Structural Engineering and Mechanics

  • 제82권3호
  • /
  • Pages.401-416
  • /
  • 2022
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Solving the contact problem of functionally graded layers resting on a HP and pressed with a uniformly distributed load by analytical and numerical methods

  • Yaylaci, Murat (Department of Civil Engineering, Recep Tayyip Erdogan University) ;
  • Sabano, Bahar Sengul (Department of Civil Engineering, Karadeniz Technical University) ;
  • Ozdemir, Mehmet Emin (Department of Civil Engineering, Cankiri Karatekin University) ;
  • Birinci, Ahmet (Department of Civil Engineering, Karadeniz Technical University)
  • 투고 : 2021.10.20
  • 심사 : 2022.04.03
  • 발행 : 2022.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

The aim of this study is to examine the frictionless double receding contact problem for two functionally graded (FG) layers pressed with a uniformly distributed load and resting on a homogeneous half plane (HP) using analytical and numerical methods. The FG layers are made of a non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layers and FG layer-HP interface is frictionless. The body force of the FG layers and homogeneous HP are ignored in the study. Firstly, an analytical solution for the contact problem has been realized using the theory of elasticity and the Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using the ANSYS package program based on FEM. Numerical results for contact lengths and contact pressures between FG layers and FG layer-HP were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio, and the heights of the FG layers for both methods. The results obtained using FEM were compared with the results found using the analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

키워드

참고문헌

  1. 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(6), 1753-1766. https://doi.org/10.1007/S00707-016-1580-Y.
  2. 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(9), 3003-3017. https://doi.org/10.1007/s00707-017-1871-y.
  3. Aizikovich, S.M., Mitrin. B.I., Seleznev. N.M., Wang, Y.C., Volkov, S.S. (2016), "Influence of a soft FGM interlayer on contact stresses under a beam on an elastic foundation", Struct. Eng. Mech., 58(4), 613-625. https://doi.org/10.12989/sem.2016.58.4.613.
  4. Arani, K.S., Zandi, Y., Pham, B.T., Muazu, 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.
  5. Arani, A.G., Kolahchi, R. and Barzoki, A.A.M. (2011), "Effect of material in-homogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating shaft", Appl. Math. Model., 35(6), 2771-2789. https://doi.org/10.1016/j.apm.2010.11.076.
  6. 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.
  7. Azizkhani, M., Kadkhodapour, J., Anaraki, A.P., Hadavand, B.S. and Kolahchi, R. (2020), "Study of body movement monitoring utilizing nano-composite strain sensors contaning Carbon nanotubes and silicone rubber", Steel Compos. Struct., 35(6), 779-788. https://doi.org/10.12989/scs.2020.35.6.779.
  8. Benaberrahmane, I., Mekerbi, M., Bouiadjra, R.B., Benyoucef, S., Selim, M.M., Tounsi, A. and Hussain, M. (2021), "Analytical evaluation of frequencies of bidirectional FG thick beams in thermal environment and resting on different foundation", Struct. Eng. Mech., 80(4), 365-375. https://doi.org/10.12989/sem.2021.80.4.365.
  9. Cao, R., Li, L., Li, X. and Mi, C. (2021), "On the frictional receding contact between a graded layer and an orthotropic substrate indented by a rigid flat-ended stamp", Mech. Mater., 158, 103847. https://doi.org/10.1016/J.MECHMAT.2021.103847.
  10. 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(7), 615-625. https://doi.org/10.1016/0020-7403(71)90032-4.
  11. Damani, B., Fekrar, A., Selim, M.M., Benrahou, K.H., Benachour, A., Tounsi, A., Bedia, E.A. and Hussain, M. (2021), "Effect of material composition on bending and dynamic properties of FG plates using quasi 3D HSDT", Struct. Eng. Mech., 78(4), 439-453. https://doi.org/10.12989/sem.2021.78.4.439.
  12. Erdogan, F. and Gupta, G.D. (1972), "On the numerical solution of singular integral equations", Quart. Appl. Math., 29(4), 525-534. https://doi.org/10.1090/QAM/408277.
  13. Farrokhian, 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.
  14. Fu, J., Haeri, H., Sarfarazi, V., Asgari, K., Ebneabbasi, P., Marji, M.F. and Guo, M. (2021), "Extended finite element method simulation and experimental test on failure behavior of defects under uniaxial compression", Mech. Adv. Mater. Struct., 1-16. https://doi.org/10.1080/15376494.2021.1989730.
  15. Galin, L.A. (1946), "Three-dimensional contact problems of the theory of elasticity for punches with a circular planform", Prikladnaya Matematika I Mekhanika, 10, 425-448.
  16. Hadji, L., Madan, R., Bhowmick, S. and Tounsi, A. (2021), "A n-order refined theory for free vibration of sandwich beams with functionally graded porous layers", Struct. Eng. Mech., 79(3), 279-288. https://doi.org/10.12989/sem.2021.79.3.279.
  17. Haeri, H. and Sarfarazi, V. (2016), "Numerical simulation of tensile failure of concrete using Particle Flow Code (PFC)", Comput. Concrete, 18(1), 39-51. https://doi.org/10.12989/cac.2016.18.1.039.
  18. Haeri, H., Maleki, M., Shahvali, H., Sarfarazi, V. and Marji, M.F. (2021), "Evaluating the fragility curve in steel-concrete structure undergoing seismic progressive collapse by finite element method", Iran J. Sci. Tech. Trans. Civil Eng., 1-14. https://doi.org/10.1007/s40996-021-00764-y.
  19. Haeri, H., Sarfarazi, V., Ebneabbasi, P., Nazari maram, A., Shahbazian, A., Marji, M.F. and Mohamadi, A.R. (2020), "XFEM and experimental simulation of failure mechanism of non-persistent joints in mortar under compression", Constr. Build. Mater., 236, 117500. https://doi.org/10.1016/j.conbuildmat.2019.117500.
  20. Haeri, H., Sarfarazi, V., Marji, M.F., Hedayat, A. and Zhu, Z. (2016), "Experimental and numerical study of shear fracture in brittle materials with interference of initial double cracks", Acta Mechanica Solida Sinica, 29(5), 555-566. https://doi.org/10.1016/S0894-9166(16)30273-7.
  21. Haeri, H., Sarfarazi, V., Yazdani, M., Shemirani, A.B. and Hedayat, A. (2018), "Experimental and numerical investigation of the center-cracked horseshoe disk method for determining the mode I fracture toughness of rock-like material", Rock Mech. Rock Eng., 51, 173-185. https://doi.org/10.1007/s00603-017-1310-3.
  22. Haeri, H., Sarfarazi, V., Zhu, Z., Hedayat, A., Nezamabadi, M.F. and Karbala, M. (2018), "Simulation of crack initiation and propagation in three point bending test using PFC2D", Struct. Eng. Mech., 66(4), 453-463. https://doi.org/10.12989/sem.2018.66.4.453.
  23. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally graded-carbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., 1099636217720373. https://doi.org/10.1177/1099636217720373.
  24. Hertz, H. (1882), "Uber die Beruhrung fester elastischer Korper", Journal fur die reine und angewandte Mathematik, 92, 156-171. https://doi.org/10.1515/crll.1882.92.156.
  25. Huber, M.T. (1904), "Zur Theorie der Beruhrung fester elastischer Korper", Annalen Der Physik, 319(6), 153-163. https://doi.org/10.1002/ANDP.19043190611.
  26. Jang, Y.H. and Ahn, S. (2007), "Frictionally-excited thermoelastic instability in functionally graded material", Wear, 262(9-10), 1102-1112. https://doi.org/10.1016/J.WEAR.2006.11.011.
  27. Keshtegar, B., Farrokhian, A., Kolahchi, R. and Trung, N.T. (2020), "Dynamic stability response of truncated nanocomposite conical shell with magnetostrictive face sheets utilizing higher order theory of sandwich panels", Eur. J. Mech.-A/Solid., 82, 104010, https://doi.org/10.1016/j.euromechsol.2020.104010.
  28. Keshtegar, B., Tabatabaei, J., Kolahchi, R. and Trung, N.T. (2020), "Dynamic stress response in the nanocomposite concrete pipes with internal fluid under the ground motion load", Adv. Concrete Constr., 9(3), 327-335. https://doi.org/10.12989/acc.2020.9.3.327.
  29. Kolahchi, R., Keshtegar, B. and Trung, N.T. (2022), "Optimization of dynamic properties for laminated multiphase nanocomposite sandwich conical shell in thermal and magnetic conditions", J. Sandw. Struct. Mater., 24(1), 643-662. https://doi.org/10.1177/10996362211020388.
  30. Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023.
  31. 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.
  32. Koizumi, M. (1993), "Concept of FGM", Ceram. Trans., 34, 3-10.
  33. 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.
  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. Motezaker, M., Jamali, M. and Kolahchi, R. (2020), "Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocal-piezoelasticity theory", J. Comput. Appl. Math., 369, 112625. https://doi.org/10.1016/j.cam.2019.112625.
  36. Oner, E., Adiyaman, G. and Birinci, A. (2017), "Continuous contact problem of a functionally graded layer resting on an elastic half plane", Arch. Mech., 69(1), 53-73.
  37. Oner, E., Sengul Sabano, B., Uzun Yaylaci, E., Adiyaman, G., Yaylaci, M. and Birinci, A. (2022), "On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods", J. Appl. Math. Mech., 102(2), e202100287. https://doi.org/10.1002/zamm.202100287.
  38. Popov, G.Y. (1972), "Plates on a linearly elastic foundation (a survey)", Soviet Appl. Mech., 8(3), 231-242. https://doi.org/10.1007/BF00887434
  39. Sarfarazi, V. and Haeri, H. (2016), "A review of experimental and numerical investigations about crack propagation", Comput. Concrete, 18(2), 235-266. https://doi.org/10.12989/cac.2016.18.2.235.
  40. Sarfarazi, V. and Haeri, H. (2018), "Three-dimensional numerical modeling of effect of bedding layer on the tensile failure behavior in hollow disc models using Particle Flow Code (PFC3D)", Struct. Eng. Mech., 68(5), 537-547. https://doi.org/10.12989/sem.2018.68.5.537.
  41. Schubert, G. (1942), "Zur Frage der Druckverteilung unter elastisch gelagerten Tragwerken", Ingenieur-Archiv, 13(3), 132-147. https://doi.org/10.1007/BF02095912.
  42. Sneddon, I.N. (1965), "The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile", Int. J. Eng. Sci., 3(1), 47-57. https://doi.org/10.1016/0020-7225(65)90019-4.
  43. Taheri, M.N., Sabet, S.A. and Kolahchi, R. (2020), "Experimental investigation of self-healing concrete after crack using nanocapsules including polymeric shell and nanoparticles core", Smart Struct. Syst., 25(3), 337-343. https://doi.org/10.12989/sss.2020.25.3.337.
  44. Taherifar, R., Zareei, S.A., Bidgoli, M.R. and Kolahchi, R. (2021), "Application of differential quadrature and Newmark methods for dynamic response in pad concrete foundation covered by piezoelectric layer", J. Comput. Appl. Math., 382, 113075. https://doi.org/10.1016/j.cam.2020.113075.
  45. 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.
  46. 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.2020.25.6.551.
  47. Yan, J., Mi, C. and Liu, Z. (2017), "A semianalytical 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.
  48. Yaylaci, M., Adiyaman, E., Oner, E. and Birinci, A. (2020), "Examination of analytical and finite element solutions regarding contact of a functionally graded layer", Struct. Eng. Mech., 76(3), 325-336. https://doi.org/10.12989/sem.2020.76.3.325.
  49. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2021), "Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM", Comput. Concrete, 27(3), 199-210. https://doi.org/10.12989/cac.2021.27.3.199.
  50. Yaylaci, M., Eyuboglu, A., Adiyaman, G., Yaylaci Uzun, E., Oner, E. and Birinci, A. (2021), "Assessment of different solution methods for receding contact problems in functionally graded layered mediums", Mech. Mater., 154, 103730. https://doi.org/10.1016/J.MECHMAT.2020.103730.
  51. Yaylaci, M., Yayli M., Yaylaci Uzun, E., Olmez, H. and Birinci, A. (2021), "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", Struct. Eng. Mech., 78(5), 585-597. https://doi.org/10.12989/sem.2021.78.5.585.