Skip to main content
SpringerLink
Log in

Contact problem of a functionally graded layer resting on a Winkler foundation

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The contact problem for a functionally graded layer supported by a Winkler foundation is considered using linear elasticity theory in this study. The layer is loaded by means of a rigid cylindrical punch that applies a concentrated force in the normal direction. Poisson’s ratio is taken as constant, and the elasticity modulus is assumed to vary exponentially through the thickness of the layer. The problem is reduced to a Cauchy-type singular integral equation with the use of Fourier integral transform technique and the boundary conditions of the problem. The numerical solution of the integral equation is performed by using Gauss–Chebyshev integration formulas. The effect of the material inhomogeneity, stiffness of the Winkler foundation and punch radius on the contact stress, the contact area and the normal stresses are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Guler M.A., Erdogan F.: Contact mechanics of graded coatings. Int. J. Solids Struct. 41, 3865–3889 (2004)

    Article  MATH  Google Scholar 

  2. Guler M.A., Erdogan F.: The frictional sliding contact problems of rigid parabolic and cylindrical stamps on graded coatings. Int. J. Mech. Sci. 49, 161–182 (2007)

    Article  Google Scholar 

  3. Liu T.J., Wang Y.S.: Axisymmetric frictionless contact problem of a functionally graded coating with exponentially varying modulus. Acta Mech. 199, 151–165 (2008)

    Article  MATH  Google Scholar 

  4. Ke L.L., Wang Y.S.: Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties. Int. J. Solids Struct. 43, 5779–5798 (2006)

    Article  MATH  Google Scholar 

  5. Ke L.L., Wang Y.S.: Two-dimensional sliding frictional contact of functionally graded materials. Eur. J. Mech. A/Solids 26, 171–188 (2007)

    Article  MATH  Google Scholar 

  6. Liu T.J., Wang Y.S., Zhang C.: Axisymmetric frictionless contact of functionally graded materials. Arch. Appl. Mech. 78, 267–282 (2008)

    Article  MATH  Google Scholar 

  7. Giannakopoulos A.E., Pallot P.: Two-dimensional contact analysis of elastic graded materials. J. Mech. Phys. Solids 48, 1597–1631 (2000)

    Article  MATH  Google Scholar 

  8. Chen P., Chen S.: Contact behaviors of a rigid punch and a homogeneous half-space coated with a graded layer. Acta Mech. 223, 563–577 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Guler M.A., Erdogan F.: Contact mechanics of two deformable elastic solids with graded coatings. Mech. Mater. 38, 633–647 (2006)

    Article  Google Scholar 

  10. Yang J., Ke L.L.: Two dimensional contact problem for a coating–graded layer–substrate structure under a rigid cylindrical punch. Int. J. Mech. Sci. 50, 985–994 (2008)

    Article  MATH  Google Scholar 

  11. El-Borgi S., Abdelmoula R., Keer L.: A receding contact problem between a functionally graded layer and a homogeneous substrate. Int. J. Solids Struct. 43, 658–674 (2006)

    Article  MATH  Google Scholar 

  12. Rhimi M., El-Borgi S., Ben Said W., Ben Jemaa F.: A receding contact axisym-metric problem between a functionally graded layer and a homogeneous substrate. Int. J. Solids Struct. 46, 3633–3642 (2009)

    Article  MATH  Google Scholar 

  13. Choi H.J.: On the plane contact problem of a functionally graded elastic layer loaded by a frictional sliding flat punch. J. Mech. Sci. Technol. 23, 2703–2713 (2009)

    Article  Google Scholar 

  14. Bakirtas I.: The problem of a rigid punch on a nonhomogeneous elastic half space. Int. J. Eng. Sci. 18, 597–610 (1980)

    Article  MATH  Google Scholar 

  15. Dempsey J.P., Zhao Z.G., Minnetyan L., Li H.: Plane contact of an elastic layer supported by a Winkler foundation. J. Appl. Mech. 57, 974–980 (1990)

    Article  Google Scholar 

  16. Dempsey J.P., Zhao Z.G., Li H.: Axisymmetric indentation of an elastic layer supported by a Winkler foundation. Int. J. Solids Struct. 27, 73–87 (1991)

    Article  Google Scholar 

  17. Birinci A., Erdol R.: A frictionless contact problem for two elastic layers supported by a Winkler foundation. Struct. Eng. Mech. 15, 331–344 (2003)

    Article  Google Scholar 

  18. Wozniak M., Hummel A., Pauk V.J.: Axisymmetric contact problems for an elastic layer resting on a rigid base with a Winkler type excavitation. Int. J. Solids Struct. 39, 4117–4131 (2002)

    Article  MATH  Google Scholar 

  19. Matysiak S.J., Pauk V.J.: Edge crack in an elastic layer resting on a Winkler foundation. Eng. Fract. Mech. 70, 2353–2361 (2003)

    Article  Google Scholar 

  20. Kadioglu S., Dag S., Yahsi S.: Crack problem for a functionally graded layer on an elastic foundation. Int. J. Fract. 94, 63–77 (1998)

    Article  Google Scholar 

  21. Erdogan F.: Mixed boundary value problems in mechanics. In: Nemat-Nasser, S. (eds) Mechanics Today, vol. 4, Pergamon Press, New York (1978)

  22. Krenk S.: On quadrature formulas for singular integral equations of the first and the second kind. Q. Appl. Math. 33, 225–232 (1975)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Civil Engineering Department, Karadeniz Technical University, 61080, Trabzon, Turkey

    İsa Çömez

Authors
  1. İsa Çömez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to İsa Çömez.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Çömez, İ. Contact problem of a functionally graded layer resting on a Winkler foundation. Acta Mech 224, 2833–2843 (2013). https://doi.org/10.1007/s00707-013-0903-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-013-0903-5

Keywords

Search

Navigation