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EN
The present article examines the problem related to the axisymmetric torsion of an elastic layer by a circular rigid disc at the symmetry plane. The layer is sandwiched between two similar elastic half-spaces with two penny-shaped cracks symmetrically located at the interfaces between the two bonded dissimilar media. The mixed boundary-value problem is transformed, by means of the Hankel integral transformation, to dual integral equations, that are reduced, to a Fredholm integral equation of the second kind. The numerical methods are used to convert the resulting system to a system of infinite algebraic equations. Some physical quantities such as the stress intensity factor and the moment are calculated and presented numerically according to some relevant parameters. The numerical results show that the discontinuities around the crack and the inclusion cause a large increase in the stresses that decay with distance from the disc-loaded. Furthermore, the dependence of the stress intensity factor on the disc size, the distance between the crack and the disc, and the shear parameter is also observerd.
EN
The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material at the symmetry plane, under an axisymmetric torsion by two circular rigid discs symmetrically located in the elastic medium. The two discs rotate with the same angle in the different direction about the axis passing through their centers. The general solution of this problem is obtained by using the Hankel transforms method. The corresponding doubly mixed boundary value problem associated with the rigid disc and the penny-shaped is reduced to a system of dual integral equations, which are transformed, to a Fredholm integral equations of the second kind. Using the quadrature rule, the resulting system is converted to a system of infinite algebraic equations. The variation in the displacement, stress and stress intensity factor are presented for some particular cases of the problem.
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