DOI https://doi.org/10.15407/pmach2017.04.031
Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 20, no. 4, 2017 (December)
Pages 31-37
Cited by J. of Mech. Eng., 2017, vol. 20, no. 4, pp. 31-37



N. M. Kalantarly, Institute of Mathematics and Mechanics of Azerbaijan National Academy of Sciences (9, F. Agaev St., Baku, AZ1141, Azerbaijan), e-mail: nailyak1975@gmail.com



The problem of finding an equally strong hole form in the crack tip and its influence on the development of a crack are considered. A criterion and method for solving the problem of preventing the brittle fracture of a body weakened by a longitudinal shear crack are proposed. The condition for brittle fracture is obtained.


Keywords: crack, longitudinal shift, optimal hole, principle of equal strength



  1. Finkel, V. M. (1977). Physical Foundations of Fracture Deceleration. Moscow: Metallurgiya (in Russian).
  2. Mirsalimov, V. M. (1971). Effect of relieving apertures on crack development. Strength of Materials, vol. 3, iss. 4, pp. 387– 389. https://doi.org/10.1007/BF01528176
  3. Mirsalimov, V. M. (1972). On a method of growing cracks inhibition. Akad. nauk Azerbajdzhanskoj SSR, serija fiz.-tehn. i mat. nauk, no. 1, pp. 34–38.
  4. Cherepanov, G. P. (1963). An Inverse Elastic-Plastic Problem under Plane Strain. Akad. nauk SSSR. Otdelenie tehn. nauk. Mehanika i mashinostroenie, no. 2, pp. 57–60.
  5. Kurshin, L. M. & Onoprienko, P. N. (1976). Determination of the shapes of doubly-connected bar sections of maximum torsional stiffness. Journal of Applied Mathematics and Mechanics, vol. 40, iss. 6, pp. 1020–1026. https://doi.org/10.1016/0021-8928(76)90144-1
  6. Cherepanov, G. P. (1974). Inverse problems of the plane theory of elasticity. Journal of Applied Mathematics and Mechanics, vol. 38, iss. 6, pp. 915–931. https://doi.org/10.1016/0021-8928(75)90085-4
  7. Mirsalimov, V. M. (1974). On the optimum shape of apertures for a perforated plate subject to bending. Journal of Applied Mechanics and Technical Physics, vol. 15, iss. 6, pp. 842–845. https://doi.org/10.1007/BF00864606
  8. Mirsalimov, V. M. (1975). Converse problem of elasticity theory for an anisotropic medium. Journal of Applied Mechanics and Technical Physics, vol. 16, iss. 4, pp. 645–648. https://doi.org/10.1007/BF00858311
  9. Banichuk, N. V. (1977). Optimality conditions in the problem of seeking the hole shapes in elastic bodies. Journal of Applied Mathematics and Mechanics, vol. 41, iss. 5, pp. 946–951. https://doi.org/10.1016/0021-8928(77)90179-4
  10. Banichuk, N. V. (1980). Shape Optimization of Elastic Solids. Moscow: Nauka (in Russian).
  11. Mirsalimov, V. M. (1977). Inverse doubly periodic problem of thermoelasticity. Mechanics of Solids, vol. 12, no. 4, pp. 147–154.
  12. Vigdergauz, S. B. (1976). Integral equations of the inverse problem of the theory of elasticity. Journal of Applied Mathematics and Mechanics, vol. 40, iss. 3, pp. 518–522. https://doi.org/10.1016/0021-8928(76)90046-0
  13. Wheeler, L. T. (1976). On the role of constant-stress surfaces in the problem of minimizing elastic stress concentration. International Journal of Solids and Structures, vol. 12, iss. 11, pp. 779–789. https://doi.org/10.1016/0020-7683(76)90042-1
  14. Vigdergauz, S. B. (1977). On a case of the inverse problem of two-dimensional theory of elasticity. Journal of Applied Mathematics and Mechanics, vol. 41, iss. 5, pp. 927–933.  https://doi.org/10.1016/0021-8928(77)90176-9
  15. Mirsalimov, V. M. (1979). A working of uniform strength in the solid rock. Soviet mining, vol. 15, no. 4, pp. 327–330. https://doi.org/10.1007/BF02499529
  16. Wheeler, L. T. (1978). On optimum profiles for the minimization of elastic stress concentration. ZAMM, vol. 58, iss. 6, pp. 235–236.
  17. Wheeler, L. T. (1992). Stress minimum forms for elastic solids. ASME. Applied Mechanics Reviews, vol. 45, iss. 1, pp. 1–12. https://doi.org/10.1115/1.3119743
  18. Сherepanov, G. P. (1995). Optimum shapes of elastic solids with infinite branches. ASME. Journal of Applied Mechanics, vol. 62, iss. 2, pp. 419–422. https://doi.org/10.1115/1.2895947
  19. Savruk, M. P. & Kravets, V. S. (2002). Application of the method of singular integral equations to the determination of the contours of equistrong holes in plates. Materials Science, vol. 38, iss. 1, pp. 34–46. https://doi.org/10.1023/A:1020116613794
  20. Mir-Salim-zada, M. V. (2007). Determination of equistrong hole shape in isotropic medium, reinforced by regular system of stringers. Materialy, tehnologii, instrumenty, vol. 12, no. 4, pp. 10–14.
  21. Сherepanov, G. P. (2015). Optimum shapes of elastic bodies: equistrong wings of aircrafts and equistrong underground tunnels. Physical Mesomechanics, vol. 18, no. 4, pp. 391–401. https://doi.org/10.1134/S1029959915040116
  22. Mirsalimov, V. M. (1984). Fracture of Elastic and Elastoplastic Solids with Cracks. Baku: Elm (in Russian).
  23. Barenblatt, G. I. & Cherepanov, G. P. (1961). On brittle cracks under longitudinal shear. Journal of Applied Mathematics and Mechanics, vol. 25, iss. 6, pp. 1654–1666. https://doi.org/10.1016/0021-8928(62)90143-0


Received 19 October 2017

Published 30 December 2017