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Mathematical modelling and numerical study for buckling study in concrete beams containing carbon nanotubes

  • 투고 : 2020.05.05
  • 심사 : 2021.05.28
  • 발행 : 2021.06.25

초록

This paper deals with the mathematical modelling and numerical study for buckling analysis in concrete beams containing carbon nanotubes (CNTs). In order to modelling the concrete structure, Euler-Bernoulli beam is utilized. For assuming the influences of CNTs in the concrete beam and the agglomeration of CNTs, the Mori-Tanaka model is utilized. The principle of Hamilton is utilized for calculating the final equations and solved by two procedures of differential quadrature (DQ) and analytical method of Navier. The comparison of obtained results from DQ and Navier methods are shown the validation of this work. In addition, the outcomes are compared with other papers in the literature. The influences of boundary condition, CNT volume fraction, CNT agglomeration, length to thickness ratio and mode number are shown on the normalized buckling load. The outcome presents with enhancing the volume fraction of reinforcing the beam by nanoparticles, the buckling load of structure is improved. Indeed, the agglomeration of CNTs can reduces the buckling load and stability of beam.

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참고문헌

  1. Abu-Obeidah, A.S., Abdalla, J.A. and Hawileh, R.A. (2021), "Shear strengthening of deficient concrete beams with marine grade aluminium alloy plates", Adv. Concrete Constr., 7, 249-262. http://dx.doi.org/10.12989/acc.2019.7.4.249.
  2. Al-Furjan, M.S.H., Farrokhian, A., Mahmoud, S.R. and Kolahchi, R. (2021), "Dynamic deflection and contact force histories of graphene platelets reinforced conical shell integrated with magnetostrictive layers subjected to low-velocity impact", Thin Wall. Struct., 163, 107706. https://doi.org/10.1016/j.tws.2021.107706.
  3. Al-Kamal, M.K. (2019), "Nominal flexural strength of highstrength concrete beams", Adv. Concrete Constr., 7, 1-9. http://dx.doi.org/10.12989/acc.2019.7.1.001.
  4. Albegmprli, H.M., Eren Gulsan, M. and Cevik, A. (2021), "Comprehensive experimental investigation on mechanical behavior for types of reinforced concrete Haunched beam", Adv. Concrete Constr., 7, 39-50. http://dx.doi.org/10.12989/acc.2019.7.1.039.
  5. Arbabi, A., Kolahchi, R. and Rabani Bidgoli, M. (2017), "Concrete columns reinforced with Zinc Oxide nanoparticles subjected to electric field: buckling analysis", Wind. Struct., 24, 431-446. http://dx.doi.org/10.12989/was.2017.24.5.431.
  6. Asghar, S., Naeem, M.N., Hussain, M., Khadimallah, M.A., Hussain, M., Iqbal, Z. and Tounsi, A. (2020a), "Effect of chiral structure for free vibration of DWCNTs: Modal analysis", Adv. Concrete Constr., 9, 577-588. http://dx.doi.org/10.12989/acc.2020.9.6.577.
  7. Asghar, S., Naeem, M.N., Hussain, M., Taj, M. and Tounsi, A. (2020b), "Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis", Comput. Concrete, 25(2), 133-144. http://doi.org/10.12989/cac.2020.25.2.133.
  8. Belbachir, N., Bourada, M., Draiche, K., Tounsi, A., Bourada, F., Bousahla, A.A. and Mahmoud, S.R. (2020), "Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory", Smart Struct. Syst., 25(4), 409-422. http://dx.doi.org/10.12989/sss.2020.25.4.409.
  9. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F., Mahmoud, S.R., Adda Bedia, E.A. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. http://dx.doi.org/10.12989/scs.2020.34.5.643.
  10. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Adda Bedia, E.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concrete, 25(2), 155-166. http://doi.org/10.12989/cac.2020.25.2.155.
  11. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of - different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. http://dx.doi.org/10.12989/sss.2020.25.2.197.
  12. Brush, D.O. and Almroth, B.O. (1975), Buckling of Bars, Plates and Shells, McGraw-Hill, New York.
  13. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  14. Fattahi, A.M. and Safaei, B. (2017), "Buckling analysis of CNT-reinforced beams with arbitrary boundary conditions", Microsyst. Technol., 23, 5079-5091. https://doi.org/10.1007/s00542-017-3345-5.
  15. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Bucklings of carbon nanotube reinforced composites", J. Sound Vib., 329, 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020
  16. Hassan, A., Elkady, H. and Shaaban, I.G. (2019), "Effect of adding carbon nanotubes on corrosion rates and steel concrete bond", Sci. Rep., 9, 6285-6297. https://doi.org/10.1038/s41598-019-42761-2.
  17. Heidarzadeh, A., Kolahchi, R. and Rabani Bidgoli, M. (2017), "Concrete pipes reinforced with AL2O3 nanoparticles considering agglomeration: Magneto-thermo-mechanical stress analysis", Int. J. Civil Eng., 16(3), 315-322. https://doi.org/10.1007/s40999-016-0130-2.
  18. Hussain, M. (2020), "Application of Kelvin's approach for material structure of CNT: Polynomial volume fraction law", Struct. Eng. Mech., 76, 129-139. https://doi.org/10.12989/sem.2020.76.1.129.
  19. Hussain, M. and Naeem, M.N. (2020), "Vibration characteristics of zigzag FGM single-walled carbon nanotubes based on Ritz method with ring-stiffeners", Ind. J. Phy., 1-12. https://doi.org/10.1007/s12648-020-01894-1.
  20. Hussain, M., Naeem, M.N. and Tounsi, A. (2020a), "Analytical vibration of FG cylindrical shell with ring support based on various configurations", Adv. Concrete Constr., 9, 557-568. https://doi.org/10.12989/acc.2020.9.6.557.
  21. Hussain, M., Naeem, M.N. and Tounsi, A. (2020e), "Numerical Study for nonlocal vibration of orthotropic SWCNTs based on Kelvin's model", Adv. Concrete Constr., 9, 301-311. https://doi.org/10.12989/acc.2020.9.3.301.
  22. Hussain, M., Naeem, M.N., Asghar, S. and Tounsi, A. (2020b), "Eringen's nonlocal model sandwich with Kelvin's theory for vibration of DWCNT", Comput. Concrete, 25, 343-354. https://doi.org/10.12989/cac.2020.25.4.343.
  23. Hussain, M., Naeem, M.N., Khan, M.S. and Tounsi, A. (2020d), "Computer adid approach for modeling of FG cylindrical shell sandwich with ring supports", Comput. Concrete, 25(5), 411-425. https://doi.org/10.12989/cac.2020.25.5.411.
  24. Hussain, M., Naeem, M.N., Shahzad, A. and He, M. (2017), "Vibrational behavior of single-walled carbon nanotubes based on cylindrical shell model using wave propagation approach", AIP Adv., 7, 45114. https://doi.org/10.1063/1.4979112.
  25. Hussain, M., Naeem, M.N., Taj, M. and Tounsi, A. (2020c), "Simulating vibrations of vibration of single-walled carbon nanotube using Rayleigh-Ritz's method", Adv. Nano Res., 8(3), 215-228. https://doi.org/10.12989/anr.2020.8.3.215.
  26. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7, 431-442. https://doi.org/10.12989/anr.2019.7.6.431.
  27. Jafarian Arani, A. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17, 567-578. http://dx.doi.org/10.12989/cac.2016.17.5.567.
  28. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Adda Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and Free vibration analysis", Comput. Concrete, 25, 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  29. Kandekar, S.B. and Talikoti, R.S. (2020), "Torsional behaviour of reinforced concrete beams retrofitted with aramid fiber", Adv. Concrete Constr., 9, 1-7. https://doi.org/10.12989/acc.2020.9.1.001.
  30. Kolahchi, R. and Kolahdouzan, F. (2021), "A numerical method for magneto-hygro-thermal dynamic stability analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions", Appl. Mater. Model., 91, 458-475. https://doi.org/10.1016/j.apm.2020.09.060.
  31. Kolahchi, R., Rabani Bidgoli, M., Beygipoor, Gh. and Fakhar, M.H. (2013), "A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field", J. Mech. Sci. Tech., 5, 2342-2355. ttps://doi.org/10.1007/s12206-015-0811-9.
  32. 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.
  33. Le, V.P.N., Bui, D.V., Chu, T.H.V., Kim, I.T., Ahn, J.H. and Dao, D.K. (2016), "Behavior of steel and concrete composite beams with a newly puzzle shape of crestbond rib shear connector: an experimental study", Struct. Eng. Mech., 60, 1001-1019. http://dx.doi.org/10.12989/sem.2016.60.6.1001.
  34. Lei, Z.X., Zhang, L.W., Liew, K.M. and Yu, J.L. (2014), "Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method", Compos. Struct., 113, 328-338. https://doi.org/10.1016/j.compstruct.2014.03.035.
  35. Li, G.Y., Wang, P.M. and Zhao, X. (2005), "Mechanical behavior and microstructure of cement composites incorporating surfacetreated multi-walled carbon nanotubes", Carbon, 43, 1239-1245. https://doi.org/10.1016/j.carbon.2004.12.017.
  36. Liew, K.M., Lei, Z.X., Yu, J.L. and Zhang, L.W. (2014), "Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach", Comput. Meth. Appl. Mech. Eng., 268, 1-17. https://doi.org/10.1016/j.cma.2013.09.001.
  37. Mahi, A., Bedia, E.A.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free buckling analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045.
  38. Matsuna, H. (2007), "Buckling and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory", Int. J. Mech. Sci., 49, 1060-1075. https://doi.org/10.1016/j.ijmecsci.2006.11.008
  39. Medani M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32, 595-560. https://doi.org/10.12989/scs.2019.32.5.595.
  40. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181-190. http://dx.doi.org/10.12989/anr.2019.7.3.181.
  41. Mehar, K., Panda, S.K., Devarajana, Y. and Choubeya, G. (2020), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 240, 406-411. https://doi.org/10.1016/j.compstruct.2019.03.002
  42. Mehri, M., Asadi, H. and Wang, Q. (2016), "Buckling and buckling analysis of a pressurized CNT reinforced functionally graded truncated conical shell under an axial compression using HDQ method", Comput. Meth. Appl. Mech. Eng., 303, 75-100. https://doi.org/10.1016/j.cma.2016.01.017
  43. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metal. Mater., 21, 571- 574. https://doi.org/10.1016/0001-6160(73)90064-3
  44. Motezaker, M., Kolahchi, R., Rajak, D.K. and Mahmoud, S.R. (2021), "Influences of fiber reinforced polymer layer on the dynamic deflection of concrete pipes containing nanoparticle subjected to earthquake load", Polym. Compos., https://doi.org/10.1002/pc.26118.
  45. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Halim Benrahou, K. and Tounsi, A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comput. Concrete, 25(3), 225-244. https://doi.org/10.12989/cac.2020.25.3.225.
  46. Raj, S.D., Ganesan, N. and Abraham, R. (2021), "Role of fibers on the performance of geopolymer concrete exterior beam column joints", Adv. Concrete Constr., 9, 115-123. https://doi.org/10.12989/acc.2020.9.2.115.
  47. Refrafi. S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Effects of hygro-thermomechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4), 311-325. https://doi.org/10.12989/cac.2020.25.4.311.
  48. Safari Bilouei, B., Kolahchi, R. and Rabani Bidgoli, M. (2017), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18, 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053.
  49. Saribiyik, A. and Caglar, N. (2016), "Flexural strengthening of RC beams with low-strength concrete using GFRP and CFRP", Struct. Eng. Mech., 60, 825-845. http://dx.doi.org/10.12989/sem.2016.58.5.825.
  50. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., 7(2), 89-98. http://dx.doi.org/10.12989/anr.2019.7.2.089.
  51. Taj, M., Hussain, M., Afsar, M.A. and Tounsi, A. (2020), "Effects of elastic medium on buckling of microtubules due to bending and torsion", Adv. Concrete Constr., 18, 411-457. https://doi.org/10.12989/acc.2020.9.5.491.
  52. Taj, M., Hussain, M., Afsar, M.A. and Tounsi, A. (2020a), "Effects of elastic medium on buckling of microtubules due to bending and torsion", Adv. Concrete Constr., 18, 411-457. https://doi.org/10.12989/acc.2020.9.5.491.
  53. Taj, M., Majeed, A., Hussain, M., Naeem, M.N., Safeer, M., Ahmad, M., Khan, H.U. and Tounsi, A. (2020b), "Non-local orthotropic elastic shell model for vibration analysis of protein microtubules", Comput. Concrete, 25, 245-253. https://doi.org/10.12989/cac.2020.25.3.245.
  54. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., AlZahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermomechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  55. Wuite, J. and Adali, S. (2005), "Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis", Compos. Struct., 71, 388-396. https://doi.org/10.1016/j.compstruct.2005.09.011.
  56. Zamanian, M., Kolahchi, R. and Rabani Bidgoli, M. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nano-particles", Wind Struct., 24, 43-57. https://doi.org/10.12989/was.2017.24.1.043.