Axisymmetric contact problem for a frictionless elastic layer indented by an elastic cylinder. (English) Zbl 0614.73116
This paper is concerned with the elastostatic contact problem of a semi- infinite cylinder compressed against a layer lying on a rigid foundation. It is assumed that all the contacting surfaces are frictionless and that only compressive normal tractions can be transmitted through the interfaces. Upon loading the contact along the layer-foundation interface shrinks to a circular area whose radius is unknown. The analysis leads to a system of singular integral equations of the second kind. The integral equations are solved numerically and the contact pressures, extent of the contact area between the layer and the foundation, and the stress intensity factor round the edge of the cylinder are calculated for various material pairs.
MSC:
| 74A55 | Theories of friction (tribology) |
| 74M15 | Contact in solid mechanics |
| 65R20 | Numerical methods for integral equations |
| 74K15 | Membranes |
| 74G70 | Stress concentrations, singularities in solid mechanics |
| 45E05 | Integral equations with kernels of Cauchy type |
Keywords:
elastostatic; semi-infinite cylinder; layer lying on a rigid foundation; frictionless; compressive normal tractions; loading; layer-foundation interface; shrinks; circular area; system of singular integral equations of the second kind; stress intensity factorReferences:
| [1] | Abramowitz, M.; Stegun, I.A. (1965): Handbook of mathematical functions. New York: Dover · Zbl 0171.38503 |
| [2] | Adams, G.G.; Bogy, D.B. (1976): The plane solution for the elastic contact problem of a semi-infinite strip and half plane. J. Appl. Mech. 43, 603-607 · Zbl 0375.73065 · doi:10.1115/1.3423940 |
| [3] | Agarwal, V.K. (1978): Axisymmetric solution of the end-problem for a semi-infinite elastic circular cylinder and its application to joined dissimilar cylinders under uniform tension. Int. J. Eng. Sci. 16, 985-998 · Zbl 0392.73082 · doi:10.1016/0020-7225(78)90056-3 |
| [4] | Civelek, M.B.; Erdogan, F. (1974): The axisymmetric double contact problem for a frictionless elastic layer. Int. J. Solids Struct. 10, 639-659 · Zbl 0298.73024 · doi:10.1016/0020-7683(74)90048-1 |
| [5] | Cook, T.S.; Erdogan, F. (1972): Stresses in bonded materials with a crack perpendicular to the interface. Int. J. Eng. Sci. 10, 677-697 · Zbl 0237.73096 · doi:10.1016/0020-7225(72)90063-8 |
| [6] | Dundurs, J.; Stippes, M. (1970): Role of elastic constants in certain contact problems. J. Appl. Mech. 37, 965-970 · doi:10.1115/1.3408725 |
| [7] | Dundurs, J.; Lee, M.S. (1972): Stress concentration at a sharp edge in contact problems. J. Elasticity 2, 109-112 · doi:10.1007/BF00046059 |
| [8] | Erdogan, F.; Gupta, G. D.; Cook, T. S.; Sib, G. C. (ed.), Numerical solution of singular integral equations (1973), The Netherlands/Leyden · Zbl 0265.73083 |
| [9] | Gecit, M.R.; Erdogan, F. (1978): Frictionless contact problem for an elastic layer under axisymmetric loading. Int. J. Solids Struct. 14, 771-785 · Zbl 0379.73018 · doi:10.1016/0020-7683(78)90034-3 |
| [10] | Gecit, M.R. (1981): Axisymmetric contact problem for an elastic layer and an elastic foundation. Int. J. Eng. Sci. 19, 747-755 · Zbl 0471.73097 · doi:10.1016/0020-7225(81)90108-7 |
| [11] | Gecit, M.R. (1986): Axisymmetric contact problem for a semi-infinite cylinder and a half space. Int. J. Eng. Sci. 24 · Zbl 0594.73111 |
| [12] | Gladwell, G.M.L. (1980): Contact problems in the classical theory of elasticity. The Netherlands/Leyden: Sijthoff and Noordhoff · Zbl 0431.73094 · doi:10.1007/978-94-009-9127-9 |
| [13] | Gupta, G.D. (1974): The analysis of the semi-infinite cylinder problem. Int. J. Solids Struct. 10, 137-148 · Zbl 0288.73015 · doi:10.1016/0020-7683(74)90013-4 |
| [14] | Keer, L.M. (1964): The contact stress problem for an elastic sphere indenting an elastic layer. J. Appl. Mech. 31, 143-145 · doi:10.1115/1.3629538 |
| [15] | Keer, L.M.; Dundurs, J.; Tsai, K.C. (1972): Problems involving a receding contact between a layer and a half space. J. Appl. Mech. 39, 1115-1120 · doi:10.1115/1.3422839 |
| [16] | Lebedev, N.N.; Ufliand, I.S. (1958): Axisymmetric contact problem for an elastic layer. J. Appl. Math. Mech. 22, 442-450 · Zbl 0088.17303 · doi:10.1016/0021-8928(58)90059-5 |
| [17] | Muskhelishvili, N.I. (1935): Some basic problems of the mathematical theory of elasticity. Moscow. English translation (1953). The Netherlands/Gröningen: P. Noordhoff · Zbl 0012.30102 |
| [18] | Muskhelishvili, N.I. (1953): Singular integral equations. The Netherlands/Gröningen: P. Noordhoff · Zbl 0051.33203 |
| [19] | Pao, Y.C.; Wu, T. S.; Chiu, Y. P. (1971): Bounds on the maximum contact stress of an indented elastic layer. J. Appl. Mech. 38, 608-614 · Zbl 0227.73131 · doi:10.1115/1.3408862 |
| [20] | Sneddon, I.N. (1951): Fourier transforms. New York: McGraw-Hill · Zbl 0038.26801 |
| [21] | Weitsman, Y. (1969): On the unbonded contact between plates and an elastic half-space. J. Appl. Mech. 36, 198-202 · Zbl 0183.53801 · doi:10.1115/1.3564607 |
| [22] | Zlatin, A.N.; Ufliand, I.S. (1976): Axisymmetric contact problem on the impression of an elastic cylinder into an elastic layer. J. Appl. Math. Mech. 40, 67-72 · Zbl 0352.73021 · doi:10.1016/0021-8928(76)90112-X |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
