Continuous contact problem of a functionally graded layer resting on an elastic half‐plane

• Autorzy: Öner, E. , Adiyaman, G. , Birinci, A.
• Języki publikacji: EN

Abstrakty

EN

In this study, the continuous contact problem of a functionally graded layer resting on an elastic half-plane and loaded by a rigid rectangular stamp is examined. The problem is solved assuming that the functionally graded (FG) layer is isotropic and the shear modulus and mass density vary exponentially throughout the layer’s thickness. However, the body force of the elastic half-plane is neglected. In addition, it is assumed that all surfaces are frictionless and only compressive stress is transferred along the contact surfaces. The mathematical problem is reduced to a singular integral equation in which the contact stress under the rigid stamp is unknown using the Fourier integral transform and boundary conditions related to the problem. This singular integral equation is solved numerically using the Gauss–Chebyshev integration formula. The dimensionless contact stress under the rigid stamp, the initial separation loads and the initial separation distances between the FG layer and the elastic half-plane are obtained for various dimensionless quantities.

Słowa kluczowe

EN

functionally graded layer; contact problem; initial separation load; initial separation distance; singular integral equation

• Czasopismo: Archives of Mechanics
• Rocznik: 2017
• Tom: Vol. 69, nr 1
• Strony: 53--73
• Opis fizyczny: Bibliogr. 34 poz., rys.

Twórcy

autor

Öner, E.

• Department of Civil Engineering Bayburt University 69000 Bayburt, Turkey,

autor

Adiyaman, G.

• Department of Civil Engineering Karadeniz Technical University 61080 Trabzon, Turkey,

autor

Birinci, A.

• Department of Civil Engineering Karadeniz Technical University 61080 Trabzon, Turkey,

Bibliografia

• 1. A.E. Giannakopoulos, P. Pallot, Two-dimensional contact analysis of elastic graded materials, J. Mech. Phys. Solids, 48, 1597–1631, 2000.
• 2. M.A. Guler, F. Erdogan, Contact mechanics of graded coatings, Int. J. Solids Struct., 41, 3865–3889, 2004.
• 3. M.A. Guler, F. Erdogan, Contact mechanics of two deformable elastic solids with graded coatings, Mech. Mater., 38, 633–647, 2006.
• 4. S. El-Borgi, R. Abdelmoula, L. Keer, A receding contact plane problem between a functionally graded layer and a homogeneous substrate, Int. J. Solids Struct., 43, 658–674, 2006.
• 5. L.L. Ke, Y.S. Wang, Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties, Int. J. Solids Struct., 43, 5779–5798, 2006.
• 6. M.A. Guler, F. Erdogan, The frictional sliding contact problems of rigid parabolic and cylindrical stamps on graded coatings. Int. J. Mech. Sci., 49, 161–182, 2007.
• 7. L.L. Ke, Y.S. Wang, Two-dimensional sliding frictional contact of functionally graded materials, Eur. J. Mech. A/Solids, 26, 171–188, 2007.
• 8. J. Yang, L.L. Ke, Two-dimensional contact problem for a coating-graded layer-substrate structure under a rigid cylindrical punch, Int. J. Mech. Sci., 50, 985–994, 2008.
• 9. T.J. Liu, Y.S. Wang, Axisymmetric frictionless contact problem of a functionally graded coating with exponentially varying modulus, Acta Mech., 199, 151–165, 2008.
• 10. T.J. Liu, Y.S. Wang, C. Zhang, Axisymmetric frictionless contact of functionally graded materials, Arch. Appl. Mech., 78, 267–282, 2008.
• 11. M. Rhimi, S. El-Borgi, W. Ben Said, F. Ben Jemaa, A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate, Int. J. Solids Struct., 46, 3633–3642, 2009.
• 12. S. Dag, M.A. Guler, B. Yildirim, A.C. Ozatag, Sliding frictional contact between a rigid punch and a laterally graded elastic medium, Int. J. Solids Struct., 46, 4038–4053, 2009.
• 13. L.L. Ke, Y.S. Wang, J. Yang, S. Kitipornchai, Sliding frictional contact analysis of functionally graded piezoelectric layered half-plane, Acta Mech., 209, 249–268, 2010.
• 14. M. Rhimi, S. El-Borgi, N. Lajnef, A double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate, Mech. Mater., 43, 787–798, 2011.
• 15. Y.T. Zhou, K.Y. Lee, Exact solutions of a new 2D frictionless contact model for orthotropic piezoelectric materials indented by a rigid sliding punch, Philos. Mag., 92, 1937–1965, 2012.
• 16. I. Comez, Contact problem of a functionally graded layer resting on a Winkler foundation, Acta Mech., 224, 2833–2843, 2013.
• 17. S. Volkov, A. Aizikovich, Y.S. Wang, I. Fedotov, Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer. Acta Mech. Sinica, 29, 196–201, 2013.
• 18. S. Dag, M.A. Guler, B. Yildirim, A.C. Ozatag, Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp, Acta Mech., 224, 1773–1789, 2013.
• 19. T.J. Liu, Y.M. Xing, Analysis of graded coatings for resistance to contact deformation and damage based on a new multi-layer model, Int. J. Mech. Sci., 81, 158–164, 2014.
• 20. A. Nikbakht, A.F. Arezoodar, M. Sadighi, A. Talezadeh, Analyzing contact problem between a functionally graded plate of finite dimensions and a rigid spherical indenter, Eur. J. Mech. A/Solids, 47, 92–100, 2014.
• 21. S. El-Borgi, S. Usman, M.A. Guler, A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate, Int. J. Solids Struct., 51, 4462–4476, 2014.
• 22. A. Vasiliev, S. Volkov, S. Aizikovich, Y.-R. Jeng, Axisymmetric contact problems of the theory of elasticity for inhomogeneous layers, J. Appl. Math. Mech., 94, 705–712, 2014.
• 23. J. Yan, X. Li, Double receding contact plane problem between a functionally graded layer and an elastic layer, Eur. J. Mech. A/Solids, 53, 143–150, 2015.
• 24. I. Comez, Contact problem for a functionally graded layer indented by a moving punch, Int. J. Mech. Sci., 100, 339–344, 2015.
• 25. L.I. Krenev, S.M. Aizikovich, Y.V. Tokovyy, Y.C. Wang, Axisymmetric problem on the indentation of a hot circular punch into an arbitrarily nonhomogeneous half-space, Int. J. Solids Struct., 59, 18–28, 2015.
• 26. Z. Wang, C. Yu, Q. Wang, An efficient method for solving three-dimensional fretting contact problems involving multilayered or functionally graded materials, Int. J. Solids Struct., 66, 46–61, 2015.
• 27. R. Kulchytsky-Zhyhailo, A.S. Bajkowski, Three-dimensional analytical elasticity solution for loaded functionally graded coated half-space, Mech. Res. Commun., 65, 43–50, 2015.
• 28. J. Ma, S. El-Borgi, L.L. Ke, Y.S. Wang, Frictional contact problem between a functionally graded magnetoelectroelastic layer and a rigid conducting flat punch with frictional heat generation, J. Therm. Stresses, 39, 245–277, 2016.
• 29. Y. Alinia, A. Beheshti, M.A. Guler, S. El-Borgi, A.A. Polycarpou, Sliding contact analysis of functionally graded coating-substrate system, Mech. Mater., 94, 142–155, 2016.
• 30. K.S. Parel, D.A. Hills, Frictional receding contact analysis of a layer on a half-plane subjected tos emi-infinite surface pressure, Int. J. Mech. Sci., 108-109, 137–143, 2016.
• 31. F. Erdogan, G. Gupta, On the numerical solutions of singular integral equations, Q. Appl. Math., 29, 525–534, 1972.
• 32. A.O. Cakiriglu, Elastik yarım düzleme oturan plaklarda temas problemi (Contact problem of plates resting on elastic half-plane) Civil Engineering Department, Karadeniz Technical University, Trabzon, Turkey, 1979 [in Turkish].
• 33. M.B. Civelek, F. Erdogan, Interface separation in a frictionless contact problem for an elastic layer, J. Appl. Mech., 43, 175–177, 1976.
• 34. M.B. Civelek, F. Erdogan, A.O. Cakiroglu, Interface separation for an elastic layer loaded by a rigid stamp, Int. J. Engng. Sci., 16, 669–679, 1978.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).