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Isogeometric thermal postbuckling of FG-GPLRC laminated plates

  • Kiani, Y. (Faculty of Engineering, Shahrekord University) ;
  • Mirzaei, M. (Department of Mechanical Engineering, Faculty of Engineering,University of Qom)
  • Received : 2019.05.01
  • Accepted : 2019.09.06
  • Published : 2019.09.25

Abstract

An analysis on thermal buckling and postbuckling of composite laminated plates reinforced with a low amount of graphene platelets is performed in the current investigation. It is assumed that graphaene platelets are randomly oriented and uniformly dispersed in each layer of the composite media. Elastic properties of the nanocomposite media are obtained by means of the modified Halpin-Tsai approach which takes into account the size effects of the graphene reinforcements. By means of the von $K{\acute{a}}rm{\acute{a}}n$ type of geometrical nonlinearity, third order shear deformation theory and nonuniform rational B-spline (NURBS) based isogeometric finite element method, the governing equations for the thermal postbuckling of nanocomposite plates in rectangular shape are established. These equations are solved by means of a direct displacement control strategy. Numerical examples are given to study the effects of boundary conditions, weight fraction of graphene platelets and distribution pattern of graphene platelets. It is shown that, with introduction of a small amount of graphene platelets into the matrix of the composite media, the critical buckling temperature of the plate may be enhanced and thermal postbuckling deflection may be alleviated.

Keywords

References

  1. Atri, H.R. and Shojaee, S. (2018), "Truncated hierarchical Bsplines in isogeometric analysis of thin shell structures", Steel Compos. Struct., Int. J., 26(2), 171-182. http://dx.doi.org/10.12989/scs.2018.26.2.171
  2. Cadelano, E., Palla, P.L., Giordano and S. and Colombo, L. (2009), "Nonlinear elasticity of monolayer graphene", Physical Review Letters, 102, Art No. 235502. https://doi.org/10.1103/PhysRevLett.102.235502
  3. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aerosp. Sci. Technol., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020
  4. Das, T.K. and Prusty, S. (2013), "Graphene-based polymer composites and their applications", Polymer-Plast. Technol. Eng., 52, 319-331. https://doi.org/10.1080/03602559.2012.751410
  5. Duc, N.D. and Nguyen, P.D. (2017), "The dynamic response and vibration of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) truncated conical shells resting on elastic foundation", Materials, 10, Article Number 1194. https://doi.org/10.3390/ma10101194
  6. Duc, N.D., Cong, P.H., Tuan, N.D., Tran, P. and Thanh, N.V. (2017a), "Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations", Thin-Wall. Struct., 115, 300-310. https://doi.org/10.1016/j.tws.2017.02.016
  7. Duc, N.D., Quan, T.Q. and Nguyen, D.P. (2017b), "New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells", Aerosp. Sci. Technol., 71, 360-372. https://doi.org/10.1016/j.ast.2017.09.031
  8. Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Methods Appl. Mech. Eng., 194, 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008
  9. Kiani, Y. (2017), "Thermal Post-Buckling of FG-CNT Reinforced Composite Plates", Compos. Struct., 159, 299-306. https://doi.org/10.1016/j.compstruct.2016.09.084
  10. Kiani, Y. (2018a), "NURBS-based isogeometric thermal postbuckling analysis of temperature dependent graphene reinforced composite laminated plates", Thin-Wall. Struct., 125, 211-219. https://doi.org/10.1016/j.tws.2018.01.024
  11. Kiani, Y. (2018b), "Thermal post-buckling of temperature dependent sandwich plates with FG-CNTRC face sheets", J. Thermal Stress., 41, 866-882. https://doi.org/10.1080/01495739.2018.1425645
  12. Kiani, Y. (2018c), "Isogeometric large amplitude free vibration of graphene reinforced laminated plates in thermal environment using NURBS formulation", Comput. Methods Appl. Mech. Eng., 332, 86-101. https://doi.org/10.1016/j.cma.2017.12.015
  13. Kiani, Y. (2019), "Buckling of functionally graded graphene reinforced conical shells under external pressure in thermal environment", Compos. Part B: Eng., 159, 128-137. https://doi.org/10.1016/j.compositesb.2018.08.052
  14. Kiani, Y. and Mirzaei, M. (2018), "Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements", Compos. Struct., 186, 114-122. https://doi.org/10.1016/j.compstruct.2017.11.086
  15. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061
  16. Kulkarni, D.D., Choi, I., Singamaneni, S.S. and Tsukruk, V.V. (2010), "Graphene oxidepolyelectrolyte nanomembranes", ACS Nano, 4, 4667-4676. https://doi.org/10.1021/nn101204d
  17. 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
  18. 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
  19. Ni, Z., Bu, H., Zou, M., Yi, H., Bi, K. and Chen, Y. (2010), "Anisotropic mechanical properties of graphene sheets from molecular dynamics", Physica B: Condensed Matter, 405, 1301-1306. https://doi.org/10.1016/j.physb.2009.11.071
  20. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V. and Firsov, I.V. (2004), "Electric filed effect in atomically thin carbon films", Science, 306, 666-669. https://doi.org/10.1126/science.1102896
  21. Parashar, A. and Mertiny, P. (2012), "Representative volume element to estimate buckling behavior of graphene/polymer nanocomposite", Nanoscale Res. Lett., 7, 515-520. https://doi.org/10.1186/1556-276X-7-515
  22. Potts, J.R., Dreyer, D.R., Bielawski, C.W. and Ruoff, R.S. (2011), "Graphene-based polymer nanocomposites", Polymer, 52, 5-25. https://doi.org/10.1016/j.polymer.2010.11.042
  23. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z. and Koratkar, N. (2009a), "Enhanced mechanical properties of nanocomposites at low graphene content", ACS Nano, 3, 3884-3990. https://doi.org/10.1021/nn9010472
  24. Rafiee, M.A., Rafiee, J., Yu, Z.Z. and Koratkar, N. (2009b), "Buckling resistant graphene nanocomposites", Appl. Phys. Lett., 95, Art No. 223103. https://doi.org/10.1063/1.3269637
  25. Raju, K.K. and Rao, G.V. (1988), "Thermal Postbuckling of a square plate resting on an elastic foundation by finite element method", Comput. Struct., 28, 195-199. https://doi.org/10.1016/0045-7949(88)90039-9
  26. Reddy, C.D., Rajendran, S. and Liew, K.M. (2006), "Equilibrium configuration and continuum elastic properties of finite sized graphene", Nanotechnology, 17, 864-870. https://doi.org/10.1088/0957-4484/17/3/042
  27. Roodsarabi, M., Khatibinia, M. and Sarafrazi, S.R. (2016), "Hybrid of topological derivative-based level set method and isogeometric analysis for structural topology optimization", Steel Compos. Struct., Int. J., 21(6), 1389-1410. http://dx.doi.org/10.12989/scs.2016.21.6.1389
  28. Scarpa, F., Adhikari, S. and Phani, A.S. (2009), "Effective elastic mechanical properties of single layer graphene sheets", Nanotechnology, 20, Art No. 065709. https://doi.org/10.1088/0957-4484/20/6/065709
  29. Shen, H.S. and Xiang, Y. (2018a), "Postbuckling behavior of functionally graded graphene-reinforced composite laminated cylindrical shells under axial compression in thermal environments", Comput. Methods Appl. Mech. Eng., 330, 64-82. https://doi.org/10.1016/j.cma.2017.10.022
  30. Shen, H.S. and Xiang, Y. (2018b), "Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical shells subjected to external pressure in thermal environments", Thin-Wall. Struct., 124, 151-160. https://doi.org/10.1016/j.tws.2017.12.005
  31. Shen, H.S., Xiang, Y. and Lin, F. (2017a), "Nonlinear bending and thermal postbuckling of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations", Eng. Struct., 140, 89-97. https://doi.org/10.1016/j.engstruct.2017.02.069
  32. Shen, H.S., Xiang, Y., Lin, F. and Hui D. (2017b), "Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments", Compos. Part B: Eng., 119, 67-78. https://doi.org/10.1016/j.compositesb.2017.03.020
  33. Shen, H.S., Xiang, Y. and Lin, F. (2017c), "Thermal buckling and postbuckling of functionally graded graphenereinforced composite laminated plates resting on elastic foundations", Thin-Wall. Struct., 118, 229-237. https://doi.org/10.1016/j.tws.2017.05.006
  34. Shen, H.S., Xiang, Y. and Lin, F. (2018), "Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical panels under axial compression in thermal environments", Int. J. Mech. Sci., 135, 398-409. https://doi.org/10.1016/j.ijmecsci.2017.11.031
  35. 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, 345-355. https://doi.org/10.1016/j.ijmecsci.2017.07.017
  36. Song, M., Yang, J. and Kitipornchai, S. (2018), "Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Part B: Eng., 134, 106-113. https://doi.org/10.1016/j.compositesb.2017.09.043
  37. Stankovich, S., Dikin, D.A., Dommett, G.H.B., Kohlhaas, K.M. Zimney, E.J., Stach, E.A., Piner, E.D., Nguyen, S.T. and Ruoff, R.S. (2006), "Graphene-based composite materials", Nature, 442, 282-286. https://doi.org /10.1038/nature04969
  38. Thanh, N.V., Khoa, N.D., Tuan, N.D., Tran, P. and Duc, N.D. (2016), "Nonlinear dynamic response and vibration of functionally graded carbon nanotube-reinforced composite (FGCNTRC) shear deformable plates with temperature-dependent material", J. Thermal Stress., 40, 1254-1274. https://doi.org/10.1080/01495739.2017.1338928
  39. Thom, D.V., Kien, N.D., Duc, N.D., Duc, D.H. and Tinh, B.Q. (2017), "Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory", Thin-Wall. Struct., 119, 687-699. https://doi.org/10.1016/j.tws.2017.07.022
  40. Vuong, P.M. and Duc, N.D. (2018), "Nonlinear response and buckling analysis of eccentrically stiffened FGM toroidal shell segments in thermal environment", Aerosp. Sci. Technol., 79, 383-398. https://doi.org/10.1016/j.ast.2018.05.058
  41. Wang, Y., Feng, C., Zhao, Z. and Yang, J. (2018a), "Buckling of graphene platelet reinforced composite cylindrical shell with cutout", Int. J. Struct. Stabil. Dyn., 18, Article Number 1850040. https://doi.org/10.1142/S0219455418500402
  42. Wang, Y., Feng, C., Zhao, Z., Lu, F. and Yang, J. (2018b), "Torsional buckling of graphene platelets (GPLs) reinforced functionally graded cylindrical shell with cutout", Compos. Struct., 197, 72-97. https://doi.org/10.1016/j.compstruct.2018.05.056
  43. Wang, Y., Feng, C., Zhao, Z. and Yang, J. (2018c), "Eigenvalue buckling of functionally graded cylindrical shells reinforced with graphene platelets (GPL)", Compos. Struct., 202, 38-46. https://doi.org/10.1016/j.compstruct.2017.10.005
  44. Wu, H., Kitipornchai, S. and Yang, J. (2017), "Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates", Mater. Des., 132, 430-441. https://doi.org/10.1016/j.matdes.2017.07.025
  45. Yang, J., Wu, H. and Kitipornchai, S. (2017), "Buckling and postbuckling of functionally graded multilayer graphene plateletreinforced composite beams", Compos. Struct., 161, 111-118. https://doi.org/10.1016/j.compstruct.2016.11.048
  46. Yang, J., Chen, D. and Kitipornchai, S. (2018a), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090
  47. Yang, Z., Yang, J., Liu, A. and Fu, J. (2018b), "Nonlinear in-plane instability of functionally graded multilayer graphene reinforced composite shallow arches", Compos. Struct.res, 204, 301-312. https://doi.org/10.1016/j.compstruct.2018.07.072
  48. Yu, Y., Shen, H.S., Wang, H. and Hui, D. (2018), "Postbuckling of sandwich plates with graphene-reinforced composite face sheets in thermal environments", Compos. Part B: Eng., 135, pp. 72-83. https://doi.org/10.1016/j.compositesb.2017.09.045
  49. Zhang, Y.Y., Wang, C.M., Cheng, Y. and Xiang, Y. (2011), "Mechanical properties of bilayer graphene sheets coupled by sp3 bonding", Carbon, 49, 4511-4517. https://doi.org/10.1016/j.carbon.2011.06.058
  50. Zhao, X., Zhang, Q., Chen, D. and Lu, P. (2010), "Enhanced mechanical properties of graphenebased poly(vinyl alcohol) composites", Macromolecules, 43, 2357-2363. https://doi.org/10.1021/ma902862u

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