On the contact problem in the band
UDC
539.3DOI:
https://doi.org/10.31429/vestnik-21-4-23-28Abstract
Based on previously performed and published mechanical and mathematical studies in the theory of two-dimensional integral equations, a zone of increased seismic hazard of the territory near an extended mountain range is identified in the work. It is known that the environment of the mountainous territory has a complex anisotropic structure. The mechanical state of an extended rock medium in the form of a strip is described by the contact problem of the action of a stamp on an anisotropic base, such as lithospheric plates. Mathematically, such contact problems are reduced to solving the two-dimensional Wiener-Hopf integral equation in a region in the form of a strip of finite width. Previously, such contact problems were studied only for isotropic bases. A method has been developed that allows us to investigate the solution of the contact problem in the anisotropic case for bands of different widths and identify zones of increased seismicity.
Keywords:
contact problem, anisotropic mountain environment, integral equation, seismic hazard zoneFunding information
The work was carried out with the financial support of the Southern Scientific Center of the Russian Academy of Sciences (state registration number of the project 122020100341-0).
References
- Лехницкий, С.Г., Теория упругости анизотропного тела. Москва, Наука, 1977. [Lekhnitsky, S.G., Teoriya uprugosti anizotropnogo tela = Theory of elasticity of an anisotropic body. Moscow, Nauka, 1977. (in Russian)]
- Кристенсен, Р., Введение в механику композитов. Москва, Мир, 1982. [Christensen, R., Vvedenie v mekhaniku kompozitov = Introduction to Mechanics of Composites. Moscow, Mir, 1982. (in Russian)]
- Kushch, V.I., Micromechanics of composites: multipole expansion approach. Oxford, Waltham, Elsevier Butterworth-Heinemann, 2013.
- McLaughlin, R., A study of the differential scheme for composite materials. International Journal of Engineering Science, 1977, vol. 15, pp. 237–244. DOI: 10.1016/0020-7225(77)90058-1
- Garces, G. Bruno G., Wanner A., Load transfer in short fibre reinforced metal matrix composites. Acta Materialia, 2007, vol. 55, pp. 5389–5400. DOI: 10.1016/j.actamat.2007.06.003
- Levandovskiy, A.N., Melnikov, B., Finite element modeling of porous material structure represented by a uniform cubic mesh. Applied Mechanics and Materials, 2015, vol. 725, pp. 928–936. DOI: 10.4028/www.scientific.net/AMM.725-726.928
- Калинчук, В.В., Белянкова, Т.И., Динамические контактные задачи для предварительно напряженных тел. Москва, Физматлит, 2002. [Kalinchuk, V.V., Belyankova, T.I., Dinamicheskie kontaktnye zadachi dlya predvaritel'no napryazhennykh tel = Dynamic contact problems for prestressed bodies. Moscow, Fizmatlit, 2002. (in Russian)]
- Бребия, К., Теллес, Ж., Вроубел, Л., Методы граничных элементов. Москва, Мир, 1987. [Brebia, K., Telles, J., Wroubel, L., Metody granichnykh elementov = Boundary Element Methods. Moscow, Mir, 1987. (in Russian)]
- Горячева, И.Г., Механика фрикционного взаимодействия. Москва, Наука, 2001. [Goryacheva, I.G., Mekhanika friktsionnogo vzaimodeystviya = Mechanics of frictional interaction. Moscow, Nauka, 2001. (in Russian)]
- Kolesnikov, V.I., Suvorova, T.V., Belyak, О.А., Modeling antifriction properties of composite based on dynamic contact problem for a heterogeneous foundation. Materials Physics and Mechanics, 2020, no. 3, pp. 17–27. DOI: 10.18720/MPM.461202014
- Айзикович, С.М., Александров, В.М., Белоконь, А.В., Кренев, Л.И., Трубчик, И.С., Контактные задачи теории упругости для неоднородных сред. Москва, Физматлит, 2006. [Aizikovich, S.M., Aleksandrov, V.M., Belokon, A.V., Krenev, L.I., Trubchik, I.S., Kontaktnye zadachi teorii uprugosti dlya neodnorodnykh sred = Contact Problems of Elasticity Theory for Inhomogeneous Media. Moscow, Fizmatlit, 2006. (in Russian)]
- Ватульян, А.О., Контактные задачи со сцеплением для анизотропного слоя. ПММ, 1977, т. 40, вып. 4, с. 727–734. [Vatulyan, A.O., Contact problems with adhesion for an anisotropic layer. Prikladnaya matematika i mekhanika = Applied Mathematics and Mechanics, 1977, vol. 40, iss. 4, pp. 727–734. (in Russian)]
- Баженов, В.Г., Игумнов, Л.А., Методы граничных интегральных уравнений и граничных элементов. Москва, Физматлит, 2008. [Bazhenov, V.G., Igumnov, L.A., Metody granichnykh integral'nykh uravneniy i granichnykh elementov = Methods of Boundary Integral Equations and Boundary Elements. Moscow, Fizmatlit, 2008. (in Russian)]
- Гуз, А.Н., Томашевский, А.Т., Шульга, Н.А., Яковлев, В.С., Технологические напряжения и деформации в композитных материалах. Киев, Вища школа, 1988. [Guz, A.N., Tomashevsky, A.T., Shulga, N.A., Yakovlev, V.S., Tekhnologicheskie napryazheniya i deformatsii v kompozitnykh materialakh = Technological Stresses and Deformations in Composite Materials. Kyiv, Vishcha school, 1988. (in Russian)]
- Акбаров, А.Н., Гузь, А.Н., Мовсумов, Э.А., Мустафаев, С.М., Механика материалов с искривленными структурами. Киев, Наукова Думка, 1995. [Akbarov, A.N., Guz, A.N., Movsumov, E.A., Mustafaev, S.M., Mekhanika materialov s iskrivlennymi strukturami = Mechanics of Materials with Curved Structures. Kyiv, Naukova Dumka, 1995. (in Russian)]
- Бабешко, В.А., Евдокимова, О.В., Бабешко, О.М., Евдокимов, В.С., К теории контактных задач для композитных сред с анизотропной структурой. ДАН, 2024, т. 518, № 5. [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., Evdokimov, V.S., On the theory of contact problems for composite media with anisotropic structure. Doklady akademii nauk = Reports of the Academy of Sciences of the Russian Federation, 2024, v. 518, no. 5. (in Russian)]
- Ворович, И.И., Александров, В.М., Бабешко, В.А., Неклассические смешанные задачи теории упругости. Москва, Наука, 1974. [Vorovich, I.I., Aleksandrov, V.M., Babeshko, V.A., Neklassicheskie smeshannye zadachi teorii uprugosti = Nonclassical Mixed Problems of Elasticity Theory. Moscow, Nauka, 1974. (in Russian)]
- Ворович, И.И., Бабешко, В.А., Динамические смешанные задачи теории упругости для неклассических областей. Москва, Наука, 1979. [Vorovich, I.I., Babeshko, V.A., Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastey = Dynamic mixed problems of elasticity theory for non-classical regions. Moscow, Nauka, 1979. (in Russian)]
- Канторович, Л.В., Акилов, Г.П., Функциональный анализ. Москва, Наука, 1977. [Kantorovich, L.V., Akilov, G.P., Funktsional'nyy analiz = Functional Analysis. Moscow, Nauka, 1977. (in Russian)]
Downloads
Downloads
Dates
Submitted
November 1, 2024
Accepted
December 2, 2024
Published
December 20, 2024
How to Cite
[1]
Evdokimova, O.V., Khripkov, D.A., Lozovoy, V.V., Pluzhnik, A.V., Gorshkova, E.M., Uafa, G.N., On the contact problem in the band. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2024, т. 21, № 4, pp. 23–28. DOI: 10.31429/vestnik-21-4-23-28
License
Copyright (c) 2024 Евдокимова О.В., Хрипков Д.А., Лозовой В.В., Плужник А.В., Горшкова Е.М., Уафа Г.Н.
This work is licensed under a Creative Commons Attribution 4.0 International License.
