Plane stress state of a strip weakened by a crack

Authors

  • V. V. Reut Odesa I. I. Mechnikov National University, 65082, Odesa, Dvoryan’ska str., 2
  • Yu. V. Molokanov Odesa I. I. Mechnikov National University, 65082, Odesa, Dvoryan’ska str., 2

DOI:

https://doi.org/10.17721/1812-5409.2019/1.42

Abstract

The plane stress elastic infinite strip problem of a finite longitudinal crack is investigated. The method that can be applied to calculate the stress state and the displacements for an infinite and semi-infinite strip with the longitudinal crack and arbitrary configuration of the boundary conditions is proposed. The main advantage of this method lies in the absence of necessity for use of the apparatus of the matrix differential calculus. Initial problem is reduced to the one-dimensional boundary value problem with the help of the generalized scheme of the integral transform method. By using the inverse integral Fourier transform, the one-dimensional problem is reduced to solving of the system of singular integral equations on a finite interval. The solution of this system was constructed with the help of the method of orthogonal polynomials by means of the second kind Chebyshev polynomials series expansion of the unknown functions. A graph of dependence of the stress intensity factor (SIF) on the geometric parameters of the problem is plotted. It is shown that the SIF for the case of the said strip tends to the SIF for the case of an infinite plane as the width of the strip approaches infinity.

Key words: plane elastic problem, infinite strip, longitudinal crack, stress state, stress intensity factor.

Pages of the article in the issue: 182-185

Language of the article: Ukrainian

References

SAVRUK, M. P., OSIV, P. N. and PROKOPCHUK, I. V. (1989) Chislennyy analiz v ploskih zadachah teorii treschin. Kiev: Naukova dumka.

SLEPYAN, L. I. (1990) Mehanika treschin. Leningrad: Sudostroenie.

SAVRUK, M. P. (1981) Dvumernye zadachi uprugosti dlya tel s treschinami. Kiev: Naukova dumka.

MYKHAS'KIV, V., STANKEVYCH, V., ZHBADYNSKYI, I. and ZHANG, C. (2009) 3-D dynamic interaction between a pennyshaped crack and a thin interlayer joining two elastic half-spaces. International Journal of Fracture. 159 (2). p.137-149.

No 1 (2019)

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How to Cite

Reut, V. V., & Molokanov, Y. V. (2019). Plane stress state of a strip weakened by a crack. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 182–185. https://doi.org/10.17721/1812-5409.2019/1.42

Issue

No. 1 (2019)

Section

Differential equations, mathematical physics and mechanics

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