Vibration of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method

Liew, 2015, Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review, Compos Struct, 120, 90, 10.1016/j.compstruct.2014.09.041 Huang, 2012, Graphene-based composites, Chem Soc Rev, 41, 666, 10.1039/C1CS15078B Stankovich, 2006, Graphene-based composite materials, Nature, 442, 282, 10.1038/nature04969 Potts, 2011, Graphene-based polymer nanocomposites, Polymer, 52, 5, 10.1016/j.polymer.2010.11.042 Das, 2013, Graphene-based polymer composites and their applications, Polym-Plast Technol Eng, 52, 319, 10.1080/03602559.2012.751410 Xu, 2009, Strong and ductile poly (vinyl alcohol)/graphene oxide composite films with a layered structure, Carbon, 47, 3538, 10.1016/j.carbon.2009.08.022 Rafiee, 2009, Enhanced mechanical properties of nanocomposites at low graphene content, ACS Nano, 3, 3884, 10.1021/nn9010472 Milani, 2013, Polypropylene/graphene nanosheet nanocomposites by in situ polymerization: synthesis, characterization and fundamental properties, Compos Sci Technol, 84, 1, 10.1016/j.compscitech.2013.05.001 Jiang, 2014, Fabrication and characterization of graphene oxide-reinforced poly (vinyl alcohol)-based hybrid composites by the sol-gel method, Compos Sci Technol, 102, 51, 10.1016/j.compscitech.2014.06.029 Bafana, 2017, Polypropylene nanocomposites reinforced with low weight percent graphene nanoplatelets, Compos Part B: Eng, 109, 101, 10.1016/j.compositesb.2016.10.048 Chandra, 2012, Vibration frequency of graphene based composites: a multiscale approach, Mater Sci Eng: B, 177, 303, 10.1016/j.mseb.2011.12.024 Rafiee, 2009, Buckling resistant graphene nanocomposites, Appl Phys Lett, 95, 10.1063/1.3269637 Parashar, 2012, Representative volume element to estimate buckling behavior of graphene/polymer nanocomposite, Nanoscale Res Lett, 7, 515, 10.1186/1556-276X-7-515 Wu, 2016, Nonlinear vibration of functionally graded carbon nanotube-reinforced composite beams with geometric imperfections, Compos Part B: Eng, 90, 86, 10.1016/j.compositesb.2015.12.007 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 Feng, 2017, Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs), Compos Part B: Eng, 110, 132, 10.1016/j.compositesb.2016.11.024 Feng, 2017, Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs), Eng Struct, 140, 110, 10.1016/j.engstruct.2017.02.052 Wu, 2017, Dynamic instability of functionally graded multilayer graphene nanocomposite beams in thermal environment, Compos Struct, 162, 244, 10.1016/j.compstruct.2016.12.001 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 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 Song, 2017, Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Compos Part B: Eng 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 Yang, 2017, 3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates, Appl Math Modell, 49, 69, 10.1016/j.apm.2017.04.044 Yang, 2017, Thermoelastic analysis of functionally graded graphene reinforced rectangular plates based on 3D elasticity, Meccanica, 52, 2275, 10.1007/s11012-016-0579-8 Zhao, 2017, Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs), Compos Struct, 180, 799, 10.1016/j.compstruct.2017.08.044 Shen, 2017, Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments, Compos Struct, 170, 80, 10.1016/j.compstruct.2017.03.001 Shen, 2017, Nonlinear bending and thermal postbuckling of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations, Eng Struct, 140, 89, 10.1016/j.engstruct.2017.02.069 Shen, 2017, Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments, Compos Part B: Eng, 119, 67, 10.1016/j.compositesb.2017.03.020 Shen, 2017, Thermal buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations, Thin-Walled Struct, 118, 229, 10.1016/j.tws.2017.05.006 Shen, 2017, Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments, Comput Methods Appl Mech Eng, 319, 175, 10.1016/j.cma.2017.02.029 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 Shen, 2017, Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical shells in thermal environments, Compos Struct, 182, 447, 10.1016/j.compstruct.2017.09.010 Barati, 2017, Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection, Compos Struct, 181, 194, 10.1016/j.compstruct.2017.08.082 Gholami, 2017, Large deflection geometrically nonlinear analysis of functionally graded multilayer graphene platelet-reinforced polymer composite rectangular plates, Compos Struct, 180, 760, 10.1016/j.compstruct.2017.08.053 Sahmani, 2017, Nonlinear instability of axially loaded functionally graded multilayer graphene platelet-reinforced nanoshells based on nonlocal strain gradient elasticity theory, Int J Mech Sci, 131, 95, 10.1016/j.ijmecsci.2017.06.052 Mirzaei, 2017, Isogeometric thermal buckling analysis of temperature dependent FG graphene reinforced laminated plates using NURBS formulation, Compos Struct, 180, 606, 10.1016/j.compstruct.2017.08.057 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 Kiani, 2018, Isogeometric large amplitude free vibration of graphene reinforced laminated plates in thermal environment using NURBS formulation, Comput Meth Appl Mech Eng, 332, 86, 10.1016/j.cma.2017.12.015 Al-Bermani, 1996, Natural frequencies of thick arbitrary quadrilateral plates using the pb-2 Ritz method, J Sound Vib, 196, 371, 10.1006/jsvi.1996.0489 Kiani, 2016, Shear buckling of FG-CNT reinforced composite plates using Chebyshev-Ritz method, Compos Part B: Eng, 105, 176, 10.1016/j.compositesb.2016.09.001 Mirzaei, 2015, Snap-through phenomenon in a thermally postbuckled temperature dependent sandwich beam with FG-CNTRC face sheets, Compos Struct, 134, 1004, 10.1016/j.compstruct.2015.09.003 Mirzaei, 2016, Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout, Beilstein J Nanotechnol, 7, 511, 10.3762/bjnano.7.45 Kiani, 2016, Free vibration of FG-CNT reinforced composite skew plates, Aerosp Sci Technol, 58, 178, 10.1016/j.ast.2016.08.018 Kiani, 2017, Free vibration of FG-CNT reinforced composite spherical shell panels using Gram-Schmidt shape functions, Compos Struct, 159, 368, 10.1016/j.compstruct.2016.09.079 Karami, 2003, An efficient differential quadrature methodology for free vibration analysis of arbitrary straight-sided quadrilateral thin plates, J Sound Vib, 263, 415, 10.1016/S0022-460X(02)01062-3 Zhang, 2014, An improved moving least-squares Ritz method for two-dimensional elasticity problems, Appl Math Comput, 246, 268, 10.1016/j.amc.2014.07.001 Zhang, 2015, An element-free IMLS-Ritz method for numerical solution of three-dimensional wave equations, Comput Methods Appl Mech Eng, 297, 116, 10.1016/j.cma.2015.08.018 Zhang, 2015, Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method, Compos Struct, 120, 189, 10.1016/j.compstruct.2014.10.009 Zhang, 2015, Computation of vibration solution for functionally graded carbon nanotube-reinforced composite thick plates resting on elastic foundations using the element-free IMLS-Ritz method, Appl Math Comput, 256, 488, 10.1016/j.amc.2015.01.066 Zhang, 2015, Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges, Int J Mech Sci, 103, 9, 10.1016/j.ijmecsci.2015.08.021 Zhang, 2015, Vibration characteristic of moderately thick functionally graded carbon nanotube reinforced composite skew plates, Compos Struct, 122, 172, 10.1016/j.compstruct.2014.11.070 Zhang, 2016, Free vibration analysis of triangular CNT-reinforced composite plates subjected to in-plane stresses using FSDT element-free method, Compos Struct, 149, 247, 10.1016/j.compstruct.2016.04.019 Zhang, 2017, On the study of the effect of in-plane forces on the frequency parameters of CNT-reinforced composite skew plates, Compos Struct, 160, 824, 10.1016/j.compstruct.2016.10.116 Zhang, 2017, Vibration analysis of CNT-reinforced thick laminated composite plates based on Reddy's higher-order shear deformation theory, Compos Struct, 160, 689, 10.1016/j.compstruct.2016.10.102 Liew, 2011, A review of meshless methods for laminated and functionally graded plates and shells, Compos Struct, 93, 2031, 10.1016/j.compstruct.2011.02.018 Zhang, 2015, Geometrically nonlinear large deformation analysis of functionally graded carbon nanotube reinforced composite straight-sided quadrilateral plates, Comput Methods Appl Mech Eng, 295, 219, 10.1016/j.cma.2015.07.006 Zhang, 2017, Geometrically nonlinear large deformation of CNT-reinforced composite plates with internal column supports, J Model Mech Mater, 1 Zhang, 2016, Element-free geometrically nonlinear analysis of quadrilateral functionally graded material plates with internal column supports, Compos Struct, 147, 99, 10.1016/j.compstruct.2016.03.034 Zhang, 2016, Geometrically nonlinear analysis of arbitrarily straight-sided quadrilateral FGM plates, Compos Struct, 154, 443, 10.1016/j.compstruct.2016.07.039 Lei, 2016, Vibration of FG-CNT reinforced composite thick quadrilateral plates resting on Pasternak foundations, Eng Anal Boundary Elem, 64, 1, 10.1016/j.enganabound.2015.11.014 Zhang, 2017, Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method, J Vib Control, 23, 1026, 10.1177/1077546315587804 Zhang, 2016, Elastodynamic analysis of quadrilateral CNT-reinforced functionally graded composite plates using FSDT element-free method, Compos Struct, 148, 144, 10.1016/j.compstruct.2016.04.006 Zhang, 2017, The IMLS-Ritz analysis of laminated CNT-reinforced composite quadrilateral plates subjected to a sudden transverse dynamic load, Compos Struct, 180, 638, 10.1016/j.compstruct.2017.07.046 Zhang, 2017, Mechanical behavior of laminated CNT-reinforced composite skew plates subjected to dynamic loading, Compos Part B: Eng, 122, 219, 10.1016/j.compositesb.2017.03.041 Affdl, 1976, The Halpin-Tsai equations: a review, Polym Eng Sci, 16, 344, 10.1002/pen.760160512 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 Belytschko, 1994, Element-free Galerkin methods, Int J Numer Methods Eng, 37, 229, 10.1002/nme.1620370205 Reddy, 1986 Yasmin, 2004, Mechanical and thermal properties of graphite platelet/epoxy composites, Polymer, 45, 8211, 10.1016/j.polymer.2004.09.054 Liu, 2007, Ab initio calculation of ideal strength and phonon instability of graphene under tension, Phys Rev B, 76, 10.1103/PhysRevB.76.064120