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

• Autorzy: Kebli B. , Berkane S. , Guerrache F.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

axisymmetric elastic deformation; contact problem; doubly mixed boundary; value; Hankel integral transforms; dual integral equations; infinite algebraic system

PL

odkształcenia sprężyste; odkształcenia symetryczne; zagadnienie kontaktowe; wartość; całkowe przekształcenie Hankela; równania całkowe dualne

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 1
• Strony: 221--237
• Opis fizyczny: Bibliogr. 10 poz., 1 rys., wykr.

Twórcy

autor

Kebli B.

• Department of Mechanical Engineering, Ecole Nationale Polytechnique, Algiers, Algeria

autor

Berkane S.

• Department of Mechanical Engineering, Ecole Nationale Polytechnique, Algiers, Algeria

autor

Guerrache F.

• Department of Mechanical Engineering, Ecole Nationale Polytechnique, Algiers, Algeria

Bibliografia

• [1] Lebedev N.N., Ufliand Ia.S.: Axisymmetric contact problem for an elastic layer, PMM, 22, 3, 320-326, 1958.
• [2] Zakorko N.V.: The axisymmetric strain of an elastic layer with a circular line of separation of the boundary conditions on both faces, PMM, 38, 1, 131-138, 1974.
• [3] Dhaliwal, R. S., Singh, B. M.: Axisymmetric contact problem for an elastic layer on a rigid foundation with a cylindrical hole. Int.J.Engng Sci., 15, 1, 421-428, 1977.
• [4] Wood, D. M.: Circular load on elastic layer, International journal for numerical and analytical methods in geomechanics, 8, 503-509, 1984.
• [5] Toshiaki, H., Takao, A., Toshiakaru, S., Takashi, K.: An axisymmetric contact problem of an elastic layer on a rigid base with a cylindrical hole. JSME International Journal, 33, 4, 461-467, 1990.
• [6] Sakamoto, M.: An elastic layer with a penny-shaped crack subjected to internal pressure, JSME Int. J. Ser. A, 46, 1, 27-36, 2003.
• [7] Sakamoto, M., Kobayashi, K.: The axisymmetric contact problem of an elastic layer subjected to a tensile stress applied over a circular region, Theor. Appl. Mech. Japan., 53, 27-36, 2004.
• [8] Sakamoto, S., Kobayashi, K.: Axisymmetric indentation of an elastic layer on a rigid foundation with a circular hole, WIT Trans. Enging. Sci., 49, 279-286, 2005.
• [9] Duffy, D. G.: Mixed boundary value problems, Boca Raton, Chapman Hall/CRC., 457, 2008.
• [10] Gradshteyn, I. S., Ryzhik, I. M.: Table of integrals- series and products, Academic Press, N. Y, 1221, 2007.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).