Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method

Zhu, 2012, A critical review of glucose biosensors based on carbon nanomaterials: carbon nanotubes and graphene, Sensors, 12, 5996, 10.3390/s120505996 Kim, 2009, Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites, Compos Sci Technol, 69, 335, 10.1016/j.compscitech.2008.10.019 Kanagaraj, 2007, Mechanical properties of high density polyethylene/carbon nanotube composites, Compos Sci Technol, 67, 3071, 10.1016/j.compscitech.2007.04.024 Coleman, 2006, Small but strong: a review of the mechanical properties of carbon nanotube–polymer composites, Carbon, 44, 1624, 10.1016/j.carbon.2006.02.038 Thostenson, 2003, On the elastic properties of carbon nanotube-based composites: modelling and characterization, J Phys D Appl Phys, 36, 573, 10.1088/0022-3727/36/5/323 Anumandla, 2006, A comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites, Compos A Appl Sci Manuf, 37, 2178, 10.1016/j.compositesa.2005.09.016 Ke, 2013, Dynamic stability of functionally graded carbon nanotube-reinforced composite beams, Mech Adv Mater Struct, 20, 28, 10.1080/15376494.2011.581412 Wu, 2016, Thermo-electro-mechanical postbuckling of piezoelectric FG-CNTRC beams with geometric imperfections, Smart Mater Struct, 25, 095022, 10.1088/0964-1726/25/9/095022 Kolahchi, 2016, Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium, Compos Struct, 150, 255, 10.1016/j.compstruct.2016.05.023 Yang, 2015, Dynamic buckling of thermo-electro-mechanically loaded FG-CNTRC beams, Int J Struct Stab Dyn, 15, 1540017, 10.1142/S0219455415400179 Wu, 2016, Nonlinear vibration of functionally graded carbon nanotube-reinforced composite beams with geometric imperfections, Compos B Eng, 90, 86, 10.1016/j.compositesb.2015.12.007 Rafiee, 2009, Enhanced mechanical properties of nanocomposites at low graphene content, ACS Nano, 3, 3884, 10.1021/nn9010472 Rashad, 2015, Development of magnesium-graphene nanoplatelets composite, J Compos Mater, 49, 285, 10.1177/0021998313518360 García-Macías, 2018, Bending and free vibration analysis of functionally graded graphene vs. Carbon nanotube reinforced composite plates, Compos Struct, 186, 123, 10.1016/j.compstruct.2017.11.076 Zaman, 2012, From carbon nanotubes and silicate layers to graphene platelets for polymer nanocomposites, Nanoscale, 4, 4578, 10.1039/c2nr30837a Li, 2016, Effect of the orientation of graphene-based nanoplatelets upon the Young’s modulus of nanocomposites, Compos Sci Technol, 123, 125, 10.1016/j.compscitech.2015.12.005 Yang, 2017, Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams, Compos Struct, 161, 111, 10.1016/j.compstruct.2016.11.048 Wu, 2017, Dynamic instability of functionally graded multilayer graphene nano-composite beams in thermal environment, Compos Struct, 162, 244, 10.1016/j.compstruct.2016.12.001 Feng, 2017, Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs), Compos B Eng, 110, 132, 10.1016/j.compositesb.2016.11.024 Song, 2018, Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Compos B Eng, 134, 106, 10.1016/j.compositesb.2017.09.043 Song, 2017, Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates, Int J Mech Sci, 131, 345, 10.1016/j.ijmecsci.2017.07.017 Song, 2017, Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Compos Struct, 159, 579, 10.1016/j.compstruct.2016.09.070 Wu, 2018, Parametric instability of thermo-mechanically loaded functionally graded graphene reinforced nanocomposite plates, Int J Mech Sci, 135, 431, 10.1016/j.ijmecsci.2017.11.039 Shen, 2017, Nonlinear vibration of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations in thermal environments, Nonlinear Dyn, 90, 899, 10.1007/s11071-017-3701-0 Kiani, 2018, Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements, Compos Struct, 186, 114, 10.1016/j.compstruct.2017.11.086 Gholami, 2018, Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates, Eng Struct, 156, 197, 10.1016/j.engstruct.2017.11.019 Yang, 2017, 3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates, Appl Math Model, 49, 69, 10.1016/j.apm.2017.04.044 Chen, 2015, Elastic buckling and static bending of shear deformable functionally graded porous beam, Compos Struct, 133, 54, 10.1016/j.compstruct.2015.07.052 Chen, 2016, Free and forced vibrations of shear deformable functionally graded porous beams, Int J Mech Sci, 108, 14, 10.1016/j.ijmecsci.2016.01.025 Chen, 2016, Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core, Thin-Walled Struct, 107, 39, 10.1016/j.tws.2016.05.025 Grygorowicz, 2016, Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core, Appl Math Mech, 37, 1361, 10.1007/s10483-016-2137-9 Shafiei, 2016, On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams, Int J Eng Sci, 106, 42, 10.1016/j.ijengsci.2016.05.007 Jabbari, 2016, Time-dependent electro–magneto–thermoelastic stresses of a poro-piezo-functionally graded material hollow sphere, J Pressure Vessel Technol, 138, 051201, 10.1115/1.4033089 Hangai, 2012, Nondestructive observation of pore structure deformation behavior of functionally graded aluminum foam by X-ray computed tomography, Mater Sci Eng, A, 556, 678, 10.1016/j.msea.2012.07.047 Koohbor, 2016, Design optimization of continuously and discretely graded foam materials for efficient energy absorption, Mater Des, 102, 151, 10.1016/j.matdes.2016.04.031 Chen, 2018, Dynamic response and energy absorption of functionally graded porous structures, Mater Des, 140, 473, 10.1016/j.matdes.2017.12.019 Kitipornchai, 2017, Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets, Mater Des, 116, 656, 10.1016/j.matdes.2016.12.061 Chen, 2017, Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams, Compos Sci Technol, 142, 235, 10.1016/j.compscitech.2017.02.008 Sahmani, 2018, Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory, Compos Struct, 186, 68, 10.1016/j.compstruct.2017.11.082 De Villoria, 2007, Mechanical model to evaluate the effect of the dispersion in nanocomposites, Acta Mater, 55, 3025, 10.1016/j.actamat.2007.01.007 Affdl, 1976, The Halpin-Tsai equations: a review, Polym Eng Sci, 16, 344, 10.1002/pen.760160512 Tjong, 2013, Recent progress in the development and properties of novel metal matrix nanocomposites reinforced with carbon nanotubes and graphene nanosheets, Mater Sci Eng: R, 74, 281, 10.1016/j.mser.2013.08.001 Ke, 2010, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Compos Struct, 92, 676, 10.1016/j.compstruct.2009.09.024 Gibson, 1982, The mechanics of three-dimensional cellular materials, Proc R Soc London A, 382, 43, 10.1098/rspa.1982.0088 Ashby, 2000 Wicklein, 2005, Numerical investigations of the elastic and plastic behaviour of an open-cell aluminium foam, Mater Sci Eng A, 397, 391, 10.1016/j.msea.2005.02.052 Grygorowicz, 2015, Elastic buckling of a sandwich beam with variable mechanical properties of the core, Thin-Walled Struct, 87, 127, 10.1016/j.tws.2014.11.014 Gibson, 1997 Choi, 1995, Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative poisson’s ratio, Int J Mech Sci, 37, 51, 10.1016/0020-7403(94)00047-N Akbaş, 2017, Stability of a non-homogenous porous plate by using generalized differential quadrature method, Int J Eng Appl Sci, 9, 147 Zhang, 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, 10.1016/j.enganabound.2015.03.004 Zhu, 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, 1450, 10.1016/j.compstruct.2011.11.010 Lei, 2013, Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment, Compos Struct, 106, 128, 10.1016/j.compstruct.2013.06.003 Kiani, 2016, Shear buckling of FG-CNT reinforced composite plates using Chebyshev-Ritz method, Compos B Eng, 105, 176, 10.1016/j.compositesb.2016.09.001 Bakshi, 2010, Carbon nanotube reinforced metal matrix composites-a review, Int Mater Rev, 55, 41, 10.1179/095066009X12572530170543 Jagannadham, 2012, Thermal conductivity of copper-graphene composite films synthesized by electrochemical deposition with exfoliated graphene platelets, Metall Mater Trans B, 43, 316, 10.1007/s11663-011-9597-z Liu, 2007, Ab initio calculation of ideal strength and phonon instability of graphene under tension, Phys Rev B, 76, 064120, 10.1103/PhysRevB.76.064120