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Mathematical Problems in Engineering
Volume 2005, Issue 2, Pages 245-268

About a stress deformation condition of a piecewise-uniform wedge with a system of collinear cracks at an antiplane deformation

1Laboratory of Strength and Materials, Department of Mechanics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, Theocaris Building, Athens 157 73, Greece
2State Engineering University of Armenia, 105 Terian Street, Yerevan 375009, Armenia
3Institute of Mechanics, National Academy of Sciences of Armenia, 24 Marshall Baghramian Avenue, Yerevan 375019, Armenia

Received 13 December 2001

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An antiplane problem of a stress deformation condition of a piecewise wedge consisting of two heterogeneous wedges with different opening angles and containing on the line of their attachment a system of arbitrary finite number of collinear cracks is investigated. With the help of Mellin's integral transformation the problem is brought to the solution of the singular integral equation relating to the density of the displacement dislocation on the cracks, which then is reduced to a system of singular integral equations with kernels being represented in the form of sums of Cauchy kernels and regular kernels. This system of equations is solved by the known numerical method. Stress intensity factors (SIF) are calculated and the behavior of characteristic geometric and physical parameters is revealed. Besides, the density of the displacement dislocation on the cracks, their evaluation, and J -integrals are calculated.