참고문헌
- 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.
- 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.
- 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.
- ANSYS (2015) Swanson Analysis Systems Inc., Houston PA, USA.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Yaylaci, M. (2017), "Comparison between numerical and analytical solutions for the receding contact problem", Sigma J. Eng. Nat. Sci., 35(2), 333-346.
- 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.
- 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.
- 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.
- 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.
- 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.