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Axisymmetric Torsion of an Elastic Layer Sandwiched between Two Elastic Half-Spaces with Two Interfaced Cracks

Madani Fateh, Kebli Belkacem

Studia Geotechnica et Mechanica

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2019

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Vol. 41, nr 2

57--66

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.

2

An axisymmetric contact problem of an elastic layer on a rigid circular base

Kebli B., Berkane S., Guerrache F.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 1

221--237

EN

An analytical solution is presented to a doubly mixed boundary value problem of an elastic layer partially resting on a rigid smooth base. A circular rigid punch is applied to the upper surface of the medium where the contact is supposed to be smooth. The case of the layer with a cylindrical hole was considered by Toshiaki and all [5]. The studied problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer formula we get an infinite algebraic system of simultaneous equations for calculating the unknown function of the problem. The truncation method is used for getting the system coefficients. A closed form solution is given for the displacements, stresses and the stress singularity factors. The stresses and displacements are then obtained as Bessel function series. For the numerical application we give some conclusions on the effects of the radius of the punch with the rigid base and the layer thickness on the displacements, stresses, the load and the stress singularity factors are discussed.

3

Axisymmetric torsion of an internally cracked elastic medium by two embedded rigid discs

Madani F., Kebli B.

Mechanics and Mechanical Engineering

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2017

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Vol. 21, nr 2

363--377

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.