Elastic crack-tip stress field in a semi-strip

In this article the plain elasticity problem for a semi-strip with a transverse crack is investigated in different cases of boundary conditions at the semi-strip’s end. Unlike many works dedicated to this subject, the fixed singularities in the singular integral equation’s kernel are considered. The integral transformations’ method is applied by a generalized scheme to reduce the initial problem to a one-dimensional problem. The one-dimensional problem is formulated as a vector boundary value problem which is solved with the help of matrix differential calculations and Green’s matrix apparatus. The problem is reduced to solve the system of three singular integral equations. Depending on the conditions given on the short edge of the semistrip, the obtained singular integral equation can have one or two fixed singularities. A special method is applied to solve this equation in regard to the singularities existence. Hence, the system of the singular integral equations (SSIE) is solved with the help of the generalized method. The stress intensity factors (SIF) are investigated for different lengths of crack. The novelty of this work is the application of a new approach allowing the consideration of fixed singularities in the problem of a transverse crack in the elastic semi-strip. The comparison of the accuracy of numerical results during the use of different approaches to solve the SSIE is calculated.

Ключові слова

Semi-strip, Transverse crack, Green’s function, Integral Transformation, Fixed singularity

Бібліографічний опис

Frattura ed Integrità Strutturale

URI

https://dspace.onu.edu.ua/handle/123456789/17954

Зібрання

Статті та доповіді ФМФІТ

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