Structural Engineering and Mechanics

  • 제66권3호
  • /
  • Pages.329-341
  • /
  • 2018
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

On the receding contact between a two-layer inhomogeneous laminate and a half-plane

  • Liu, Zhixin (Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University) ;
  • Yan, Jie (Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University) ;
  • Mi, Changwen (Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University)
  • 투고 : 2017.09.27
  • 심사 : 2018.03.19
  • 발행 : 2018.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper considers the smooth receding contact problem between a homogeneous half-plane and a composite laminate composed of an inhomogeneously coated elastic layer. The inhomogeneity of the elastic modulus of the coating is approximated by an exponential function along the thickness dimension. The three-component structure is pressed together by either a concentrated force or uniform pressures applied at the top surface of the composite laminate. Both semianalytical and finite element analysis are performed to solve for the extent of contact and the contact pressure. In the semianalytical formulation, Fourier integral transformation of governing equations and boundary conditions leads to a singular integral equation of Cauchy-type, which can be numerically integrated by Gauss-Chebyshev quadrature to a desired degree of accuracy. In the finite element modeling, the functionally graded coating is divided into homogeneous sublayers and the shear modulus of each sublayer is assigned at its lower boundary following the predefined exponential variation. In postprocessing, the stresses of any node belonging to sublayer interfaces are averaged over its surrounding elements. The results obtained from the semianalytical analysis are successfully validated against literature results and those of the finite element modeling. Extensive parametric studies suggest the practicability of optimizing the receding contact peak stress and the extent of contact in multilayered structures by the introduction of functionally graded coatings.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Natural Science Foundation of Jiangsu Province, Central Universities

참고문헌

  1. Adibelli, H., Comez, I. and Erdol, R. (2013), "Receding contact problem for a coated layer and a half-plane loaded by a rigid cylindrical stamp", Arch. Mech., 65(3), 219-236.
  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 Mech., 227(6), 1753-1766. https://doi.org/10.1007/s00707-016-1580-y
  3. Adiyaman, G., Oner, E. and Birinci, A. (2017), "Continuous and discontinuous contact problem of a functionally graded layer resting on a rigid foundation", Acta Mech., 228(9), 3003-3017. https://doi.org/10.1007/s00707-017-1871-y
  4. 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
  5. Balci, M.N., Dag, S. and Yildirim, B. (2016), "Subsurface stresses in graded coatings subjected to frictional contact with heat generation", J. Therm. Stress., 40(4), 517-534.
  6. Birinci, A., Adiyaman, G., Yaylaci, M. and Oner, E. (2015), "Analysis of continuous and discontinuous cases of a contact problem using analytical method and FEM", Lat. Am. J. Sol. Struct., 12(9), 1771-1789. https://doi.org/10.1590/1679-78251574
  7. Civelek, M. and Erdogan, F. (1974), "The axisymmetric double contact problem for a frictionless elastic layer", Int. J. Sol. Struct., 10(6), 639-659. https://doi.org/10.1016/0020-7683(74)90048-1
  8. Comez, I. (2010), "Frictional contact problem for a rigid cylindrical stamp and an elastic layer resting on a half plane", Int. J. Sol. Struct., 47(7-8), 1090-1097. https://doi.org/10.1016/j.ijsolstr.2010.01.003
  9. Comez, I., Birinci, A. and Erdol, R. (2004), "Double receding contact problem for a rigid stamp and two elastic layers", Eur. J. Mech. A-Sol., 23(2), 301-309. https://doi.org/10.1016/j.euromechsol.2003.09.006
  10. Comez, I., El-Borgi, S., Kahya, V. and Erdol, R. (2016), "Receding contact problem for two-layer functionally graded media indented by a rigid punch", Acta Mech., 227(9), 2493-2504. https://doi.org/10.1007/s00707-016-1648-8
  11. El-Borgi, S., Abdelmoula, R. and Keer, L. (2006), "A receding contact plane problem between a functionally graded layer and a homogeneous substrate", Int. J. Sol. Struct., 43(3-4), 658-674. https://doi.org/10.1016/j.ijsolstr.2005.04.017
  12. El-Borgi, S., Usman, S. and Guler, M.A. (2014), "A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate", Int. J. Sol. Struct., 51(25-26), 4462-4476. https://doi.org/10.1016/j.ijsolstr.2014.09.017
  13. Erdogan, F. and Gupta, G.D. (1972), "On the numerical solution of singular integral equations", Q. Appl. Math., 29(4), 525-534. https://doi.org/10.1090/qam/408277
  14. Erdogan, F. and Ratwani, M. (1974), "The contract problem for an elastic layer supported by two elastic quarter planes", J. Appl. Mech., 41(3), 673-678. https://doi.org/10.1115/1.3423369
  15. Gecit, M.R. (1986), "Axisymmetric contact problem for a frictionless elastic layer indented by an elastic cylinder", Comput. Mech., 1(2), 91-104. https://doi.org/10.1007/BF00277694
  16. Guler, M.A., Kucuksucu, A., Yilmaz, K.B. and Yildirim, B. (2017), "On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium", Int. J. Mech. Sci., 120, 12-29. https://doi.org/10.1016/j.ijmecsci.2016.11.004
  17. Itou, S. and Shima, Y. (1999), "Stress intensity factors around a cylindrical crack in an interfacial zone in composite materials", Int. J. Sol. Struct., 36(5), 697-709. https://doi.org/10.1016/S0020-7683(98)00041-9
  18. Johnson, K.L. (1985), Contact Mechanics, Cambridge University Press, London, U.K.
  19. Kauzlarich, J.J. and Greenwood, J.A. (2001), "Contact between a centrally loaded plate and a rigid or elastic base, with application to pivoted pad bearings", P. I. Mech. Eng. C-J. Mec., 215(6), 623-628. https://doi.org/10.1243/0954406011523965
  20. Keer, L.M. and Chantaramungkorn, K. (1972), "Loss of contact between an elastic layer and half-space", J. Elast., 2(3), 191-197. https://doi.org/10.1007/BF00125527
  21. Keer, L.M., Dundurs, J. and Tsai, K.C. (1972), "Problems involving a receding contact between a layer and a half space", J. Appl. Mech., 39(4), 1115-1120. https://doi.org/10.1115/1.3422839
  22. Li, X. (2013), Integral Equations, Boundary Value Problems and Related Problems, World Scientific Publishing, Singapore.
  23. Mi, C. (2017), "Surface mechanics induced stress disturbances in an elastic half-space subjected to tangential surface loads", Eur. J. Mech. A-Sol., 65, 59-69. https://doi.org/10.1016/j.euromechsol.2017.03.006
  24. Oner, E., Yaylaci, M. and Birinci, A. (2014), "Solution of a receding contact problem using an analytical method and a finite element method", J. Mech. Mater. Struct., 9(3), 333-345. https://doi.org/10.2140/jomms.2014.9.333
  25. Ortega, J.M. and Rheinboldt, W.C. (1987), Iterative Solution of Nonlinear Equations in Several Variables, Society for Industrial and Applied Mathematics, Philadelphia, U.S.A.
  26. Parel, K. and Hills, D. (2016), "Frictional receding contact analysis of a layer on a half-plane subjected to semi-infinite surface pressure", Int. J. Mech. Sci., 108-109, 137-143. https://doi.org/10.1016/j.ijmecsci.2016.01.022
  27. Rhimi, M., El-Borgi, S. and Lajnef, N. (2011), "A double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate", Mech. Mater., 43(12), 787-798. https://doi.org/10.1016/j.mechmat.2011.08.013
  28. Rhimi, M., El-Borgi, S., Ben, S.W. and Jemaa, F.B. (2009), "A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate", Int. J. Sol. Struct., 46(20), 3633-3642. https://doi.org/10.1016/j.ijsolstr.2009.06.008
  29. Roncevic, B. and Siminiati, D. (2010), "Two-dimensional receding contact analysis with NX Nastran", Adv. Eng., 4(1), 69-74.
  30. Roncevic, B., Bakic, A. and Kodvanj, J. (2016), "Numerical and experimental analysis of a frictionless receding contact between cylindrical indenter, layer and substrate", T. Famena, 40(2), 1-18.
  31. Tsai, K.C., Dundurs, J. and Keer, L.M. (1974), "Elastic layer pressed against a half space", J. Appl. Mech., 41(3), 703-707. https://doi.org/10.1115/1.3423375
  32. Turan, M., Adiyaman, G., Kahya, V. and Birinci, A. (2016), "Axisymmetric analysis of a functionally graded layer resting on elastic substrate", Struct. Eng. Mech., 58(3), 423-442. https://doi.org/10.12989/sem.2016.58.3.423
  33. White, R. (2010), Asymptotic Analysis of Differential Equations, Imperial College Press, Singapore.
  34. Yan, J. and Li, X. (2015), "Double receding contact plane problem between a functionally graded layer and an elastic layer", Eur. J. Mech. A-Sol., 53, 143-150. https://doi.org/10.1016/j.euromechsol.2015.04.001
  35. Yan, J. and Mi, C. (2017a), "Double contact analysis of multilayered elastic structures involving functionally graded materials", Arch. Mech., 69(3), 199-221.
  36. Yan, J. and Mi, C. (2017b), "On the receding contact between an inhomogeneously coated elastic layer and a homogeneous halfplane", Mech. Mater., 112, 18-27. https://doi.org/10.1016/j.mechmat.2017.05.007
  37. 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
  38. Yaylaci, M., Oner, E. and Birinci, A. (2014), "Comparison between analytical and ANSYS calculations for a receding contact problem", J. Eng. Mech., 140(9), 04014070. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000781

피인용 문헌

  1. Tuning stress concentrations through embedded functionally graded shells vol.13, pp.3, 2018, https://doi.org/10.2140/jomms.2018.13.311
  2. Analytical solutions for displacements and stresses in functionally graded thick-walled spheres subjected to a unidirectional outer tension vol.15, pp.5, 2018, https://doi.org/10.2140/jomms.2020.15.585
  3. Examination of analytical and finite element solutions regarding contact of a functionally graded layer vol.76, pp.3, 2018, https://doi.org/10.12989/sem.2020.76.3.325
  4. Frictionless contact mechanics of an orthotropic coating/isotropic substrate system vol.28, pp.2, 2021, https://doi.org/10.12989/cac.2021.28.2.209