Mathematical Problems in Engineering
Volume 2005 (2005), Issue 2, Pages 245-268
doi:10.1155/MPE.2005.245
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 D. I. Bardzokas et al. 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.
Abstract
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.