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

doi:10.1007/s10483-017-2217-6

Abstract

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.

Key words: analytical solutions, maximal helicity, chaotic lines of force, transverse crack, fixed singularity, singular integral equation (SIE), semi-strip, Green's function, integral transformation

2010 MSC Number:

Z. ZHURAVLOVA. Stress analysis near the tips of a transverse crack in an elastic semi-strip. Applied Mathematics and Mechanics (English Edition), 2017, 38(7): 935-956.

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