DOI QR코드

DOI QR Code

Finite element modeling of contact between an elastic layer and two elastic quarter planes

  • Yaylaci, Murat (Department of Civil Engineering, Recep Tayyip Erdogan University) ;
  • Avcar, Mehmet (Department of Civil Engineering, Suleyman Demirel University)
  • Received : 2020.05.19
  • Accepted : 2020.07.08
  • Published : 2020.08.25

Abstract

In this study, a two dimensional model of receding contact problem has been analyzed using finite element method (FEM) based software ANSYS and ABAQUS. For this aim finite element modeling of elastic layer and two homogeneous, isotropic and symmetrical elastic quarter planes pressed by means of a rigid circular punch has been presented. Mass forces and friction are neglected in the solution. Since the problem is examined for the plane state, the thickness along the z-axis direction is taken as a unit. In order to check the accuracy of the present models, the obtained results are compared with the available results of the open literature as well as the results of two software are compared using Root Mean Square Error (RMSE) and good agreements are found. Numerical analyses are performed considering different values of the external load, rigid circular radius, quarter planes span length and material properties. The contact lengths and contact stresses of these values are examined, and their results are presented. Consequently, it is concluded that the considered non-dimensional quantities have noteworthy influence on the contact lengths and contact stress distributions, additionally if FEM analysis is used correctly, it can be an efficient alternative method to the analytical solutions that need time.

Keywords

References

  1. ABAQUS (2017), ABAQUS/Standard: User's Manual, Dassault Systemes Simulia, Johnston, RI.
  2. Adiyaman, G., Birinci, A., Oner, E. and Yaylaci, M. (2016), "A receding contact problem between a functionally graded layer and two homogeneous quarter plane", Acta Mech., 227(6), 1753-1766. https://doi.org/10.1007/s00707-016-1580-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. Akgoz, B. and Civalek, O. (2015), "A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory", Acta Mech., 226, 2277-2294. https://doi.org/10.1007/s00707-015-1308-4.
  5. Aksogan, O., Akavci, S. and Becker, A.A. (1996), "A comparative study of the contact problem of an elastic layer supported by two elastic quarter planes", J. Fac. Eng. Arch. Cukurova Univ., 11, 25-31.
  6. Aksogan, O., Akavci, S. and Becker, A.A. (1997), "The solution of the nonsymmetrical contact problem of an elastic layer supported by two elastic quarter planes using three different methods", J. Fac. Eng. Arch. Cukurova Univ., 12, 1-14.
  7. Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by $SiO_2$ nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140.
  8. ANSYS (2013), Swanson Analysis Systems Inc., Houston, PA, USA.
  9. Arbabi, A., Kolahchi, R. and Bidgoli, M.R. (2020), "Experimental study for ZnO nanofibers effect on the smart and mechanical properties of concrete", Smart Struct. Syst., 25(1), 97-104. https://doi.org/10.12989/sss.2020.25.1.097.
  10. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  11. Cakiroglu, A.O. and Cakiroglu, F.L. (1991), "Continuous and discontinuous contact problems for strips on an elastic semi-infinite plane", Int. J. Eng. Sci., 29(1), 99-111. https://doi.org/10.1016/0020-7225(91)90080-M.
  12. Civalek, O. and Demir, C. (2016) "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method", Appl. Math. Comput., 289, 335-352. https://doi.org/10.1016/j.amc.2016.05.034.
  13. Comez, I., Kahya, V. and Erdol, R. (2018), "Plane receding contact problem for a functionally graded layer supported by two quarter-planes". Arch. Mech., 70(6), 485-504. https://doi.org/10.24423/aom.2846.
  14. Erdogan, F. and Ratwani, M. (1974), "The contact problem for an elastic layer supported by two elastic quarter planes", ASME J. Appl. Mech., 41(3), 673-677. https://doi.org/10.1115/1.3423369.
  15. Farokhian, A. and Kolahchi, R. (2020), "Frequency and instability responses in nanocomposite plate assuming different distribution of CNTs", Struct. Eng. Mech., 73(5), 555-563. https://doi.org/10.12989/sem.2020.73.5.555.
  16. Gandhi, V.C., Kumaravelan, R., Ramesh, S. and Sriram, K. (2015), "Analysis of material dependency in an elastic-plastic contact models using contact mechanics approach", Struct Eng. Mech., 53(5), 1051-1066. https://doi.org/10.12989/sem.2015.53.5.1051.
  17. Ghamari, A., Kurdi, J., Shemirani, A.B. and Haeri, H. (2020), "Experimental investigating the properties of fiber reinforced concrete by combining different fibers", Comput. Concrete, 25(6), 509-516. https://doi.org/10.12989/cac.2020.25.6.509.
  18. Guler, M.A. and Erdogan, F. (2004), "Contact mechanics of graded coatings", Int. J. Solid. Struct., 41(14), 3865-3889. https://doi.org/10.1016/j.ijsolstr.2004.02.025.
  19. Gurses, M., Akgoz, B. and Civalek, O. (2012), "Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation", Appl. Math. Comput., 219, 3226-3240. https://doi.org/10.1016/j.amc.2012.09.062.
  20. Haeri, H. and Marji, M.F. (2016), "Simulating the crack propagation and cracks coalescence underneath TBM disc cutters", Arab. J. Geosci., 9(2), 124. https://doi.org/10.1007/s12517-015-2137-4.
  21. Haeri, H. and Sarfarazi, V. (2016), "The deformable multilaminate for predicting the elasto-plastic behavior of rocks", Comput. Concrete, 18(2), 201-214. https://doi.org/10.12989/cac.2016.18.2.201.
  22. Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Nouri, A.H. (2019), "Dynamic response of auxetic honeycomb plates integrated with agglomerated CNT-reinforced face sheets subjected to blast load based on visco-sinusoidal theory", Int. J. Mech. Sci., 153, 391-401. https://doi.org/10.1016/j.ijmecsci.2019.02.008.
  23. Hanson, M.T. and Keer, L.M. (1989), "Stress analysis and contact problems for an elastic quarter-plane", Q. J. Mech. Appl. Math., 42(3), 364-383. https://doi.org/10.1093/qjmam/42.3.364.
  24. Hertz, H. (1881), "On the contact of elastic solids", J. Reine Angew. Math., 92, 156-171. Translated and reprinted in English in Hertz's Miscellaneous Papers, Macmillan & Co., London, 1896, Ch. 5.
  25. Hertz, H. (1882), "On hardness", Verh. Ver. Beforderung Gewerbe Fleisses 61, 410. Translated and reprinted in English in Hertz's Miscellaneous Papers, Macmillan &Co, London, 1896, Ch. 6.
  26. Hussain, M., Naeem, M.N., Khan, M.S. and Tounsi, A. (2020), "Computer-aided approach for modelling of FG cylindrical shell sandwich with ring supports", Comput. Concrete, 25(5), 411-425. https://doi.org/10.12989/cac.2020.25.5.411.
  27. Kahya, V., Ozsahin, T.S., Birinci, A. and Erdol, R. (2007), "A receding contact problem for an anisotropic elastic medium consisting of a layer and a half plane", Int. J. Solid. Struct., 44(17), 5695-5710. https://doi.org/10.1016/j.ijsolstr.2007.01.020.
  28. Keer, L.M., Dundurs, J. and Tsai, K.C. (1972), "Problem involving a receding contact problem between a layer and half space", ASME J. Appl. Mech., 39(4), 1115-1120. https://doi.org/10.1115/1.3422839.
  29. Keer, L.M., Lee, J.C. and Mura, T. (1984), "A contact problem for the elastic quarter space", Int. J. Solid. Struct., 20(5), 513-524. https://doi.org/10.1016/0020-7683(84)90016-7.
  30. Kolahchi, R., Zhu, S.P., Keshtegar, B. and Trung, N.T. (2020), "Dynamic buckling optimization of laminated aircraft conical shells with hybrid nanocomposite martial", Aerosp. Sci. Technol., 98, 105656. https://doi.org/10.1016/j.ast.2019.105656.
  31. Kuo, C.H. (2008), "Contact stress analysis of an elastic half-plane containing multiple inclusions", Int. J. Solid. Struct., 45(16), 4562-4573. https://doi.org/10.1016/j.ijsolstr.2008.03.032.
  32. Lazzari, P.M., Lazzari, B.M. and Pacheco, A.R. (2017), "Structural analysis of a prestressed segmented girder using contact elements in ANSYS", Comput. Concrete, 20(3), 319-327. https://doi.org/10.12989/cac.2017.20.3.319.
  33. Liu, C.H., Cheng, I., Tsai, A.C., Wang, L.J. and Hsu, J.Y. (2010), "Using multiple point constraints in finite element analysis of two-dimensional contact problems", Struct. Eng. Mech., 36(1), 95-110. https://doi.org/10.12989/sem.2010.36.1.095.
  34. Liu, Z., Yan, J. and Mi, C. (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.
  35. Oner, E., Yaylaci, M. and Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from FEM", Struct. Eng. Mech., 54(4), 607-622. https://doi.org/10.12989/sem.2015.54.4.607.
  36. Pindera, M.J. and Lane, M.S. (1993), "Frictionless contact of layered half-planes analysis Part I: Analysis", J. Appl. Mech., 60(3), 633-639. https://doi.org/ 10.1115/1.2900851.
  37. Ratwani, M. and Erdogan, F. (1973), "On the plane contact problem for a frictionless elastic layer", Int.J. Solid. Struct., 9(8), 921-936. https://doi.org/10.1016/0020-7683(73)90021-8.
  38. Rhimi, M., El-Borgi, S. and Lajnef, N. (2011), "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.
  39. Rhimi, M., El-Borgi, S., Said, B.W. and Jemaa, B.F. (2009), "A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate", Int. J. Solid. Struct., 46(20), 3633-3642. https://doi.org/10.1016/j.ijsolstr.2009.06.008.
  40. Shrestha, R., Smith, S.T. and Samali, B. (2013), "Finite element modelling of FRP-strengthened RC beam-column connections with ANSYS", Comput. Concrete, 11(1), 1-20. https://doi.org/10.12989/cac.2013.11.1.001.
  41. Spence, D.A. (1975), "The Hertz contact problem with finite friction", J. Elasticit., 5(3-4), 297-319. https://doi.org/10.1007/BF00126993.
  42. Stoner, J.G. and Polak, M.A. (2020), "Finite element modelling of GFRP reinforced concrete beams", Comput. Concrete, 25(4), 369-382. https://doi.org/10.12989/cac.2020.25.4.369.
  43. Taherifar, R., Mahmoudi, M., Nasr Esfahani, M.H., Khuzani, N.A., Esfahani, S.N. and Chinaei, F. (2019), "Buckling analysis of concrete plates reinforced by piezoelectric nanoparticles", Comput. Concrete, 23(4), 295-301. https://doi.org/10.12989/cac.2019.23.4.295.
  44. Tigdemir, M., Jafarzadyeganeh, M., Bayrak, M.C. and Avcar, M. (2018), "Numerical modelling of wheel on the snow", Int. J. Eng. Appl. Sci., 10(2), 64-72. http://dx.doi.org/10.24107/ijeas.437861.
  45. Vasiliev, A.S., Volkov, S.S., Aizikovich, S.M. and Mitrin, B.I. (2017), "Plane contact problem on indentation of a flat punch into a transversely-isotropic half-plane with functionally graded transversely-isotropic coating", Z. Angew. Math. Phys., 68(1), 4. https://doi.org/10.1007/s00033-016-0746-8.
  46. Vasudevan, G. and Kothandaraman, S. (2015), "RC beams retrofitted using external bars with additional anchorages-a finite element study", Comput. Concrete, 16(3), 415-428. https://doi.org/10.12989/cac.2015.16.3.415.
  47. 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.
  48. Yaylaci, M., Bayrak, M.C. and Avcar, M. (2019b), "Finite element modeling of receding contact problem", Int. J. Eng. Appl. Sci., 11(4), 468-475. https://doi.org/10.24107/ijeas.646718.
  49. Yaylaci, M., Oner, E. and Birinci, A. (2014), "Comparison between analytical and ANSYS calculations for a receding contact problem", ASCE J. Eng. Mech., 140(9), 1-10. https://doi.org/ 10.1061/(ASCE)EM.1943-7889.0000781.
  50. Yaylaci, M., Terzi, C. and Avcar, M. (2019a) "Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane", Struct. Eng. Mech., 72(6), 775. https://doi.org/10.12989/sem.2019.72.6.775.
  51. Zhang, Y., Zhao, K., Li, Y., Gu, J., Ye, Z. and Ma, J. (2018), "Study on the local damage of SFRC with different fraction under contact blast loading", Comput. Concrete, 22(1), 63-70. https://doi.org/10.12989/cac.2018.22.1.063.
  52. Zhou, S. and Gao, X.L. (2013), "Solutions of half-space and half-plane contact problems based on surface elasticity", Z. Angew. Math. Phys., 64(1), 145-166. https://doi.org/10.1007/s00033-012-0205-0.

Cited by

  1. Study of tensile behavior of Y shape non-persistent joint using experimental test and numerical simulation vol.26, pp.6, 2020, https://doi.org/10.12989/cac.2020.26.6.565
  2. Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation vol.38, pp.1, 2020, https://doi.org/10.12989/scs.2021.38.1.001
  3. Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position vol.39, pp.1, 2021, https://doi.org/10.12989/scs.2021.39.1.051
  4. On the free vibration response of laminated composite plates via FEM vol.39, pp.2, 2020, https://doi.org/10.12989/scs.2021.39.2.149
  5. Thermoelastic response of functionally graded sandwich plates using a simple integral HSDT vol.91, pp.7, 2020, https://doi.org/10.1007/s00419-021-01973-7
  6. An efficient higher order shear deformation theory for free vibration analysis of functionally graded shells vol.40, pp.2, 2020, https://doi.org/10.12989/scs.2021.40.2.307
  7. Z shape joints under uniaxial compression vol.12, pp.2, 2020, https://doi.org/10.12989/acc.2021.12.2.105