The axisymmetric double contact problem for a frictionless elastic layer indented by an elastic cylinder. (English) Zbl 0594.73110
Summary: This paper is concerned with the smooth receding contact between an elastic layer and a half space when the layer is compressed by a frictionless semi-infinite elastic cylinder. Upon loading, the contact along the layer-subspace interface shrinks to a circular area, radius of which 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 contact and the stess intensity factor round the edge of the cylinder are calculated for various material combinations.
MSC:
| 74A55 | Theories of friction (tribology) |
| 74M15 | Contact in solid mechanics |
| 65R20 | Numerical methods for integral equations |
Keywords:
axisymmetric double contact problem; uniform; compression; no tensile traction; smooth receding contact; elastic layer; half space; frictionless semi-infinite elastic cylinder; system of singular integral equations of the second kind; contact pressures; extent of contact; stess intensity factorCitations:
Zbl 0594.73111References:
| [1] | Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity (1953), Noordhoff: Noordhoff Groningen, Holland · Zbl 0052.41402 |
| [2] | Sneddon, I. N., Fourier Transforms (1951), McGraw-Hill: McGraw-Hill New York, N.Y · Zbl 0099.28401 |
| [3] | Lebedev, N. N.; Ufliand, I. S., Axisymmetric Contact Problem for an Elastic Layer, Journal of Applied Mathematics and Mechanics (PMM), 22, 320-326 (1958) · Zbl 0088.17303 |
| [4] | Pao, Y. C.; Wu, T. S.; Chiu, Y. P., Bounds on the Maximum Contact Stress of an Indented Elastic Layer, ASME Journal of Applied Mechanics, 38, 608-614 (1971) · Zbl 0227.73131 |
| [5] | Zlatin, A. N.; Ufliand, I. S., Axisymmetric Contact Problem on the Impression of an Elastic Cylinder into an Elastic Layer, Journal of Applied Mathematics and Mechanics (PMM), 40, 79-84 (1976) · Zbl 0352.73021 |
| [6] | Dundurs, J.; Stippes, M., Role of Elastic Constants in Certain Contact Problems, ASME Journal of Applied Mechanics, 37, 965-970 (1970) |
| [7] | Weitsman, Y., On the Unbonded Contact Between Plates and an Elastic Half Space, ASME Journal of Applied Mechanics, 36, 198-202 (1969) · Zbl 0183.53801 |
| [8] | Pu, S. L.; Hussain, M. A., Note on the Unbonded Contact Between Plates and an Elastic Half Space, ASME Journal of Applied Mechanics, 37, 859-861 (1970) · Zbl 0202.24902 |
| [9] | Gecit, M. R., Axisymmetric Contact Problem for a Semi-infinite Cylinder and a Half Space, Int. J. Engng Sci., 24, 1245-1256 (1986) · Zbl 0594.73111 |
| [10] | Gecit, M. R., Axisymmetric Contact Problem for a Frictionless Elastic Layer Indented by an Elastic Cylinder, Computational Mechanics: An International Journal, 1 (1986) · Zbl 0614.73116 |
| [11] | Galin, L. A., Contact Problems in the Theory of Elasticity (1961), North Carolina State College: North Carolina State College Raleigh, N.C · Zbl 0366.73056 |
| [12] | Ufliand, I. S., Survey of Articles on the Applications of Integral Transforms in the Theory of Elasticity (1965), North Carolina State College: North Carolina State College Raleigh, N.C |
| [13] | Gladwell, G. M.L., Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff (1980), Alphen aan den Rijn: Alphen aan den Rijn The Netherlands · Zbl 0431.73094 |
| [14] | Gecit, M. R.; Erdogan, F., Frictionless Contact Problem for an Elastic Layer under Axisymmetric Loading, Int. J. Solids and Structures, 14, 771-785 (1978) · Zbl 0379.73018 |
| [15] | Civelek, M. B.; Erdogan, F., The Axisymmetric Double Contact Problem for a Frictionless Elastic Layer, Int. J. Solids and Structures, 10, 639-659 (1974) · Zbl 0298.73024 |
| [16] | Gecit, M. R., Axisymmetric Contact Problem for an Elastic Layer and an Elastic Foundation, Int. J. Engng Sci., 19, 747-755 (1981) · Zbl 0471.73097 |
| [17] | Muskhelishvili, N. I., Singular Integral Equations (1953), P. Noordhoff: P. Noordhoff Groningen, Holland · Zbl 0051.33203 |
| [18] | Adams, G. G.; Bogy, D. B., The Plane Solution for the Elastic Contact Problem of a Semi-infinite Strip and Half Plane, ASME Journal of Applied Mechanics, 43, 603-607 (1976) · Zbl 0375.73065 |
| [19] | Dundurs, J.; Lee, M. S., Stress Concentration at a Sharp Edge in Contact Problems, Journal of Elasticity, 2, 109-112 (1972) |
| [20] | Cook, T. S.; Erdogan, F., Stresses in Bonded Materials with a Crack Perpendicular to the Interface, Int. J. Engng Sci., 10, 677-697 (1972) · Zbl 0237.73096 |
| [21] | Erdogan, F.; Gupta, G. D.; Cook, T. S., Numerical Solution of Singular Integral Equations, (Sih, G. C., Methods of Analysis and Solutions of Crack Problems (1973), Noordhoff: Noordhoff Leyden) · Zbl 0265.73083 |
| [22] | Keer, L. M.; Dundurs, J.; Tsai, K. C., Problems Involving a Receding Contact Between a Layer and a Half Space, ASME Journal of Applied Mechanics, 39, 1115-1120 (1972) |
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.
