DOI QR코드

DOI QR Code

Continuous and discontinuous contact problem for a layered composite resting on simple supports

  • Birinci, Ahmet (Civil Engineering Department, Karadeniz Technical University) ;
  • Erdol, Ragip (Civil Engineering Department, Karadeniz Technical University)
  • 발행 : 2001.07.25

초록

The frictionless contact problem for a layered composite which consists of two elastic layers having different elastic constants and heights resting on two simple supports is considered. The external load is applied to the layered composite through a rigid stamp. For values of the resultant compressive force P acting on the stamp vertically which are less than a critical value $P_{cr}$ and for small flexibility of the layered composite, the continuous contact along the layer - the layer and the stamp - the layered composite is maintained. However, if the flexibility of the layered composite increases and if tensile tractions are not allowed on the interface, for P > $P_{cr}$, a separation may be occurred between the stamp and the layered composite or two elastic layers interface along a certain finite region. The problem is formulated and solved for both cases by using Theory of Elasticity and Integral Transform Technique. Numerical results for $P_{cr}$, separation initiation distance, contact stresses, distances determining the separation area, and the vertical displacement in the separation zone between two elastic layers are given.

키워드

참고문헌

  1. Birinci, A., and Erdöl, R. (1999), "Frictionless contact between a rigid stamp and an elastic layered composite resting on simple supports", Mathematical & Computational Applications, 4(3), 261-272. https://doi.org/10.3390/mca4030261
  2. Caklroglu, A.O. (1979), Contact Problem of Plates Resting on Elastic Half-plane, Thesis (in Turkish), CivilEngineering Department, K.T.U., Trabzon, Turkey.
  3. Caklroglu, A.O., and Çaklroglu, F.L. (1991), "Continuous and discontinuous contact problems for strips on anelastic semi-infinite plane", Int. J. Eng. Science, 29(1), 99-111. https://doi.org/10.1016/0020-7225(91)90080-M
  4. Civelek, M.B., and Erdogan, F. (1974), "The axisymmetric double contact problem for a frictionless elastic layer", Int. J. Solids and Structures, 10, 639-659. https://doi.org/10.1016/0020-7683(74)90048-1
  5. Civelek, M.B., and Erdogan, F. (1975), "The frictionless contact problem for an elastic layer under gravity", J.Appl. Mech., 42(97), 136-140. https://doi.org/10.1115/1.3423504
  6. Civelek, M.B., and Erdogan, F. (1976), "Interface separation in a frictionless contact problem for an elasticlayer", J. Appl. Mech., 43, 175-177. https://doi.org/10.1115/1.3423775
  7. Civelek, M.B., Erdogan, F., and Caklroglu, A.O. (1978), "Interface separation for an elastic layer loaded by a rigid stamp", Int. J. Eng. Science, 16, 669-679. https://doi.org/10.1016/0020-7225(78)90044-7
  8. Erdogan, F., and Gupta, G. (1972), "On the numerical solutions of singular integral equations", Quarterly J. Appl. Math., 29, 525-534. https://doi.org/10.1090/qam/408277
  9. Erdogan, F., and Ratwani, M. (1974), "The contact problem for an elastic layer supported by two quarter planes", J. Appl. Mech., 41(96), 673-678. https://doi.org/10.1115/1.3423369
  10. Galin, L.A. (1961), Contact Problems in the Theory of Elasticity, North Carolina State College TranslationSeries, Raleigh.
  11. Geçit, M.R. (1980), "A Tensionless contact without friction between an elastic layer and an elastic foundation",Int. J. Solids and Struct., 16, 387-396. https://doi.org/10.1016/0020-7683(80)90037-2
  12. Geçit, M.R. (1981), "Axisymmetric contact problem for an elastic layer and elastic foundation", Int. J. Eng. Sci.,19, 747-755. https://doi.org/10.1016/0020-7225(81)90108-7
  13. Geçit, M.R., and Gökplnar, S. (1985), "Frictionless contact between an elastic layer and a rigid rounded support",The Arabian J. Sci. and Eng., 10, 243-251.
  14. Geçit, M.R., and Yaplcl, H. (1986), "Contact problem for an elastic layer on rigid flat supports", The Arabian J.Sci. and Eng., 11(3), 235-242.
  15. Geçit, M.R. (1986), "Axisymmetric contact problem for a semi-infinite cylinder and a half space", Int. J. Eng. Sci., 24(8), 1245-1256. https://doi.org/10.1016/0020-7225(86)90054-6
  16. Hertz, H. (1895), Gessammelte Worke von Heinrich Hertz, Leipzig.
  17. Muskhelishvili, N.I. (1958), Singular Integral Equations, Noordhoff Int. Pub., Leyden, The Netherlands.
  18. Sneddon, I.N. (1972), The Use of Integral Transforms, Mc Graw-Hill Inc., New York.
  19. Uffliand, I.S. (1965), Survey Articles on the Applications of Integral Transforms in the Theory of Elasticity,North Carolina State College Translation Series, Raleigh.

피인용 문헌

  1. Analytical solution of a contact problem and comparison with the results from FEM vol.54, pp.4, 2015, https://doi.org/10.12989/sem.2015.54.4.607
  2. The pressure distribution in nips of systems of flexible rubber-covered rollers vol.64, pp.1, 2012, https://doi.org/10.1016/j.ijmecsci.2012.07.006
  3. A frictionless contact problem for two elastic layers supported by a Winkler foundation vol.15, pp.3, 2003, https://doi.org/10.12989/sem.2003.15.3.331
  4. Contact Problem for an Elastic Layer on an Elastic Half Plane Loaded by Means of Three Rigid Flat Punches vol.2013, 2013, https://doi.org/10.1155/2013/137427
  5. Double receding contact problem for a rigid stamp and two elastic layers vol.23, pp.2, 2004, https://doi.org/10.1016/j.euromechsol.2003.09.006
  6. A double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate vol.43, pp.12, 2011, https://doi.org/10.1016/j.mechmat.2011.08.013
  7. Continuous contact problem for two elastic layers resting on an elastic half-infinite plane vol.9, pp.1, 2014, https://doi.org/10.2140/jomms.2014.9.105
  8. A receding contact problem for an anisotropic elastic medium consisting of a layer and a half plane vol.44, pp.17, 2007, https://doi.org/10.1016/j.ijsolstr.2007.01.020
  9. A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate vol.46, pp.20, 2009, https://doi.org/10.1016/j.ijsolstr.2009.06.008
  10. Prediction of contact lengths between an elastic layer and two elastic circular punches with neural networks vol.18, pp.4, 2004, https://doi.org/10.12989/sem.2004.18.4.441
  11. Continuous and discontinuous contact problems of a homogeneous piezoelectric layer pressed by a conducting rigid flat punch vol.231, pp.3, 2020, https://doi.org/10.1007/s00707-019-02551-3
  12. Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM vol.27, pp.3, 2001, https://doi.org/10.12989/cac.2021.27.3.199