Structural Engineering and Mechanics

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Three-dimensional modelling of functionally graded beams using Saint-Venant's beam theory

  • Khebizi, Mourad (Department of Civil Engineering, Mentouri University of Constantine) ;
  • Guenfoud, Hamza (Civil Engineering and Hydraulic Laboratory, University of Guelma) ;
  • Guenfoud, Mohamed (Civil Engineering and Hydraulic Laboratory, University of Guelma) ;
  • El Fatmi, Rached (University of Tunis El Manar, National Engineering School of Tunis)
  • Received : 2018.12.06
  • Accepted : 2019.06.02
  • Published : 2019.10.25
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Abstract

In this paper, the mechanical behaviour of functionally graded material beams is studied using the 3D Saint-Venant's theory, in which the section is free to warp in and out of its plane (Poisson's effects and out-of-plane warpings). The material properties of the FGM beam are distributed continuously through the thickness by several distributions, such as power-law distribution, exponential distribution, Mori-Tanaka schema and sigmoid distribution. The proposed method has been applied to study a simply supported FGM beam. The numerical results obtained are compared to other models in the literature, which show a high performance of the 3D exact theory used to describe the stress and strain fields in FGM beams.

Keywords

References

  1. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O.A. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057.
  2. Ben-Oumrane, S., Tounsi, A., Mechab, I., Bachir, B.M., Meradjah, M. and Adda, B.E.A. (2009), "A theoretical analysis of flexional bending of Al/$Al_2O_3$ S-FGM thick beams", Comput. Mater. Sci., 44, 1344-1350. https://doi.org/10.1016/j.commatsci.2008.09.001.
  3. Delale, F. and Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", J. Appl. Mech, 50(3), 609-614. https://doi.org/10.1115/1.3167098.
  4. Ebrahimi, F. and Barati, M.R. (2017), "Vibration analysis of embedded size dependent FG nanobeams based on third-order shear deformation beam theory", Struct. Eng. Mech., 61(6), 721-736. https://doi.org/10.12989/sem.2017.61.6.721.
  5. El Fatmi, R. (2012), "A Matlab tool to compute the mechanical characteristics of any composite section". Revue des Composites et des Materiaux Avances, 3, 395-413. https://doi.org/10.3166/rcma.22.395-413
  6. El Fatmi, R. (2016), "A Refined 1D beam theory built on 3D saintvenant's solution to compute homogeneous and composite beams", J. Mech. Mat.Struct., 11(4), 345-378. https://doi.org/10.2140/jomms.2016.11.345.
  7. El Fatmi, R. (2018), "Manuel de l'utilisateur du code", CSB Crosssection & beam analysis.
  8. El Fatmi, R. and Zenzri, H. (2002), "On the structural behavior and the Saint Venant solution in the exact beam theory Application to laminated composite beams", Comput. Struct., 80, 1441-1456. https://doi.org/10.1016/S0045-7949(02)00090-1.
  9. Filippi, M., Carrera, E. and Zenkour, A.M. (2015), "Static analyses of FGM beams by various theories and finite elements", Compos. Part B, 72, 1-9. https://doi.org/10.1016/j.compositesb.2014.12.004.
  10. Guenfoud, H. (2019), "Modelisation par elements finis speciaux des structures en materiaux a gradient fonctionnel", Ph.D. Dissertation, University of 8 Mai 1945, Guelma, Algeria.
  11. Guenfoud, H., Ziou, H., Himeur, M. and Guenfoud, M. (2016), "Analyses of a composite functionally graded material beam with a new transverse shear deformation function", J. Appl. Eng. Sci. Technol., 2(2), 105-113. http://revues.univbiskra.dz/index.php/jaest/article/view/1898.
  12. Hadji, L., Daouadji, T. H., Meziane, M. A. A., Tlidji, Y. and Bedia, E. A. A. (2016), "Analysis of functionally graded beam using a new first-order shear deformation theory". Struct. Eng. Mech., 57(2), 315-325. http://dx.doi.org/10.12989/sem.2016.57.2.315.
  13. 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-viscopiezoelasticity theories", J. Sandwich Struct. Mater. 0(00) 1-33. https://doi.org/10.1177/1099636217720373.
  14. Hosseini, H. and Kolahchi, R. (2018), "Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment", Physica E Low diemnsion. Syst. Nanostruct., 102, 101-109. https://doi.org/10.1016/j.physe.2018.04.037.
  15. Kaci, A., Belakhdar, K., Tounsi, A. and Bedia, E. A. A. (2014), "Nonlinear cylindrical bending analysis of E-FGM plates with variable thickness", Steel Compos. Struct., 16(4), 339-356. be.khalil@gmail.com. https://doi.org/10.12989/scs.2014.16.4.339
  16. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361.
  17. Karami, B., Janghorban, M. and Tounsi, A. (2018b) "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  18. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018c), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099.
  19. Karami, B., Shahsavari, D., Nazemosadat, S. M. R., LI, L. and Ebrahimi, A. (2018a), "Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation", Steel Compos. Struct. 29(3), 349-362. https://doi.org/10.12989/scs.2018.29.3.349.
  20. Khebizi M, Guenfoud H. and Guenfoud M. (2018), "Numerical modelling of soil-foundation interaction by a new non-linear macro-element", Geomech. Eng., 14(4), 377-386. https://doi.org/10.12989/gae.2018.14.4.000.
  21. Khebizi M. and Guenfoud M. (2015), "Numerical modelling of the damaging behaviour of the reinforced concrete structures by multi-layers beams elements", Comput. Concrete, 15(4), 547-562. https://doi.org/10.12989/cac.2015.15.4.547
  22. Khebizi M., Guenfoud H. and Guenfoud M. (2018), "Contribution to the damage modelling of reinforced concrete structures", MATEC Web of Conferences, 149. https://doi.org/10.1051/matecconf/201814901052.
  23. Kolahchi, R., Zarei, M. S., Hajmohammad, M. H., Nouri, A., (2017), "Wave propagation of embedded viscoelastic FG-CNTreinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039.
  24. Kolahchi, R., Bidgoli, A. M. M. and Heydari, M. M. (2015), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., 55(5), 1001-1014. http://dx.doi.org/10.12989/sem.2015.55.5.1001.
  25. Kolahchi, R., Keshtegar, B., Fakhar, M. H. (2017), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-viscopiezoelasticity theories using Grey Wolf algorithm", J. Sandwich Struct. Mater., 0(00) 1-25. https://doi.org/10.1177/1099636217731071.
  26. Kolahchi, R., Safari, M., 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.
  27. Ladevere, P. and Simmmonds, J. (1998), "Nous concepts for linear beam theory with arbitrary geometry and loading", Europ. J. Mech. A Solid., 17 (3), 377-402. https://doi.org/10.1016/S0997-7538(98)80051-X.
  28. Lahmar, M. (2017), "Equilibre thermo-elastique d'une poutre de section composite quelconque", Ph.D. Dissertation, El Manar University, Tunis.
  29. Lee, C.Y. and Kim, J.H. (2013), "Thermal post-buckling and snapthrough instabilities of FGM panels in hypersonic flows", Aerosp. Sci. Technol., 30, 175-182. https://doi.org/10.1016/j.ast.2013.08.001.
  30. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNTreinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel and Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889.
  31. Naccache, F. and El-Fatmi, R. (2018), "Buckling analysis of homogeneous or composite I-beams using a 1D refined beam theory built on Saint Venant's solution", Thin-Walled Struct., 127, 822-831. https://doi.org/10.1016/j.tws.2018.02.028.
  32. Nejad, M.Z., Hadi, A., Omidavari, A. and Rastgoo, A. (2018), "Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's non-local elasticity theory", Struct. Eng. Mech., 67(4), 417-425. https://doi.org/10.12989/sem.2018.67.4.417.
  33. Pradhan, K.K. and Chakraverty, S. (2013), "Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method", Compos. Part B, 51, 175-184. https://doi.org/10.1016/j.compositesb.2013.02.027.
  34. Sankar, B.V. (2001) "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61, 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0.
  35. Simsek, M. (2009), "Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method", Int. J. of Eng. Appl. Sci., 1(3), 1-11.
  36. Zenkour, A. M. (2007), "Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate", Arch. Appl. Mech., 77(4), 197-214. https://doi.org/10.1007/s00419-006-0084-y.
  37. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Modelling, 30, 67-84. https://doi.org/10.1016/j.apm.2005.03.009.
  38. Ziou, H. (2017), "Contribution a la modelisation des structures en Materiaux a Gradient Fonctionnel", Ph.D. Dissertation, Mohamed Khider University, Biskra, Algeria.
  39. Ziou, H., Guenfoud, H. and Guenfoud, M. (2016), "Numerical modelling of a Timoshenko FGM beam using the finite element method", Struct. Eng., 7(3), 239-261.
  40. Ziou, H., Guenfoud, H., Himeur, M. and Guenfoud, M. (2017a), "Numerical modeling of a Timoshenko FGM beam using the finite element method", Courrier du Savoir, 24, 59-66.
  41. Ziou, H., Guenfoud, H., Himeur, M., and Guenfoud, M. (2017b), "An efficient finite element model for vibration analysis of the FGM nonlocal based on Euler-Bernoulli beam theory", Congres Algerien de Mecanique, Constantine, Algeria, 26-30 November.