Geodesic
The problem of a longitudinal crack with a filler in a strip
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 315-322.

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The method of the solution the problem of the central longitudinal crack with a filler in a strip is proposed. It is assumed that the jumps of the components of displacement vector is proportional to the corresponding stresses at its upper edge. Fourier's method of integral transformation is used. The problem is reduced to a system of integro-differential equations. The effects of influence of thickness, mechanical properties of a strip and a filler of the crack on Mode I and Mode II stresses intensity factors (SIFs) are examined. The following conclusions are made: increase the width of a strip and the coefficient that characterizes a filler leads to reduction of SIFs; increase of shear modulus and Poisson's ratio of a strip leads to the increase of SIF. 
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N. N. Antonenko. The problem of a longitudinal crack with a filler in a strip. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 315-322. http://geodesic.mathdoc.fr/item/ISU_2015_15_3_a9/

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