Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Mathematical modelling of the stability of carbon nanotube-reinforced panels

  • Sobhani Aragh, B. (Young Researchers and Elite Club, Arak Branch, Islamic Azad University)
  • Received : 2017.01.21
  • Accepted : 2017.06.02
  • Published : 2017.08.30
⟨ Previous Next ⟩

Abstract

The present paper studies the stability analysis of the continuously graded CNT-Reinforced Composite (CNTRC) panel stiffened by rings and stringers. The Stiffened Panel (SP) subjected to axial and lateral loads is reinforced by agglomerated CNTs smoothly graded through the thickness. A two-parameter Eshelby-Mori-Tanaka (EMT) model is adopted to derive the effective material moduli of the CNTRC. The stability equations of the CNRTC SP are obtained by means of the adjacent equilibrium criterion. Notwithstanding most available literature in which the stiffener effects were smeared out over the respective stiffener spacing, in the present work, the stiffeners are modeled as Euler-Bernoulli beams. The Generalized Differential Quadrature Method (GDQM) is employed to discretize the stability equations. A numerical study is performed to investigate the influences of different types of parameters involved on the critical buckling of the SP reinforced by agglomerated CNTs. The results achieved reveal that continuously distributing of CNTs adjacent to the inner and outer panel's surface results in improving the stiffness of the SP and, as a consequence, inclining the critical buckling load. Furthermore, it has been concluded that the decline rate of buckling load intensity factor owing to the increase of the panel angle is significantly more sensible for the smaller values of panel angle.

Keywords

References

  1. Bich, D.H., Van Dung, D., Nam, V.H. and Phuong, N.T. (2013), "Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression", Int. J. Mech. Sci., 74, 190-200. https://doi.org/10.1016/j.ijmecsci.2013.06.002
  2. Bououdina, M. (Editor) (2014), Handbook of Research on Nanoscience, Nanotechnology, and Advanced Materials, IGI Global.
  3. Brush, D.O. and Almroth, B.O. (1975), Buckling of Bars, Plates, and Shells, McGraw-Hill Book Co., New York, NY, USA, 394 p.
  4. Cristescu, N.D., Craciun, E.M. and Soos, E. (2003), Mechanics of Elastic Composites, CRC Press.
  5. Duc, N.D. and Thang, P.T. (2014), "Nonlinear buckling of imperfect eccentrically stiffened metal-ceramic-metal S-FGM thin circular cylindrical shells with temperature-dependent properties in thermal environments", Int. J. Mech. Sci., 81, 17-25. https://doi.org/10.1016/j.ijmecsci.2014.01.016
  6. Dung, V.D. and Chan, D.Q. (2017), "Analytical investigation on mechanical buckling of FGM truncated conical shells reinforced by orthogonal stiffeners based on FSDT", Compos. Struct., 159, 827-841. https://doi.org/10.1016/j.compstruct.2016.10.006
  7. Dung, V.D. and Hoa, K.L. (2013), "Research on nonlinear torsional buckling and post-buckling of eccentrically stiffened functionally graded thin circular cylindrical shells", Compos. Part B: Eng., 51, 300-309. https://doi.org/10.1016/j.compositesb.2013.03.030
  8. Eshelby, J.D. (1957), "The determination of the elastic field of an ellipsoidal inclusion, and related problems", Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society of London, August, Vol. 241, No. 1226, pp. 376-396.
  9. Fantuzzi, N., Tornabene, F., Bacciocchi, M. and Dimitri, R. (2016), "Free vibration analysis of arbitrarily shaped functionally graded carbon nanotube-reinforced plates", Compos. Part B: Eng., 115, 384-408.
  10. Fidelus, J.D., Wiesel, E., Gojny, F.H., Schulte, K. and Wagner, H.D. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nano-composites", Compos. Part A: Appl. Sci. Manuf., 36(11), 1555-1561. https://doi.org/10.1016/j.compositesa.2005.02.006
  11. Formica, G. and Lacarbonara, W. (2017), "Three-dimensional modeling of interfacial stick-slip in carbon nanotube nanocomposites", Int. J. Plastic., 88, 204-217. https://doi.org/10.1016/j.ijplas.2016.10.012
  12. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329(10), 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020
  13. Garcia-Macias, E., Rodriguez-Tembleque, L., Castro-Triguero, R. and Saez, A. (2017), "Buckling analysis of functionally graded carbon nanotube-reinforced curved panels under axial compression and shear", Compos. Part B: Eng., 108, 243-256. https://doi.org/10.1016/j.compositesb.2016.10.002
  14. Gkikas, G., Barkoula, N.M. and Paipetis, A.S. (2012), "Effect of dispersion conditions on the thermo-mechanical and toughness properties of multi walled carbon nanotubes-reinforced epoxy", Compos. Part B: Eng., 43(6), 2697-2705. https://doi.org/10.1016/j.compositesb.2012.01.070
  15. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Computat. Mater. Sci., 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011
  16. Hedayati, H. and Sobhani Aragh, B. (2012), "Influence of graded agglomerated CNTs on vibration of CNT-reinforced annular sectorial plates resting on Pasternak foundation", Appl. Math. Computat., 218(17), 8715-8735. https://doi.org/10.1016/j.amc.2012.01.080
  17. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0
  18. Kamarian, S., Salim, M., Dimitri, R. and Tornabene, F. (2016), "Free vibration analysis of conical shells reinforced with agglomerated carbon nanotubes", Int. J. Mech. Sci., 108, 157-165.
  19. Lei, Z.X., Liew, K.M. and Yu, J.L. (2013), "Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method", Compos. Struct., 98, 160-168. https://doi.org/10.1016/j.compstruct.2012.11.006
  20. Lim, C.W., Ma, Y.F., Kitipornchai, S., Wang, C.M. and Yuen, R.K. (2003), "Buckling of vertical cylindrical shells under combined end pressure and body force", J. Eng. Mech., 129(8), 876-884. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:8(876)
  21. Low, I.M. (Editor) (2014), Advances in Ceramic Matrix Composites, Woodhead Publishing.
  22. 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 Compos. Struct., Int. J., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  23. Meguid, S.A. and Sun, Y. (2004), "On the tensile and shear strength of nano-reinforced composite interfaces", Mater. Des., 25(4), 289-296. https://doi.org/10.1016/j.matdes.2003.10.018
  24. Mehrabadi, S.J. and Sobhani Aragh, B. (2014), "Stress analysis of functionally graded open cylindrical shell reinforced by agglomerated carbon nanotubes", Thin-Wall. Struct., 80, 130-141. https://doi.org/10.1016/j.tws.2014.02.016
  25. Mo, C.B., Cha, S.I., Kim, K.T., Lee, K.H. and Hong, S.H. (2005), "Fabrication of carbon nanotube reinforced alumina matrix nano-composite by sol-gel process", Mater. Sci. Eng.: A, 395(1), 124-128. https://doi.org/10.1016/j.msea.2004.12.031
  26. Moradi-Dastjerdi, R. (2016), "Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube", Struct. Eng. Mech., Int. J., 57(3), 441-456. https://doi.org/10.12989/sem.2016.57.3.441
  27. Moradi-Dastjerdi, R. and Momeni-Khabisi, H. (2016), "Dynamic analysis of functionally graded nanocomposite plates reinforced by wavy carbon nanotube", Steel Compos. Struct., Int. J., 22(2), 277-299. https://doi.org/10.12989/scs.2016.22.2.277
  28. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metal., 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  29. Najafizadeh, M.M., Hasani, A. and Khazaeinejad, P. (2009), "Mechanical stability of functionally graded stiffened cylindrical shells", Appl. Math. Model., 33(2), 1151-1157. https://doi.org/10.1016/j.apm.2008.01.009
  30. Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P., Nguyen-Xuan, H. and Vo, T.P. (2017), "A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory", Comput. Method. Appl. Mech. Eng., 313, 904-940. https://doi.org/10.1016/j.cma.2016.10.002
  31. Odegard, G.M., Gates, T.S., Wise, K.E., Park, C. and Siochi, E.J. (2003), "Constitutive modeling of nanotube-reinforced polymer composites", Compos. Sci. Technol., 63(11), 1671-1687. https://doi.org/10.1016/S0266-3538(03)00063-0
  32. Phung-Van, P., Abdel-Wahab, M., Liew, K.M., Bordas, S.P. and Nguyen-Xuan, H. (2015), "Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory", Compos. Struct., 123, 137-149. https://doi.org/10.1016/j.compstruct.2014.12.021
  33. Phung-Van, P., Ferreira, A.J., Nguyen-Xuan, H. and Wahab, M.A. (2017a), "An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates", Compos. Part B: Eng., 118, 125-134. https://doi.org/10.1016/j.compositesb.2017.03.012
  34. Phung-Van, P., Lieu, Q.X., Nguyen-Xuan, H. and Wahab, M.A. (2017b), "Size-dependent isogeometric analysis of functionally graded carbon nanotube-reinforced composite nanoplates", Compos. Struct., 166, 120-135. https://doi.org/10.1016/j.compstruct.2017.01.049
  35. Reddy, J.N. (1984), "A refined nonlinear theory of plates with transverse shear deformation", Int. J. Solids Struct., 20(9), 881-896. https://doi.org/10.1016/0020-7683(84)90056-8
  36. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
  37. Reddy, J.N. and Chin, C.D. (1998), "Thermo-mechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626. https://doi.org/10.1080/01495739808956165
  38. Selim, B.A., Zhang, L.W. and Liew, K.M. (2015), "Vibration analysis of CNT reinforced functionally graded composite plates in a thermal environment based on Reddy's higher-order shear deformation theory", Compos. Struct., 156, 276-290.
  39. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  40. Shen, H.S. (2011), "Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells", Compos. Struct., 93(8), 2096-2108. https://doi.org/10.1016/j.compstruct.2011.02.011
  41. Shen, H.S. (2012), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells", Compos. Part B: Eng., 43(3), 1030-1038. https://doi.org/10.1016/j.compositesb.2011.10.004
  42. Shen, H.S. (2016), Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press.
  43. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotubereinforced composite plates", Mater. Des., 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048
  44. Shi, D.L., Feng, X.Q., Huang, Y.Y., Hwang, K.C. and Gao, H. (2004), "The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites", J. Eng. Mater. Technol., 126(3), 250-257. https://doi.org/10.1115/1.1751182
  45. Shu, C. (2012), Differential Quadrature and its Application in Engineering, Springer Science & Business Media.
  46. Sobhaniaragh, B. (2014), "Vibration and thermal stress analyses of functionally graded materials", Ph.D. Dissertation; Ghent University, Belgium.
  47. Sobhani Aragh, B., Barati, A.N. and Hedayati, H. (2012), "Eshelby-Mori-Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels", Compos. Part B: Eng., 43(4), 1943-1954. https://doi.org/10.1016/j.compositesb.2012.01.004
  48. Sobhani Aragh, B., Farahani, E.B. and Barati, A.N. (2013), "Natural frequency analysis of continuously graded carbon nanotube-reinforced cylindrical shells based on third-order shear deformation theory", Math. Mech. Solids, 18(3), 264-284. https://doi.org/10.1177/1081286512438794
  49. Talo, M., Krause, B., Pionteck, J., Lanzara, G. and Lacarbonara, W. (2016), "An updated micromechanical model based on morphological characterization of carbon nanotube nanocomposites", Compos. Part B: Eng., 115, 70-78.
  50. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2016), "Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells", Compos. Part B: Eng., 89, 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016
  51. Tran, L.V., Phung-Van, P., Lee, J., Wahab, M.A. and Nguyen-Xuan, H. (2016), "Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates", Compos. Struct., 140, 655-667. https://doi.org/10.1016/j.compstruct.2016.01.001
  52. Wang, C.Y. and Zhang, L.C. (2008), "A critical assessment of the elastic properties and effective wall thickness of single-walled carbon nanotubes", Nanotechnology, 19(7), 075705. https://doi.org/10.1088/0957-4484/19/7/075705
  53. Wang, M., Li, Z.M. and Qiao, P. (2016), "Semi-analytical solutions to buckling and free vibration analysis of carbon nanotube-reinforced composite thin plates", Compos. Struct., 144, 33-43. https://doi.org/10.1016/j.compstruct.2016.02.025
  54. Zhang, L.W., Lei, Z.X. and Liew, K.M. (2015), "An element-free IMLS-Ritz framework for buckling analysis of FG-CNT reinforced composite thick plates resting on Winkler foundations", Eng. Anal. Boundary Elem., 58, 7-17. https://doi.org/10.1016/j.enganabound.2015.03.004
  55. Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010