Analytical solution of the equilibrium of the transverse crack in a composite elastic plane

Authors

  • Sobol B.V. Don State Technical University, Rostov-on-Don, Российская Федерация
  • Rashidova E.V. Don State Technical University, Rostov-on-Don, Российская Федерация
  • Borisova E.V. Don State Technical University, Rostov-on-Don, Российская Федерация

UDC

539.3

Abstract

The problem of stress concentration in the vicinity of the crack tip of finite length perpendicularly located to the interface between two elastic half-planes was reviewed. The usage of integral discontinuous solutions method enabled us to reduce the problem to solving a singular integral equation of the first kind with Cauchy kernel. We reviewed the limiting case of the problem when the half-plane without the crack is absent and the boundary of the body under review is free from stress. The solution of the integral equation is constructed in the form of an asymptotic expansion with respect to the small parameter characterizing the relative distance between the crack and the interface. In order to determine the effectiveness of obtained expansions we construct the solution of the same problem by collocation method. It was executed a comparison of the results with the known ones, previously obtained by numerical methods. The values of the normal stress intensity factor in the vicinity of the crack tip for various combinations of geometrical and physical parameters of the problem were obtained.

Keywords:

crack, half-plane, stress intensity factor, influence factor

Acknowledgement

Исследование выполнено при финансовой поддержке РФФИ (14-08-00142_а).

Author Infos

Boris V. Sobol

д-р тех. наук, профессор, заведующий кафедрой информационных технологий Донского государственного технического университета

e-mail: b.sobol@mail.ru

Elena V. Rashidova

канд. физ.-мат. наук, доцент, профессор кафедры информационных технологий Донского государственного технического университета

e-mail: el.rash@mail.ru

Ekaterina V. Borisova

старший преподаватель кафедры информационных технологий Донского государственного технического университета

e-mail: brkate1@rambler.ru

References

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Issue

2014. No. 4

Pages

69-78

Submitted

2014-10-07

Published

2014-12-22

How to Cite

Sobol B.V., Rashidova E.V., Borisova E.V. Analytical solution of the equilibrium of the transverse crack in a composite elastic plane. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2014, no. 4, pp. 69-78. (In Russian)

Copyright (c) 2014 Sobol B.V., Rashidova E.V., Borisova E.V.

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