Pure bending of strip (beam) with the arbitrarily oriented cross-cutting crack

Authors

  • V. K. Opanasovych Ivan Franko National University of L’viv, 79000, L’viv, Universytetska str., 1
  • M. S. Slobodyan Ivan Franko National University of L’viv, 79000, L’viv, Universytetska str., 1
  • O. V. Bilash Hetman Petro Sahaidachnyi National Army Academy, 79012, L’viv, Heroes of Maidan street, 32

DOI:

https://doi.org/10.17721/1812-5409.2019/1.32

Abstract

The problem of pure bending of strip (beam) with transverse rectilinear crack, edges of which are free from acuter load, is investigated in this paper. Under bending moment its edges may not contact or smoothly contact throughout its area length or part. Dependently on where it is located.Using methods of theory of functions of complex variable and complex potentials the problem at issue has been reduced to the problems of linear conjugation, their analytical solution is found. Explicit expressions on complex potentials is written. Based on the energy criterion of destruction stress intensity factors are determined. Limit value of moment when the crack begins to propagate is found. For the case when crack edges partially contact, area length of contact of her edges is determined. Numerical analysis of critical moment of failure of strip (beams) is performed under various parameters of the problem, which are related to the mechanical state of crack. The corresponding graphic dependencies are constructed.

Key words: crack, strip (beam), complex potentials, bending moment, stress intensity factors.

Pages of the article in the issue: 142-145

Language of the article: Ukrainian

References

PANASYUK, V. (2001) Vybrani pratsi (1954-1970). Lviv: Material science.

MUSKHELISHVILI, N. (1966) Nekotoryie osnovnyie zadachi matematicheskoi teorii upruhosti. M.: Nauka.

SAVRUK, M. (1988) Mehanika razrysheniya i prochnosti materialov : spravochnoe posobie : v 4 t. / obshch. red. V.V. Panasyuk. T. 2. Koyeffitsiyenty intensyvnosti napryageniy v telax s treshchinami. Kiev: Naukova dumka.

ZEHNDER, A. and M. VIZ (2005 ) Fracture mechanics of thin plates shells under combined membrane, bending and twisting loads. Applied Mechanics Reviews. 58. – p. 37 – 48.

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How to Cite

Opanasovych, V. K., Slobodyan, M. S., & Bilash, O. V. (2019). Pure bending of strip (beam) with the arbitrarily oriented cross-cutting crack. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (1), 142–145. https://doi.org/10.17721/1812-5409.2019/1.32

Issue

Section

Differential equations, mathematical physics and mechanics