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Stress analysis near the tips of a transverse crack in an elastic semi-strip

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Abstract

The plane elastic problem for a semi-strip with a transverse crack is investigated. The initial problem is reduced to a one-dimensional continuous problem by use of an integral transformation method with a generalized scheme. The one-dimensional problem is first formulated as a vector boundary problem, and then reduced to a system of three singular integral equations (SIEs). The system is solved by use of an orthogonal polynomial method and a special generalized method. The contribution of this work is the consideration of kernel fixed singularities in solving the system. The crack length and its location relative to the semi-strip’s lateral sides are investigated to simplify the problem’s statement. This simplification reduces the initial problem to a system of two SIEs.

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Acknowledgements

Gratitude to S. DYKE for the editing of the article text.

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  1. Institute of Mathematics, Economics and Mechanics, Odessa I. I. Mechnikov National University, Odessa, 65082, Ukraine

    Z. Zhuravlova

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  1. Z. Zhuravlova
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Zhuravlova, Z. Stress analysis near the tips of a transverse crack in an elastic semi-strip. Appl. Math. Mech.-Engl. Ed. 38, 935–956 (2017). https://doi.org/10.1007/s10483-017-2217-6

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  • DOI: https://doi.org/10.1007/s10483-017-2217-6

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