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Stretch of an elastic plane with a lattice of straight cuts

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Abstract

Exact analytical solutions have been obtained for problems in the elasticity theory for a plane with a vertical lattice of straight cuts. Two main problems have been considered. In the first problem, the cut edges are free of external forces and the plane at infinity is stretched by constant external stresses and, in the second problem, the cut edges are loaded by concentrated normal forces and there are no stresses at infinity.

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References

  1. H. Nisitani and Y. Murakami, “Interaction of elasto-plastic cracks subjected to a uniform tensile stress in an infinite or a semi-infinite plate,” in Proc. Int. Conf. on Mechanical Behavior of Materials, Kyoto, Japan, Aug. 15–20, 1971 (Society of Materials Science, Japan, Kyoto, 1972), Vol. 1, pp. 346–356.

    Google Scholar 

  2. Stress Intensity Factors Handbook, Ed. by Y. Murakami (Pergamon, Oxford, 1986; Mir, Moscow, 1990), Vol.1.

  3. Yu. M. Dal’, “On the local flexure of a stretched plate with a crack,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 135–141 (1978).

    Google Scholar 

  4. N. N. Polyakhov, Jr. and N. N. Polyakhov, “Tension of a plane with a lattice of cuts without shear,” Vestn. Leningr. Univ., Ser. 1: Mat., Mekh., Astron. 2 (7), 85–90 (1981).

    MATH  Google Scholar 

  5. G. V. Kolosov, Application of the Complex Variable to the Theory of Elasticity (ONTI, Leningrad, 1935) [in Russian].

    Google Scholar 

  6. Yu. M. Dal’, “About Kolosov’s formulas in plane problem of the theory of elasticity in the presence of periodical cuts,” Vestn. S.-Peterb. Univ., Ser. 1: Mat., Mekh., Astron. 59 (2), 228–236 (2014).

    Google Scholar 

  7. N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity (Nauka, Moscow, 1966; Springer-Verlag, Dordrecht, 1977).

    MATH  Google Scholar 

  8. M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable, 4th ed. (Nauka, Moscow, 1973) [in Russian].

    MATH  Google Scholar 

  9. V. V. Novozhilov, Theory of Elasticity (Sudpromgiz, Leningrad, 1958; Pergamon, Oxford, 1961).

    MATH  Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russia

    Yu. M. Dahl

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  1. Yu. M. Dahl
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Original Russian Text © Yu.M. Dahl, 2016, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2016, No. 2, pp. 276–285.

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Dahl, Y.M. Stretch of an elastic plane with a lattice of straight cuts. Vestnik St.Petersb. Univ.Math. 49, 174–182 (2016). https://doi.org/10.3103/S1063454116020059

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  • DOI: https://doi.org/10.3103/S1063454116020059

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