The stretch of elastic plane with the lattice of straight cuts
DOI:
https://doi.org/10.21638/11701/spbu01.2016.211Abstract
The closed-form solutions of the elasticity theory for the plane with a set of straight cuts are obtained. Two basic cases are studied. The first one is as follows: both borders of cuts are free whereas the plane is stretched out by external stresses applied at the infinity. In the second case both borders of cuts are loaded by concentrated normal forces while no stress is applied at the infinity. Refs 9. Figs 8.Downloads
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References
Литература
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4. Поляхов Н.Н. (мл.), Поляхов Н. Н. Растяжение плоскости с решеткой разрезов без выноса // Вестник ЛГУ. 1981. Вып. 2, № 7. С. 85-90.
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7. Мусхелишвили Н.И. Некоторые основные задачи математической теории упругости. М.: Наука, 1966. 707 с.
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9. Новожилов В.В. Теория упругости. Л.: Судпромгиз, 1958. 370 с.
References
1. Nisitani H., Murakami Y., “Interaction of elasto-plastic cracks subjected to a uniform tensile stress in an infinite or a semi-infinite plate”, Mechanical behavior of materials. Proceedings of the International Conference of Mechanical behavior of materials 1, 346–356 (1972).
2. Reference book of stress intensity coefficients 1 (Ed. Yu.Murokami, Mir, Moscow, 1990, 448 p.) [in Russian].
3. Dahl Yu.M., “About local bend of stretched plate with a crack”, Izvestiya AN SSSR. MTT (4), 135–141 (1978) [in Russian].
4. Polyahov N.N. (ml.), Polyahov N.N., “Tension of plane with the set of cuts without shear”, Vestnik Leningrad. Univ. Issue 2, N7, 85–90 (1981) [in Russian].
5. Kolosov G.V., Application of complex variable to theory of elasticity (Leningrad, Moscow, 1935, 215 p.) [in Russian].
6. Dahl Yu.M., “About Kolosov’s formulas in a plane problem of theory of elasticity in the presence of periodical cuts”, Vestnik St. Petersburg Univ. Ser. 1 1(59), Issue 2, 228–236 (2014) [in Russian].
7. Muschelishwili N. I., Some basic problems of the mathematical theory of elasticity (Nauka, Moscow, 1966, 707 p.) [in Russian].
8. Lavrentiev M.A., Shabat B.V., Methods of theory of the functions complex variable (Nauka, Moscow, 1973, 736 p.) [in Russian].
9. Novozilov V.V., Theory of elasticity (Sudpromgiz, Leningrad, 1958, 370 p.) [in Russian].
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Published
2020-10-19
How to Cite
Dahl, Y. M. (2020). The stretch of elastic plane with the lattice of straight cuts. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 3(2), 1. https://doi.org/10.21638/11701/spbu01.2016.211
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Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
