DOI QR코드

DOI QR Code

Effect of laminate configuration on the free vibration/buckling of FG Graphene/PMMA composites

  • Received : 2019.06.03
  • Accepted : 2019.10.01
  • Published : 2020.02.25

Abstract

In this research, buckling and free vibration of rectangular polymeric laminate reinforced by graphene sheets are investigated. Various patterns are considered for augmentation of each laminate. Critical buckling load is evaluated for different parameters, including boundary conditions, reinforcement pattern, loading regime, and laminate geometric states. Furthermore, vibration analysis is investigated for square laminate. Elastic properties of the composite are calculated using a combination of both molecular dynamics (MD) and the rule of mixture (MR). Kinematics of the plate is approximated based on the first shear deformation theory (FSDT). The current analysis is performed based on the energy method. For the numerical investigation, Ritz method is applied, and for shape functions, Chebyshev polynomials are utilized. It is found that the number of layers is effective on the buckling load and natural frequency of laminates which made from non-uniform layers.

Keywords

References

  1. Akgoz, B. and Civalek, O. (2017), "A size-dependent beam model for stability of axially loaded carbon nanotubes surrounded by Pasternak elastic foundation", Compos. Struct., 176, 1028-1038. https://doi.org/10.1016/j.compstruct.2017.06.039
  2. Akgoz, B. and Civalek, O. (2018), "Vibrational characteristics of embedded microbeams lying on a two-parameter elastic foundation in thermal environment", Compos. Part B: Eng., 150, 68-77. https://doi.org/10.1016/j.compositesb.2018.05.049
  3. Alibeigi, B., Tadi Beni, Y. and Mehralian, F. (2018), "On the thermal buckling of magneto-electro-elastic piezoelectric nanobeams", Eur. Phys. J. Plus, 133, 133. https://doi.org/10.1140/epjp/i2018-11954-7
  4. Aydogdu, M. (2014), "On the vibration of aligned carbon nanotube reinforced composite beams", Adv. Nano Res., Int. J., 2(4), 199-210. https://doi.org/10.12989/ANR.2014.2.4.199
  5. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., Int. J., 3(1), 29-37. https://doi.org/10.12989/ANR.2015.3.1.029
  6. Chen, S., Sun, S., Li, C., Pittman, C.U., Lacy, T.E., Hu, S. and Gwaltney, S.R. (2018), "Molecular dynamics simulations of the aggregation behaviour of overlapped graphene sheets in linear aliphatic hydrocarbons", Molecul. Simul., 44(12), 947-953. https://doi.org/10.1080/08927022.2018.1465569
  7. Dastjerdi, S. and Akgoz, B. (2018), "New static and dynamic analyses of macro and nano FGM plates using exact threedimensional elasticity in thermal environment", Compos. Struct., 192, 626-641. https://doi.org/10.1016/j.compstruct.2018.03.058
  8. Ebnali Samani, M. and Tadi Beni, Y. (2018), "Size dependent thermo-mechanical buckling of the flexoelectric nanobeam", Mater. Res. Express, 5(8), 085018. https://doi.org/10.1088/2053-1591/aad2ca
  9. Ebrahimi, F. and Habibi, S. (2017), "Low-velocity impact response of laminated FG-CNT reinforced composite plates in thermal environment", Adv. Nano Res., Int. J., 5(2), 69-97. https://doi.org/10.12989/anr.2017.5.2.069
  10. Emdadi, M., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method", Adv. Nano Res., Int. J., 7(2), 109-123. https://doi.org/10.12989/anr.2019.7.2.109
  11. Fan, Y., Xiang, Y. and Shen, H.-S. (2019), "Nonlinear forced vibration of FG-GRC laminated plates resting on visco- Pasternak foundations", Compos. Struct., 209, 443-452. https://doi.org/10.1016/j.compstruct.2018.10.084
  12. Ghobadi, A., Tadi Beni, Y. and Golestanian, H. (2019), "Size dependent thermo-electro-mechanical nonlinear bending analysis of flexoelectric nano-plate in the presence of magnetic field", Int. J. Mech. Sci., 152, 118-137. https://doi.org/10.1016/j.ijmecsci.2018.12.049
  13. 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
  14. Huang, B.Z. and Atluri, S.N. (1995), "A simple method to follow post-buckling paths in finite element analysis", Comput. Struct., 57(3), 477-489. https://doi.org/10.1016/0045-7949(94)00623-B
  15. Jaiganesh, V., Manivannan, S. and Maruthu, B. (2015), "Rapid Prototyping of Polymethyl Methacrylate as Replacement and Support of Spine in Human", Biomed. Res., 26(4), S62-65.
  16. Jia, L. and Qingsheng, Y. (2009), "Molecular dynamics simulation for mechanical properties of CNT/Polyethylene composites", J. Phys.: Conference Series, 188, 012052. https://doi.org/10.1088/1742-6596/188/1/012052
  17. Jia, W., Li, Z., Wu, Z., Wang, L., Wu, B., Wang, Y., Cao, Y. and Li, J. (2018), "Graphene oxide as a filler to improve the performance of $PAN-LiClO_{4}$ flexible solid polymer electrolyte", Solid State Ionics, 315, 7-13. https://doi.org/10.1016/j.ssi.2017.11.026
  18. Karimi Zeverdejani, M., Tadi Beni, Y. and Kiani, Y. (2019), "Multi-scale Buckling and Post-buckling analysis of functionally graded Laminated Composite Plates Reinforced by Defective Graphene Sheets", Int. J. Struct. Stabil. Dyn., 2050001 https://doi.org/10.1142/S0219455420500017
  19. Kaushik, B.K. and Majumder, M.K. (2015), "Carbon Nanotube: Properties and Applications", In: Carbon Nanotube Based VLSI Interconnects: Analysis and Design, (B.K. Kaushik and M.K. Majumder Eds.), New Delhi: Springer India, pp. 17-37.
  20. Kheibari, F. and Tadi Beni, Y. (2017), "Size dependent electromechanical vibration of single-walled piezoelectric nanotubes using thin shell model", Mater. Des., 114, 572-583. https://doi.org/10.1016/j.matdes.2016.10.041
  21. Kiani, Y. (2017), "Buckling of FG-CNT-reinforced composite plates subjected to parabolic loading", Acta Mechanica, 228(4), 1303-1319. https:10.1007/s00707-016-1781-4
  22. Kiani, Y., Dimitri, R. and Tornabene, F. (2018a), "Free vibration of FG-CNT reinforced composite skew cylindrical shells using the Chebyshev-Ritz formulation", Compos. Part B: Eng., 147, 169-177. https://doi.org/10.1016/j.compositesb.2018.04.028
  23. Kiani, Y., Dimitri, R. and Tornabene, F. (2018b), "Free vibration study of composite conical panels reinforced with FG-CNTs", Eng. Struct., 172, 472-482. https://doi.org/10.1016/j.engstruct.2018.06.006
  24. Kocman, M., Pykal, M. and Jurecka, P. (2014), "Electric quadrupole moment of graphene and its effect on intermolecular interactions", Phys. Chem. Chem. Phys., 16(7), 3144-3152. https://doi.org/10.1039/c3cp54701a
  25. Li, Y., Wang, Q. and Wang, S. (2019), "A review on enhancement of mechanical and tribological properties of polymer composites reinforced by carbon nanotubes and graphene sheet: Molecular dynamics simulations", Compos. Part B: Eng., 160, 348-361. https://doi.org/10.1016/j.compositesb.2018.12.026
  26. Lin, F., Xiang, Y. and Shen, H.-S. (2017), "Temperature dependent mechanical properties of graphene reinforced polymer nanocomposites - A molecular dynamics simulation", Compos. Part B: Eng., 111, 261-269. https://doi.org/10.1016/j.compositesb.2016.12.004
  27. Malekzadeh, P. and Zarei, A.R. (2014), "Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers", Thin-Wall. Struct., 82, 221-232. https://doi.org/10.1016/j.tws.2014.04.016
  28. Mehralian, F. and Tadi Beni, Y. (2016), "Size-dependent torsional buckling analysis of functionally graded cylindrical shell", Compos. Part B: Eng., 94, 11-25. https://doi.org/10.1016/j.compositesb.2016.03.048
  29. Mehralian, F., Tadi Beni, Y. and Ansari, R. (2016a), "On the size dependent buckling of anisotropic piezoelectric cylindrical shells under combined axial compression and lateral pressure", Int. J. Mech. Sci., 119, 155-169. https://doi.org/10.1016/j.ijmecsci.2016.10.006
  30. Mehralian, F., Tadi Beni, Y. and Ansari, R. (2016b), "Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell", Compos. Struct., 152, 45-61. https://doi.org/10.1016/j.compstruct.2016.05.024
  31. Mirzaei, M. and Kiani, Y. (2016), "Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels", Compos. Struct., 142, 45-56. https://doi.org/10.1016/j.compstruct.2015.12.071
  32. Mirzaei, M. and Kiani, Y. (2017), "Isogeometric thermal buckling analysis of temperature dependent FG graphene reinforced laminated plates using NURBS formulation", Compos. Struct., 180, 606-616. https://doi.org/10.1016/j.compstruct.2017.08.057
  33. Mittal, G., Dhand, V., Rhee, K.Y., Park, S.-J. and Lee, W.R. (2015), "A review on carbon nanotubes and graphene as fillers in reinforced polymer nanocomposites", J. Ind. Eng. Chem., 21, 11-25. https://doi.org/10.1016/j.jiec.2014.03.022
  34. Mohammadimehr, M., Emdadi, M., Afshari, H. and Rousta Navi, B. (2018), "Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydrothermo-magneto-mechanical loadings using DQM", Int. J. Smart Nano Mater., 9, 233-260. https://doi.org/10.1080/19475411.2017.1377312
  35. Mohtashami, M. and Tadi Beni, Y. (2019), "Size-Dependent Buckling and Vibrations of Piezoelectric Nanobeam with Finite Element Method", Iran. J. Sci. Technol., Transact. Civil Eng., 43, 563-576. https://doi.org/10.1007/s40996-018-00229-9
  36. Nemeth, M.P. (1986), "Importance of anisotropy on buckling of compression-loaded symmetric composite plates", AIAA Journal, 24(11), 1831-1835. https://doi.org/10.2514/3.9531
  37. Nguyen-Quang, K., Vo-Duy, T., Dang-Trung, H. and Nguyen-Thoi, T. (2018), "An isogeometric approach for dynamic response of laminated FG-CNT reinforced composite plates integrated with piezoelectric layers", Comput. Methods Appl. Mech. Eng., 332, 25-46. https://doi.org/10.1016/j.cma.2017.12.010
  38. Ramanathan, T., Stankovich, S., Dikin, D.A., Liu, H., Shen, H., Nguyen, S.T. and Brinson, L.C. (2007), "Graphitic nanofillers in PMMA nanocomposites-An investigation of particle size and dispersion and their influence on nanocomposite properties", J. Polym. Sci. Part B: Polym. Phys., 45(15), 2097-2112. https://doi.org/10.1002/polb.21187
  39. Reddy, C.D., Rajendran, S. and Liew, K.M. (2005), "Equivalent continuum modeling of graphene sheets", Int. J. Nanosci., 4(4), 631-636. https://doi.org/10.1142/S0219581X05003528
  40. Rodriguez-Perez, M., Villanueva-Cab, J. and Pal, U. (2017), "Evaluation of thermally and chemically reduced graphene oxide films as counter electrodes on dye-sensitized solar cells", Adv. Nano Res., Int. J., 5(3), 231-244. https://doi.org/10.12989/anr.2017.5.3.231
  41. Sakhaee-Pour, A. (2009), "Elastic properties of single-layered graphene sheet", Solid State Commun., 149(1), 91-95. https://doi.org/10.1016/j.ssc.2008.09.050
  42. Sayyad, A.S. and Ghugal, Y.M. (2014), "On the Buckling of Isotropic, Transversely Isotropic and Laminated Composite Rectangular Plates", Int. J. Struct. Stabil. Dyn., 14, 1450020. https://doi.org/10.1142/S0219455414500205
  43. Shiu, S.-C. and Tsai, J.-L. (2014), "Characterizing thermal and mechanical properties of graphene/epoxy nanocomposites", Compos. Part B: Eng., 56, 691-697. https://doi.org/10.1016/j.compositesb.2013.09.007
  44. Shen, H.-S. and Xiang, Y. (2018), "Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical shells subjected to external pressure in thermal environments", Thin-Walled Structures, 124, 151-160. https://doi.org/10.1016/j.tws.2017.12.005
  45. Shen, H.-S. and Xiang, Y. (2019), "Torsional postbuckling behavior of FG-GRC laminated cylindrical shells in thermal environments", Thin-Wall. Struct., 135, 560-574. https://doi.org/10.1016/j.tws.2018.11.025
  46. Shen, H.-S., Lin, F. and Xiang, Y. (2017a), "Nonlinear bending and thermal postbuckling of functionally graded graphenereinforced composite laminated beams resting on elastic foundations", Eng. Struct., 140, 89-97. https://doi.org/10.1016/j.engstruct.2017.02.069
  47. Shen, H.-S., Xiang, Y. and Fan, Y. (2017b), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical shells in thermal environments", Compos. Struct., 182, 447-456. https://doi.org/10.1016/j.compstruct.2017.09.010
  48. Shen, H.-S., Xiang, Y., Fan, Y. and Hui, D. (2018), "Nonlinear bending analysis of FG-GRC laminated cylindrical panels on elastic foundations in thermal environments", Compos. Part B: Eng., 141, 148-157. https://doi.org/10.1016/j.compositesb.2017.12.048
  49. Shojaeian, M. and Tadi Beni, Y. (2015), "Size-dependent electromechanical buckling of functionally graded electrostatic nano-bridges", Sensors Actuators A: Phys., 232, 49-62. https://doi.org/10.1016/j.sna.2015.04.025
  50. Soleimani, I. and Tadi Beni, Y. (2018), "Vibration analysis of nanotubes based on two-node size dependent axisymmetric shell element", Arch. Civil Mech. Eng., 18, 1345-1358. https://doi.org/10.1016/j.acme.2018.04.009
  51. Song, M., Yang, J., Kitipornchai, S. and Zhu, W. (2017), "Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates", Int. J. Mech. Sci., 131-132, 345-355. https://doi.org/10.1016/j.ijmecsci.2017.07.017
  52. Tadi Beni, Y. (2016), "Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams", J. Intel. Mater. Syst. Struct., 27, 2199-2215. https://doi.org/10.1177/1045389X15624798
  53. Tadi Beni, Y. and Mehralian, F. (2017), "Size-dependent torsional buckling of carbon nano-peapods based on the modified couple stress theory", Int. J. Appl. Mech., 9(2), 1750030. https://doi.org/10.1142/S1758825117500302
  54. Tadi Beni, Y., Mehralian, F. and Razavi, H. (2015), "Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory", Compos. Struct., 120, 65-78. https://doi.org/10.1016/j.compstruct.2014.09.065
  55. Tadi Beni, Y., Karimi Zeverdejani, M. and Mehralian, F. (2017), "Buckling analysis of orthotropic protein microtubules under axial and radial compression based on couple stress theory", Mathe. Biosci., 292, 18-29. https://doi.org/10.1016/j.mbs.2017.07.002
  56. Tam, M., Yang, Z., Zhao, S. and Yang, L. (2019), "Vibration and buckling characteristics of functionally graded graphene nanoplatelets reinforced composite beams with open edge cracks", Materials, 12, 1412. https://doi.org/10.3390/ma12091412
  57. Van Krevelen, D.W. and Te Nijenhuis, K. (2009), Chapter 13 - "Mechanical Properties of Solid Polymers", In: Properties of Polymers (Fourth Edition), (D.W. Van Krevelen and K. Te Nijenhuis Eds.), Elsevier, Amsterdam, Netherlands, pp. 383-503.
  58. Walter, T.R., Bujanda, A.A., Rodriguez-Santiago, V., Yim, J.H., Baeza, J.A. and Pappas, D.D. (2016), "Enhanced Mechanical Performance of Woven Composite Laminates Using Plasma Treated Polymeric Fabrics", In: Advanced Composites for Aerospace, Marine, and Land Applications, (T. Sano, T.S. Srivatsan and M.W. Peretti Eds.), Cham: Springer International Publishing, pp. 231-242.
  59. Zhang, Y. and Park, S.l. (2018), "Influence of the nanoscaled hybrid based on nanodiamond@graphene oxide architecture on the rheological and thermo-physical performances of carboxylated-polymeric composites", Compos. Part A: Appl. Sci. Manuf., 112, 356-364. https://doi.org/10.1016/j.compositesa.2018.06.020
  60. Zhang, Y. and Park, S.l. (2019), "Imidazolium-optimized conductive interfaces in multilayer graphene nanoplatelet/epoxy composites for thermal management applications and electroactive devices", Polymer, 168, 53-60. https://doi.org/10.1016/j.polymer.2019.01.086
  61. Zhang, Y., Ge, X., Li, M., Deng, F., Oh, J. and Cho, U. (2018a), "The properties of rice bran carbon/nitrile-butadiene rubber composites fabricated by latex compounding method", Polym. Compos., 39(S2), E687-E696. https://doi.org/10.1002/pc.24126
  62. Zhang, Z., Li, Y., Wu, H., Zhang, H., Wu, H., Jiang, S. and Chai, G. (2018b), "Mechanical analysis of functionally graded graphene oxide-reinforced composite beams based on the firstorder shear deformation theory", Mech. Adv. Mater. Struct., 1-9. https://doi.org/10.1080/15376494.2018.1444216

Cited by

  1. Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC vol.10, pp.2, 2020, https://doi.org/10.12989/anr.2021.10.2.115