Structural Engineering and Mechanics

  • 제91권5호
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  • Pages.459-468
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  • 2024
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

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Receding contact problem of an orthotropic layer supported by rigid quarter planes

  • Huseyin Oguz (Department of Mathematics, Science and Art Faculty, Kutahya Dumlupinar University) ;
  • Ilkem Turhan Cetinkaya (Department of Mathematics, Science and Art Faculty, Kutahya Dumlupinar University) ;
  • Isa Comez (Department of Civil Engineering, Engineering Faculty, Karadeniz Technical University)
  • 투고 : 2023.09.20
  • 심사 : 2024.08.02
  • 발행 : 2024.09.10
⟨ 이전 논문 다음 논문 ⟩

초록

This study presents a frictionless receding contact problem for an orthotropic elastic layer. It is assumed that the layer is supported by two rigid quarter planes and the material of the layer is orthotropic. The layer of thickness h is indented by a rigid cylindrical punch of radius R. The problem is modeled by using the singular integral equation method with the help of the Fourier transform technique. Applying the boundary conditions of the problem the system of singular integral equations is obtained. In this system, the unknowns are the contact stresses and contact widths under the punch and between the layer and rigid quarter planes. The Gauss-Chebyshev integration method is applied to the obtained system of singular integral equations of Cauchy type. Five different orthotropic materials are considered during the analysis. Numerical results are presented to interpret the effect of the material property and the other parameters on the contact stress and the contact width.

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참고문헌

  1. Adams, G.G. (2022), "The contact stress distribution in the receding contact of an elastic layer with a rigid base", Int. J. Solid. Struct., 238, 111384. https://doi.org/10.1016/j.ijsolstr.2021.111384.
  2. Adiyaman, G., Birinci, A., Oner, E. and Yaylaci, M. (2016), "A receding contact problem between a functionally graded layer and two homogeneous quarter planes", Acta Mechanica, 227(6), 1753-1766. https://doi.org/10.1007/s00707-016-1580-y.
  3. Adiyaman, G., Yaylaci, M. and Birinci, A. (2015), "Analytical and finite element solution of a receding contact problem", Struct. Eng. Mech., 54(1), 69-85. https://doi.org/10.12989/sem.2015.54.1.069.
  4. Arslan, O. and Dag, S. (2018), "Contact mechanics problem between an orthotropic graded coating and a rigid punch of an arbitrary profile", Int. J. Mech. Sci., 135, 541-554. https://doi.org/10.1016/j.ijmecsci.2017.12.017.
  5. Bakirtas, I. (1980), "The problem of a rigid punch on a nonhomogeneous elastic half space", Int. J. Eng. Sci., 18(4), 597-610. https://doi.org/10.1016/0020-7225(80)90132-9.
  6. Binienda, W.K. and Pindera, M.J. (1994), "Frictionless contact of layered metal-matrix and polymer-matrix composite half planes", Compos. Sci. Technol., 50(1), 119-128. https://doi.org/10.1016/0266-3538(94)90131-7.
  7. Cao, R. and Mi, C. (2022), "On the receding contact between a graded and a homogeneous layer due to a flat-ended indenter", Math. Mech. Solid., 27(5), 775-793. https://doi.org/10.1177/10812865211043152.
  8. Cao, R., Li, L., Li, X. and Mi, C. (2021), "On the frictional receding contact between a graded layer and an orthotropic substrate indented by a rigid flat-ended stamp", Mech. Mater., 158, 103847. https://doi.org/10.1016/j.mechmat.2021.103847.
  9. Choi, H.J. and Thangjitham, S. (1991), "Stress analysis of multilayered anisotropic elastic media", J. Appl. Mech., 58(2), 382-387. https://doi.org/10.1115/1.2897197.
  10. Civelek, M.B. and Erdogan, F. (1974), "The axisymmetric double contact problem for a frictionless elastic layer", Int. J. Solid. Struct., 10(6), 639-659. https://doi.org/10.1016/0020-7683(74)90048-1.
  11. Comez, I., Alinia, Y., Guler, M.A. and El-Borgi, S. (2021), "Partial slip contact analysis for a monoclinic half plane", Math. Mech. Solid., 26(3), 401-421. https://doi.org/10.1177/1081286520962836.
  12. Comez, I., Birinci, A. and Erdol, R. (2004), "Double receding contact problem for a rigid stamp and two elastic layers", Eur. J. Mech.-A/Solid., 23(2), 301-309. https://doi.org/10.1016/j.euromechsol.2003.09.006.
  13. Comez, I., Kahya, V. and Erdol, R. (2018), "Plane receding contact problem for a functionally graded layer supported by two quarter-planes", Arch. Mech., 70(6), 485-504. http://doi.org/10.24423/aom.2846.
  14. Dempsey, J.P., Zhao, Z.G. and Li, H. (1991), "Axisymmetric indentation of an elastic layer supported by a Winkler foundation", Int. J. Solid. Struct., 27(1), 73-87. https://doi.org/10.1016/0020-7683(91)90146-7.
  15. Dundurs, J. and Lee, M.S. (1972), "Stress concentration at a sharp edge in contact problems", J. Elast., 2(2), 109-112. https://doi.org/10.1007/BF00046059.
  16. Erdogan, F. and Ratwani, M. (1974), "The contract problem for an elastic layer supported by two elastic quarter planes", J. Appl. Mech., 41, 673-677. https://doi.org/10.1115/1.3423369.
  17. Erdogan, F., Gupta, G. and Cook, T.S. (1973), "Numerical solution of singular integral equations", Methods of Analysis and Solutions of Crack Problems, Springer, Dordrecht.
  18. Fabrikant, V.I. and Sankar, T.S. (1986), "Concentrated force underneath a punch bonded to a transversely isotropic halfspace", Int. J. Eng. Sci., 24(1), 111-117. https://doi.org/10.1016/0020-7225(86)90153-9.
  19. Fan, H. and Keer, L.M. (1994), "Two-dimensional contact on an anisotropic elastic half-space", J. Appl. Mech., 61(2), 250-255. https://doi.org/10.1115/1.2901437.
  20. Gecit, M.R. (1986), "The axisymmetric double contact problem for a frictionless elastic layer indented by an elastic cylinder", Int. J. Eng. Sci., 24(9), 1571-1584. https://doi.org/10.1016/0020-7225(86)90164-3.
  21. Hasebe, N. (2021), "Analysis of a mixed boundary value problem for an orthotropic elasticity using a mapping function", Int. J. Solid. Struct., 208, 154-166. https://doi.org/10.1016/j.ijsolstr.2020.10.029.
  22. Hassani, M., Monfared, M.M. and Salarvand, A. (2023), "Multiple unequal cracks between an FGM orthotropic layer and an orthotropic substrate under mixed mode concentrated loads", Struct. Eng. Mech., 86(4), 535-546. https://doi.org/10.12989/sem.2023.86.4.535.
  23. Kahya, V., Ozsahin, T.S., Birinci, A. and Erdol, R. (2007), "A receding contact problem for an anisotropic elastic medium consisting of a layer and a half plane", Int. J. Solid. Struct., 44(17), 5695-5710. https://doi.org/10.1016/j.ijsolstr.2007.01.020.
  24. King, R.B. (1987), "Elastic analysis of some punch problems for a layered medium", Int. J. Eng. Sci., 23(12), 1657-1664. https://doi.org/10.1016/0020-7683(87)90116-8.
  25. Liu, Z., Yan, J. and Mi, C. (2018), "On the receding contact between a two-layer inhomogeneous laminate and a half-plane", Struct. Eng. Mech., 66(3), 329-341. https://doi.org/10.12989/sem.2018.66.3.329.
  26. Loboda, V.V. and Tauchert, T.R. (1985), "The elastic contact problem for dissimilar orthotropic semi-infinite and infinite strips", Int. J. Eng. Sci., 23(12), 1337-1349. https://doi.org/10.1016/0020-7225(85)90112-0.
  27. Ma, L.F. and Korsunsky, A.M. (2004), "Fundamental formulation for frictional contact problems of coated systems", Int. J. Solid. Struct., 41(11-12), 2837-2854. https://doi.org/10.1016/j.ijsolstr.2003.12.022.
  28. Muskhelishvili, N.I. (1997), Singular Integral Equations, Noordhoff, Groningen.
  29. Nguyen-Hoang, M. and Becker, W. (2021), "Stress analysis of finite orthotropic plates loaded by a bolted joint", Compos. Struct., 276, 114454. https://doi.org/10.1016/j.compstruct.2021.114454.
  30. Nowell, D. and Hills, D.A. (1988), "Contact problems incorporating elastic layers", Int. J. Solid. Struct., 24(1), 105-115. https://doi.org/10.1016/0020-7683(88)90102-3.
  31. Oner, E. (2021), "Two-dimensional frictionless contact analysis of an orthotropic layer under gravity", J. Mech. Mater. Struct., 16(4), 573-594. https://doi.org/10.2140/jomms.2021.16.573.
  32. Parel, K.S. (2021). Plane frictional receding contact of a thin layer pressed onto a substrate by finite pressure distributions", Eur. J. Mech.-A/Solid., 90, 104309. https://doi.org/10.1016/j.euromechsol.2021.104309.
  33. Pindera, M.J. and Lane, M.S. (1993), "Frictionless contact of layered half-planes, Part I: Analysis", J. Appl. Mech., 60(3), 633-639. https://doi.org/10.1115/1.2900851.
  34. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
  35. Sellam, S., Draiche, K., Tlidji, Y., Addou, F.Y. and Benachour, A. (2020), "A simple analytical model for free vibration and buckling analysis of orthotropic rectangular plates", Struct. Eng. Mech., 75(2), 157-174. https://doi.org/10.12989/sem.2020.75.2.157.
  36. Weitsman, Y. (1969), "On the unbonded contact between plates and an elastic half space", J. Appl. Mech., 36(2), 198-202. https://doi.org/10.1115/1.3564607.
  37. Yan, J. and Li, X. (2015), "Double receding contact plane problem between a functionally graded layer and an elastic layer", Eur. J. Mech.-A/Solid., 53, 143-150. https://doi.org/10.1016/j.euromechsol.2015.04.001.
  38. Yan, J. and Mi, C. (2017), "Double contact analysis of multilayered elastic structures involving functionally graded materials", Arch. Mech., 69(3), 199-221.
  39. Yan, J. and Wang, C. (2022), "Receding contact problem of multilayered elastic structures involving functionally graded materials", Crystal., 12(3), 354.
  40. Yaylaci, M. and Birinci, A. (2013), "The receding contact problem of two elastic layers supported by two elastic quarter planes. Struct. Eng. Mech., 48(2), 241-255. https://doi.org/10.12989/sem.2013.48.2.241.
  41. Yildirim, B., Yilmaz, K.B., Comez, I. and Guler, M.A. (2019), "Double frictional receding contact problem for an orthotropic layer loaded by normal and tangential forces", Meccanica, 54(14), 2183-2206. https://doi.org/10.1007/s11012-019-01058-4.
  42. Yusufoglu, E. and Turhan, I. (2012), "A mixed boundary value problem in orthotropic strip containing a crack", J. Franklin Inst., 349(9), 2750-2769. https://doi.org/10.1016/j.jfranklin.2012.09.001.
  43. Yusufoglu, E. and Turhan, I. (2013), "A numerical approach for a crack problem by Gauss-Chebyshev quadrature", Arch. Appl. Mech., 83, 1535-1547. https://doi.org/10.1007/s00419-013-0760-7.
  44. Zhang, J., Zhou, C., Ullah, S., Zhong, Y. and Li, R. (2019), "Twodimensional generalized finite integral transform method for new analytic bending solutions of orthotropic rectangular thin foundation plates", Appl. Math. Lett., 92, 8-14. https://doi.org/10.1016/j.aml.2018.12.019.