Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analyzing the contact problem of a functionally graded layer resting on an elastic half plane with theory of elasticity, finite element method and multilayer perceptron

  • Yaylaci, Murat (Department of Civil Engineering, Recep Tayyip Erdogan University) ;
  • Yayli, Mujgen (Department of Civil Engineering, Recep Tayyip Erdogan University) ;
  • Yaylaci, Ecren Uzun (Surmene Faculty of Marine Science, Karadeniz Technical University) ;
  • Olmez, Hasan (Department of Marine Engineering Operations, Karadeniz Technical University) ;
  • Birinci, Ahmet (Department of Civil Engineering, Karadeniz Technical University)
  • Received : 2020.06.02
  • Accepted : 2021.04.12
  • Published : 2021.06.10
⟨ Previous Next ⟩

Abstract

This paper presents a comparative study of analytical method, finite element method (FEM) and Multilayer Perceptron (MLP) for analysis of a contact problem. The problem consists of a functionally graded (FG) layer resting on a half plane and pressed with distributed load from the top. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. The problem is reduced a system of integral equation in which the contact pressure are unknown functions. The numerical solution of the integral equation was carried out with Gauss-Jacobi integration formulation. Secondly, finite element model of the problem is constituted using ANSYS software and the two-dimensional analysis of the problem is carried out. The results show that contact areas and the contact stresses obtained from FEM provide boundary conditions of the problem as well as analytical results. Thirdly, the contact problem has been extended based on the MLP. The MLP with three-layer was used to calculate the contact distances. Material properties and loading states were created by giving examples of different values were used at the training and test stages of MLP. Program code was rewritten in C++. As a result, average deviation values such as 0.375 and 1.465 was obtained for FEM and MLP respectively. The contact areas and contact stresses obtained from FEM and MLP are very close to results obtained from analytical method. Finally, this study provides evidence that there is a good agreement between three methods and the stiffness parameters has an important effect on the contact stresses and contact areas.

Keywords

References

  1. Abanoz, M., Yaylaci, M. and Birinci, A. (2019), "Contact problems between a functionally graded layer and a rigid support", J. Struct. Eng. Appl. Mech., 2(1), 25-35. https://doi.org/10.31462/jseam.2019.01025035.
  2. Adiyaman, G., Birinci, A., Oner, E. and Yaylaci, M. (2016), "A receding contact problem between a functionally graded layer and two homogeneous quarter planes", Acta Mechanica, 227, 1753-1766. https://doi.org/10.1007/s00707-016-1580-y.
  3. Adiyaman, G., Oner, E. and Birinci, A. (2017), "Continuous and discontinuous contact problem of a functionally graded layer resting on a rigid foundation", Acta Mechanica, 228, 303-317. https://doi.org/10.1007/s00707-017-1871-y.
  4. Anil, O. and Uyaroglu, B. (2013), "Nonlinear finite element analysis of loading transferred from column to socket base", Comput. Concrete, 11(5), 475-492. https://doi.org/10.12989/cac.2013.11.5.475.
  5. ANSYS (2013), Mechanical APDL, ANSYS Contact Technology Guide, Ansys, Inc., Canonsburg, Pennsylvania, U.S.A.
  6. Arani, K.S., Zandi, Y., Pham, B.T., Mu'azu, M.A., Katebi, J., Mohammadhassani, M., Khalafi, S., Mohamad, E.T., Wakil, K. and Khorami, M. (2019), "Computational optimized finite element modelling of mechanical interaction of concrete with fiber reinforced polymer", Comput. Concrete, 23(1), 61-68. https://doi.org/10.12989/CAC.2019.23.1.061.
  7. Aydogmus, H.Y., Erdal, H.I., Karakurt, O., Namli, E., Turkan, Y. S. and Erdal, H. (2015), "A comparative assessment of bagging ensemble models for modeling concrete slump flow", Comput. Concrete, 16(5), 741-757. https://doi.org/10.12989/cac.2015.16.5.741.
  8. Bouderba, B. (2018), "Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory", Steel Compos. Struct., 27(3), 311-325. https://doi.org/10.12989/scs.2018.27.3.311.
  9. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085.
  10. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/GAE.2019.18.2.161.
  11. Cakiroglu, E., Comez, I. and Erdol, R. (2005), "Application of artificial neural networks to a double receding contact problem with a rigid stamp", Struct. Eng. Mech., 21(2), 205-220-205. http://dx.doi.org/10.12989/sem.2005.21.2.205.
  12. Chan, S.K. and Tuba, I.S. (1971), "A finite element method for contact problems of solid bodies-Part I. Theory and validation", Int. J. Mech. Sci., 13, 615-625.https://doi.org/10.1016/0020-7403(71)90032-4.
  13. Choi, H.J. (2009), "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. https://doi.org/10.1007/s12206-009-0734-4.
  14. 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.
  15. 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.
  16. Duy, H.T., Van, T.N. and Noh, H. C. (2014), "Eigen analysis of functionally graded beams with variable cross-section resting on elastic supports and elastic foundation", Struct. Eng. Mech., 52(5), 1033-1049. https://doi.org/10.12989/SEM.2014.52.5.1033.
  17. 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.
  18. Erdogan, F. and Guler, M.A. (2000), "Contact mechanics of FGM coatings", Project: Basic Problems on Fracture and Contact Mechanics of Functionally Graded Materials.
  19. Erdogan, F. and Gupta, G.D. (1972), "On the numerical solution of singular integral equations", Quart. J. Appl. Math., 29, 525-534. https://doi.org/10.1090/qam/408277
  20. Erdogan, F., Gupta, G.D. and Cook, T.S. (1973), "Numerical solution of singular integral equations, in methods of analysis and solution of crack problems", Noordhoff, Groningen.
  21. Gardner, M.W. and Dorling, S.R. (1998), "Artificial neural networks (The multilayer perceptron)-A review of applications in the atmospheric sciences", Atmosph. Envir., 32, 2627-2636. https://doi.org/10.1016/S1352-2310(97)00447-0.
  22. Gorski, J., Klepka, A., Dziedziech, K., Mrowka, J., Radecki, R. and Dworakowski, Z. (2020), "Identification of the stick and slip motion between contact surfaces using artificial neural networks", Nonlin. Dyn., 100, 225-242. https://doi.org/10.1007/s11071-020-05515-8
  23. 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.
  24. Hattori, G. and Serpa, A.L. (2015), "Contact stiffness estimation in ANSYS using simplified models and artificial neural networks", Finite Elem. Anal. Des., 97, 43-53. https://doi.org/10.1016/j.finel.2015.01.003.
  25. Hoque, M., Rattanawangcharoen, N., Shah, A.H. and Desai, Y.M. (2007), "3D nonlinear mixed finite-element analysis of RC beams and plates with and without FRP reinforcement", Comput. Concrete, 4(2), 135-156. https://doi.org/10.12989/cac.2007.4.2.135.
  26. Jahedi, R., Adibnazari, S. and Farrahi, G.H. (2014), "Performance analysis of functionally graded coatings in contact with cylindrical rollers", Adv. Mech. Eng., 7(2), 1-12. https://doi.org/10.1155/2014/456848.
  27. Jana, T., Mitra, A. and Sahoo, P. (2019), "Finite element-based contact analysis of a radially functionally graded hemisphere and a rigid flat", Int. J. Surf. Sci. Eng., 13(2-3), 156-180. https://doi.org/10.1504/IJSURFSE.2019.102366.
  28. Kavzoglu, T. (2001), "An investigation of the design and use of feedforward artificial neural networks in the classification of remotely sensed images", Ph.D. Dissertation, School of Geography, University of Nottingham.
  29. Kim, S. and Aboutaha, R.S. (2004), "Finite element analysis of carbon fiber-reinforced polymer (CFRP) strengthened reinforced concrete beams", Comput. Concrete, 1(4), 401-416. https://doi.org/10.12989/cac.2004.1.4.401.
  30. Krenk, S. (1975), "On quadrate formulas for singular integral-equations of 1st and 2nd kind", Quart. Appl. Math., 33(3), 225-232. https://doi.org/10.1090/qam/448967
  31. Lazzari, P.M., Filho, A.C., 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.
  32. Le Cun, Y., Denker, J.S. and Solla, S.A. (1990), "Optimal brain damage", Adv. Neur. Inform. Proc. Syst., 2, 598-605.
  33. Lezgy-Nazargah, M. (2015), "A three-dimensional exact state-space solution for cylindrical bending of continuously nonhomogenous piezoelectric laminated plates with arbitrary gradient composition", Arch. Mech., 67(1), 25-51.
  34. Lezgy-Nazargah, M. (2015), "Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach", Aerosp. Sci. Technol., 45, 154-164. https://doi.org/10.1016/j.ast.2015.05.006.
  35. Lezgy-Nazargah, M. and Cheraghi, N. (2017), "An exact Peano Series solution for bending analysis of imperfect layered FG neutral magneto-electro-elastic plates resting on elastic foundations", Mech. Adv. Mater. Struct., 24(3) 183-199. https://doi.org/10.1080/15376494.2015.1124951.
  36. Lezgy-Nazargah, M. and Meshkani, Z. (2018), "An efficient partial mixed finite element model for static and free vibration analyses of FGM plates rested on two-parameter elastic foundations", Struct. Eng. Mech., 66(5), 665-676. https://doi.org/10.12989/sem.2018.66.5.665.
  37. Lezgy-Nazargah, M., Divandar, S.M., Vidal, P. and Polit, O. (2017), "Assessment of FGPM shunt damping for vibration reduction of laminated composite beams", J. Sound Vib., 389, 101-118. https://doi.org/10.1016/j.jsv.2016.11.023.
  38. 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.
  39. Mazloom, M. and Yoosefi, M.M. (2013), "Predicting the indirect tensile strength of self-compacting concrete using artificial neural networks", Comput. Concrete, 12(3), 285-301. https://doi.org/10.12989/cac.2013.12.3.285.
  40. 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.
  41. Oner, E., Adiyaman, G. and Birinci, A.H.M.E.T. (2017), "Continuous contact problem of a functionally graded layer resting on an elastic half-plane", Arch. Mech., 69(1), 53-73. https://doi.org/10.24423/aom.2846.
  42. 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. http://doi.org/10.12989/sem.2015.54.4.607.
  43. Oztemel, E. (2003), Yapay Sinir Aglari, Papatya Yayincilik, Istanbul, Turkey.
  44. Pituba, J.J.C. and Neto, E.A.S (2015), "Modeling of unilateral effect in brittle materials by a mesoscopic scale approach", Comput. Concrete, 15(5), 735-758. https://doi.org/10.12989/cac.2015.15.5.735.
  45. Rapettoa, M.P., Almqvista, A., Larssona, R. and Lugt, P.M. (2009), "On the influence of surface roughness on real area of contact in normal, dry, friction free, rough contact by using a neural network", Wear, 266(5-6), 592-595. https://doi.org/10.1016/j.wear.2008.04.059.
  46. Rhimi, M., El-Borgi, S. and Lajnef, N. (2011), "A 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.
  47. Serafinska, A., Graf, W. and Kaliske, M. (2018), "Artificial neural networks-based friction law for elastomeric materials applied in finite element sliding contact simulations", Complexity-Complex Algorithms for Data-Driven Model Learning in Science and Engineering, 1-15.
  48. Shafiee, A.A., Daneshmand, F., Askari, E. and Mahzoon, M. (2014), "Dynamic behavior of a functionally graded plate resting on Winkler elastic foundation and in contact with fluid", Struct. Eng. Mech., 50(1), 53-71. https://doi.org/10.12989/sem.2014.50.1.053.
  49. Solberg, J.M., Jones, R.E. and Papadopoulos, P. (2007), "A family of simple two-pass dual formulations for the finite element solution of contact problems", Comput. Meth. Appl. Mech. Eng., 196, 782-802. https://doi.org/10.1016/j.cma.2006.05.011.
  50. Taj, M., Majeed, A., Hussain, M., Naeem, M. N., Safeer, M., Ahmad, M., Khan, H.U. and Tounsi, A. (2020), "Non-local orthotropic elastic shell model for vibration analysis of protein microtubules", Comput. Concrete, 25(3), 245-253. https://doi.org/10.12989/cac.2020.25.3.245.
  51. Tang, C.W., Lin, Y. and Kuo, S.F. (2007), "Investigation on correlation between pulse velocity and compressive strength of concrete using ANNs", Comput. Concrete, 4(6), 477-497. https://doi.org/10.12989/cac.2007.4.6.477.
  52. Trinh, T.H., Nguyen, D.K., Gan, B.S. and Alexandrov, S. (2016), "Post-buckling responses of elastoplastic FGM beams on nonlinear elastic foundation", Struct. Eng. Mech., 58(3), 515-532. https://doi.org/10.12989/sem.2016.58.3.515.
  53. Turan, M., Adiyaman, G., Kahya, V. and Birinci, A. (2016), "Axisymmetric analysis of a functionally graded layer resting on elastic substrate", Struct. Eng. Mech., 58(3),423-442. https://doi.org/10.12989/sem.2016.58.3.423.
  54. Uzun Yaylaci, E., Yaylaci, M., Olmez, H. and Birinci, A. (2020). "Artificial neural network calculations for a receding contact problem", Comput. Concrete, 25(6), 551-563. https://doi.org/10.12989/cac.2020.25.6.000.
  55. Xiaoqiang, R., Wujun, C., Gongyi, F. and Shilin, D. (2005), "Neural network model for solving elastoplastic contact problem", Chinese Journal of Applied Mechanics, 01.
  56. Yan, H., Jiang, Y., Zheng, J., Peng, C. and Li, Q. (2006). "A multilayer perceptron based medical decision support system for heart disease diagnosis", Exp. Syst. Appl., 30, 272-81. https://doi.org/10.1016/j.eswa.2005.07.022.
  57. Yan, J. and Li, X. (2015), "Double receding contact plane problem between a functionally graded layer and an elastic layer", Eur. J. Mech.-A/Solid., 53, 143-150. https://doi.org/10.1016/j.euromechsol.2015.04.001.
  58. Yan, J. and Mi, C. (2018), "On the receding contact between a homogeneous elastic layer and a half-plane substrate coated with FGMs", Int. J. Comput. Meth., 15(1), 1-21. https://doi.org/10.1142/S0219876218440085.
  59. Yan, J., Mi, C. and Liu, Z. (2017), "A semi-analytical and finite element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane", Math. Mech. Solid., 24(2), 448-464. https://doi.org/10.1177/1081286517744600.
  60. Yaylaci, M. and Avcar, M. (2020), "Finite element modeling of contact between an elastic layer and two elastic quarter planes", Comput. Concrete, 26(2), 107-114. https://doi.org/10.12989/cac.2020.26.2.107.
  61. Yaylaci, M., Oner, E., Adiyaman, G. and Birinci, A. (2019), "A Finite Element modelling for interface separation in contact problem of functionally graded layer and homogeneous half space", 3rd International Conference on Advanced Engineering Technologies-(ICADET-19), Bayburt, Turkey, September.
  62. Yaylaci, M., Terzi, C. and Avcar, M. (2019), "Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane", Struct. Eng. Mech., 72(6),775-783.https://doi.org/10.12989/sem.2019.72.6.775.

Cited by

  1. Influence of non-persistent joint sets on the failure behaviour of concrete under uniaxial compression test vol.28, pp.3, 2021, https://doi.org/10.12989/cac.2021.28.3.289