Postbuckling Behavior of Functionally Graded Multilayer Graphene Nanocomposite Plate under Mechanical and Thermal Loads on Elastic Foundations

Abstract

This paper presents an analytical approach to postbuckling behaviors of functionally graded multilayer nanocomposite plates reinforced by a low content of graphene platelets (GPLs) using the first order shear deformation theory, stress function and von Karman-type nonlinear kinematics and include the effect of an initial geometric imperfection. The weight fraction of GPL nano fillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC). The modified Halpin-Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young’s modulus of GPLRC layers. The plate is assumed to resting on Pasternak foundation model and subjected to mechanical and thermal loads. The results show the influences of the GPL distribution pattern, weight fraction, geometry, elastic foundations, mechanical and temperature loads on the postbuckling behaviors of FG multilayer GPLRC plates.

Keywords: Postbuckling; Graphene nanocomposite plate; First order shear deformation plate theory.

References

[1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A. Firsov, Electric filed effect in atomically thin carbon films, Science 306 (2004) 666–669. http://doi.org/ 10.1126/science.1102896.
[2] K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, A.K. Geim, Two-dimensional atomic crystals, Proceedings of the National Academy of Sciences of the United States of America 102 (2005) 10451–10453. https://doi.org/10.1073/pnas.0502848102.
[3] C.D. Reddy, S. Rajendran, K.M. Liew, Equilibrium configuration and continuum elastic properties of finite sized graphene, Nanotechnology 17 (2006) 864-870. https://doi. org/10.1088/0957-4484/17/3/042.
[4] C. Lee, X.D. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (2008) 385–388. http://doi.org/10.1126/ science.1157996.
[5] F. Scarpa, S. Adhikari, A.S. Phani, Effective elastic mechanical properties of single layer graphene sheets, Nanotechnology 20 (2009) 065709. https://doi.org/10.1088/0957-4484/20/6/ 065709.
[6] Y.X. Xu, W.J. Hong, H. Bai, C. Li, G.Q. Shi, Strong and ductile poly(vinylalcohol)/graphene oxide composite films with a layered structure, Carbon 47 (2009) 3538–3543. https://doi.org/ 10.1016/j.carbon.2009.08.022.
[7] J.R. Potts, D.R. Dreyer, C.W. Bielawski, R.S. Ruoff, Graphene-based polymer nanocomposites, Polymer 52 (2011) 5-25. https://doi.org/10.1016/j .polymer.2010.11.042.
[8] T.K. Das, S. Prusty, Graphene-based polymer composites and their applications, Polymer-Plastics Technology and Engineering 52 (2013) 319-331. https://doi.org/10.1080/03602559.2012. 751410.
[9] M. Song, J. Yang, S. Kitipornchai, W. Zhud, Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates, International Journal of Mechanical Sciences 131–132 (2017) 345–355. https://doi.org/10.1016/j.ijmecsci.2017.07.017.
[10] H.S. Shen, Y. Xiang, F. Lin, D. Hui, Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments, Composites Part B 119 (2017) 67-78. https://doi.org/10.1016/j.compositesb.2017. 03.020.
[11] H. Wu, S. Kitipornchai, J. Yang, Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates, Materials and Design 132 (2017) 430–441. https://doi.org/10. 1016/j.matdes.2017.07.025.
[12] J. Yang, H. Wu, S. Kitipornchai, Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams, Composite Structures 161 (2017) 111–118. https://doi.org/10.1016/j.compstruct.2016.11.048.
[13] H.S. Shen, Y. Xiang, Y. Fan, Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical panels under axial compression in thermal environments, International Journal of Mechanical Sciences 135 (2018) 398–409. https://doi.org/10.1016/j.ijme csci.2017.11.031.
[14] M.D. Rasool, B. Kamran, Stability analysis of multifunctional smart sandwich plates with graphene nanocomposite and porous layers, International Journal of Mechanical Sciences 167 (2019) 105283. https://doi.org/10.1016/j.ijmecs ci.2019.105283.
[15] J.J. Mao, W. Zhang, Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces, Composite Structures 216 (2019) 392–405. https://doi.org/10.1016/j. compstruct.2019.02.095.
[16] P.H. Cong, N.D. Duc, New approach to investigate nonlinear dynamic response and vibration of functionally graded multilayer graphene nanocomposite plate on viscoelastic Pasternak medium in thermal environment, Acta Mechanica 229 (2018) 651-3670. https://doi.org/ 10.1007/s00707-018-2178-3.
[17] N.D. Duc, N.D. Lam, T.Q. Quan, P.M. Quang, N.V. Quyen, Nonlinear post-buckling and vibration of 2D penta-graphene composite plates, Acta Mechanica (2019), https://doi.org/10. 1007/s00707-019-02546-0.
[18] N.D. Duc, P.T. Lam, N.V. Quyen, V.D. Quang, Nonlinear Dynamic Response and Vibration of 2D Penta-graphene Composite Plates Resting on Elastic Foundation in Thermal Environments, VNU Journal of Science: Mathematics-Physics 35(3) (2019) 13-29. https:// doi.org/10.25073/2588-1124/vnumap. 4371.
[19] J.N. Reddy, Mechanics of laminated composite plates and shells; theory and analysis, Boca Raton: CRC Press, 2004.
[20] H.S. Shen, A two-step perturbation method in nonlinear analysis of beams, plates and shells, John Wiley & Sons Inc., 2013.