Computers and Concrete

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analysis of discontinuous contact problem in two functionally graded layers resting on a rigid plane by using finite element method

  • Polat, Alper (Department of Civil Engineering, Munzur University) ;
  • Kaya, Yusuf (Department of Civil Engineering, Gumushane University)
  • Received : 2020.12.07
  • Accepted : 2022.04.12
  • Published : 2022.04.25
⟨ Previous Next ⟩

Abstract

In this study, the problem of discontinuous contact in two functionally graded (FG) layers resting on a rigid plane and loaded by two rigid blocks is solved by the finite element method (FEM). Separate analyzes are made for the cases where the top surfaces of the problem layers are metal, the bottom surfaces are ceramic and the top surfaces are ceramic and the bottom surfaces are metal. For the problem, it is accepted that all surfaces are frictionless. A two-dimensional FEM analysis of the problem is made by using a special macro added to the ANSYS package program The solution of this study, which has no analytical solution in the literature, is given with FEM. Analyzes are made by loading different Q and P loads on the blocks. The normal stress (σy) distributions at the interfaces of FG layers and between the substrate and the rigid plane interface are obtained. In addition, the starting and ending points of the separations between these surfaces are determined. The normal stresses (σx, σy) and shear stresses (τxy) at the point of separation are obtained along the depth. The results obtained are shown in graphics and tables. With this method, effective results are obtained in a very short time. In addition, analytically complex and long problems can be solved with this method.

Keywords

References

  1. Abhilash, M.N. and Murthy, H. (2014), "Finite element analysis of 2-D elastic contacts involving FGMs", Int. J. Comput. Method. Eng. Sci. Mech., 15(3), 253-257. https://doi.org/10.1080/15502287.2014.882445.
  2. Adiyaman, G., O ner, E. and Birinci, A. (2017), "Continuous and discontinuous contact problem of a functionally graded layer resting on a rigid foundation", Acta Mechanica, 228, 3003-3017. https://doi.org/10.1007/s00707-017-1871-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. ANSYS (2015) Swanson Analysis Systems Inc., Houston PA, USA.
  5. Arslan, O. (2020), "Plane contact problem between a rigid punch and a bidirectional functionally graded medium", Eur. J. Mech., 80, 103925, 1-14. https://doi.org/10.1016/j.euromechsol.2019.103925.
  6. Balci, N.M. and Dag, S. (2019), "Solution of the dynamic frictional contact problem between a functionally graded coating and a moving cylindrical punch", Int. J. Solid. Struct., 161, 267-281. https://doi.org/10.1016/j.ijsolstr.2018.11.020.
  7. Chan, S.K. and Tuba, I.S. (1971), "A finite element method for contact problems of solid bodies-i. theory and validation", Int. J. Mech. Sci., 13(7), 615-625. https://doi.org/10.1016/0020-7403(71)90032-4.
  8. Chen, W.T. and Engel, P.A. (1972), "Impact and contact stress analysis in multilayered media", Int. J. Solid. Struct., 8, 1257-1281. https://doi.org/10.1016/0020-7683(72)90079-0.
  9. Chidlow, S.J., Chong, W.W.F. and Teodorescu, M. (2013), "On the two-dimensional solution of both adhesive and non-adhesive contact problems involving functionally graded materials", Eur. J. Mech. A Solid., 39, 86-103. https://doi.org/10.1016/j.euromechsol.2012.10.008.
  10. Comez, I. (2019), "Continuous and discontinuous contact problem of a functionally graded layer pressed by a rigid cylindrical punch", Eur. J. Mech. A Solid., 73, 437-448. https://doi.org/10.1016/j.euromechsol.2018.10.009.
  11. Comez, I. (2019), "Frictional moving contact problem of an orthotropic layer indented by a rigid cylindrical punch", Mech. Mater., 133, 120-127. https://doi.org/10.1016/j.mechmat.2019.02.012.
  12. El-Borgi, S., Abdelmoula, R. and Keer, L. (2006), "A receding contact problem between a functionally graded layer and a homogeneous substrate", Int. J. Solid. Struct., 43, 658-674. https://doi.org/10.1016/j.ijsolstr.2005.04.017.
  13. Frank, E.T., Lepech, M.D. and Billington, L.S. (2018), "Finite element models of reinforced ECC beams subjected to various cyclic deformation.", Comput. Concrete, 22(3), 305-317. https://doi.org/10.12989/cac.2018.22.3.305.
  14. Giannakopoulos, A.E. and Pallot, P. (2000), "Two-dimensional contact analysis of elastic graded materials", J. Mech. Phys. Solid., 48(8), 1597-1631. https://doi.org/10.1016/S0022-5096(99)00068-X.
  15. 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.
  16. Huang, J., Nguyen, T.N. and Zhou, K. (2018), "An isogeometric-meshfree coupling approach for contact problems by using the third medium method", Int. J. Mech. Sci., 148, 327-336. https://doi.org/10.1016/j.ijmecsci.2018.08.031.
  17. Kaya, Y. (2020). "Contact problem of two layers that different elastic properties loaded by two rigid flat blocks and resiing on a rigid plane", Ph.D. Thesis of Philosophy, Karadeniz Technical University, Trabzon.
  18. Kaya, Y., Polat, A. and Ozsahin, T.S. (2018), "Comparison of FEM solution with analytical solution of continuous and discontinuous contact problem", Sigma J. Eng. Nat. Sci., 36(4), 977-992.
  19. Kaya, Y., Polat, A. and Ozsahin, T.S. (2020), "Analytical and finite element solutions of continuous contact problem in functionally graded layer", Eur. Phys. J. Plus, 135(1), 1-21. https://doi.org/10.1140/epjp/s13360-020-00138-9.
  20. Liu, Z.X., Yan, J. and Mi, C.W. (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.
  21. Loboda, V.V. and Tauchert, T.R. (1985), "The elastic conctact problem for dissimilar orthrotrophic semi-infinite and infinite strips", Int. J. Eng. Sci., 23(12), 1337-1349. https://doi.org/10.1016/0020-7225(85)90112-0.
  22. Lou, T., Lopez, S.M.R. and Lopez, A.V. (2015), "Numerical modelling of nonlinear behaviour of prestressed concrete continuous beams", Comput. Concrete, 15(3), 391-410. https://doi.org/10.12989/cac.2015.15.3.391.
  23. 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.
  24. Ma, L.F., Korsunsky, A.M. and Sun, K. (2006), "Contact of coated systems under sliding conditions", ASME J. Tribology, 128(4), 886-890. https://doi.org/10.1115/1.2345415.
  25. Nguyen, T.N., Weidong, L, Huang, J., Narasimalu, S. and Zhou, K. (2019), "An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems", Int. J. Numer. Method. Eng., 120(2), 209-230. https://doi.org/10.1002/nme.6132.
  26. Nikbakht, A., Arezoodar, A.F., Sadighi, M., Zucchelli, A. and Lari A.F. (2013), "Frictionless elastic contact analysis of a functionally graded vitreous enameled low carbon steel plate and a rigid spherical indenter", Compos. Struct., 96, 484-501. https://doi.org/10.1016/j.compstruct.2012.08.044.
  27. Ozsahin, T.S. and Cakiroglu, A.O. (2003), "Iki elastik blok yardimi ile yuklenmis elastik tabakada temas problemi", XIII. Ulusal Mekanik Kongresi, 8-12 Eylul, Gaziantep.
  28. Patra, R., Barik, S.P. and Chaudhuri, P.K. (2017), "Frictionless contact of a rigid punch indenting an elastic layer having piezoelectric properties, Acta Mechanica, 228, 367-384. https://doi.org/10.1007/s00707-016-1700-8.
  29. Polat, A. (2021), "Examination of contact problem between functionally graded punch and functionally graded layer resting on elastic plane", Struct. Eng. Mech., 78(2), 135-143. https://doi.org/10.12989/sem.2021.78.2.135.
  30. Polat, A., Kaya, Y. and Ozsahin, T.S. (2018), "Analytical solution to continuous contact problem for a functionally graded layer loaded through two dissimilar rigid punches", Meccanica, 53(14), 3565-3577. https://doi.org/10.1007/s11012-018-0902-7.
  31. Polat, A., Kaya, Y., Kouider, B. and Ozsahin, T.S. (2019), "Frictionless contact problem for a functionally graded layer loaded through two rigid punches using finite element method", J. Mech., 35(5), 591-600. https://doi.org/10.1017/jmech.2018.55.
  32. Su, J., Ke L.L., El- Borgi, S., Xiang, Y. and Wang Y.S. (2018), "An effective method for the sliding frictional contact of conducting cylindirical punch on FGPMs", Int. J. Solid. Struct., 141-142, 127-136. https://doi.org/10.1016/j.ijsolstr.2018.02.017.
  33. Weidong, L., Nguyen, T.N. and Zhou, K. (2020), "An isogeometric-meshfree collocation approach for two-dimensional elastic fracture problems with contact loading", Eng. Fract. Mech., 223. https://doi.org/10.1016/j.engfracmech.2019.106779.
  34. Yan, J. and Mi, C. (2020), "On the receding contact between a homogeneous elastic layer and a half-plane substrate coated with functionally graded materials", Int. J. Comput. Method., 17(1), 1-21. https://doi.org/10.1142/S0219876218440085.
  35. Yaylaci, M. (2017), "Comparison between numerical and analytical solutions for the receding contact problem", Sigma J. Eng. Nat. Sci., 35(2), 333-346.
  36. Yaylaci, M. and Avcar, M. (2020), "Finite element modeling of contact between an elastic layer and two elastic quarter planes", Compute. Concrete, 26(2), 107-114. https://doi.org/10.12989/cac.2020.26.2.107.
  37. Yildirim, B., Yilmaz, K.B., Comez, I. and ve 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.
  38. Yilmaz, K.B., Comez, I., Guler, M.A. and ve Yildirim, B. (2019), "Analytical and finite element solution of the sliding frictional contact problem for a homogeneous orthotropic coating-isotropic substrate system", ZAMM-J. Appl. Math. Mech. Zeitschrift fur Angewandte Mathematik und Mechanik, 99, 3. https://doi.org/10.1002/zamm.201800117.
  39. Yilmaz, K.B., Comez, I., Yildirim, B., Guler, M.A. and El-Borgi, S. (2018), "Frictional receding contact problem for a graded bilayer system indented by a rigid punch", Int. J. Mech. Sci., 141, 127-142. https://doi.org/10.1016/j.ijmecsci.2018.03.041.
  40. Yousefzadeh, Sh., Jafari, A.A., Mohammadzadeh, A. and Najafi, M. (2018), "Dynamic response of functionally graded annular/circular plate in contact with bounded fluid under harmonic load", Struct. Eng. Mech., 65(5), 523-533. https://doi.org/10.12989/sem.2018.65.5.523.