме покрытий с трещинами в наноматериалах и сейсмологии // МТТ. 2013. № 5. С. 39-45. [Babeshko V.A., Babeshko O.M., Evdokimova O.V, Fedorenko A.G., Shestopalov V.L. K probleme pokrytiy s treshchinami v nanomaterialakh i seysmologii [On the problem of cracks in coatings with nanomaterials and seismology]. Mekhanika tverdogo tela [Mechanics of Solids], 2013, no. 5, pp. 39-45. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. К проблеме физико-механического предвестника стартового землетрясения: место, время, интенсивность // ДАН. 2016. Т. 466. № 6. С. 664-669. [Babeshko V.A., Evdokimova O.V., Babeshko O.M. K probleme fiziko-mekhanicheskogo predvestnika startovogo zemletryaseniya: mesto, vremya, intensivnost' [On the problem of physical and mechanical precursor starting earthquake: place, time, intensity]. Doklady Akademii nauk [Rep. Academy of Sciences], 2016, vol. 466, no. 6, pp. 664-669. (In Russian)]
- Ворович И.И., Бабешко В.А. Динамические смешанные задачи теории упругости для неклассических областей. М.: Наука, 1979. 320 с. [Vorovich I.I., Babeshko V.A. Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastey [Dynamic mixed problem in elasticity theory for nonclassical fields]. Moscow, Nauka Publ., 1979, 320 p. (In Russian)]
- Ворович И.И., Александров В.М., Бабешко В.А. Неклассические смешанные задачи теории упругости. М.: Наука, 1974. 456 с. [Vorovich I.I., Aleksandrov V.M., Babeshko V.A. Neklassicheskie smeshannye zadachi teorii uprugosti [Non-classical mixed problem in elasticity theory]. Moscow, Nauka Publ., 1974, 456 p. (In Russian)]
- Бабешко В.А. Обобщенный метод факторизации в пространственных динамических смешанных задачах теории упругости. М.: Наука, 1984. 256 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]. Moscow, Nauka Publ., 1984, 256 p. (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 roof collapse at the mine workings]. Izvestiya AN SSSR. Otdelenie tekhnicheskikh nauk [Proc. of the USSR Academy of Sciences. Department of Technical Sciences], 1955, no. 11, pp. 73-82. (In Russian)]
- Евдокимова О.В. О способах формирования блочных структур с неоднородностями // Экологический вестник научных центров Черноморского экономического сотрудничества. 2016, № 1. С. 42-48. [Evdokimova O.V. O sposobah formirovania blochnih struktur s neodnorodnostami [About formation methods of block structures with inhomogeneity]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo Ekonomocheskogo sotrudnichestva [Ecologikal Bulletin of Research Centers of the Black Sea Economic Cooperation], 2016, vol. 447, no. 1, pp. 42-48. (In Russian)]
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Copyright (c) 2016 Евдокимова О.В., Бабешко О.М., Бабешко В.А.
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