Buckling and postbuckling of dielectric composite beam reinforced with Graphene Platelets (GPLs)

Hu, 2014, Graphene-polymer nanocomposites for structural and functional applications, Prog. Polym. Sci., 39, 1934, 10.1016/j.progpolymsci.2014.03.001 Kim, 2010, Graphene/polymer nanocomposites, Macromolecules, 43, 6515, 10.1021/ma100572e Rafiee, 2009, Enhanced mechanical properties of nanocomposites at low graphene content, ACS Nano, 3, 3884, 10.1021/nn9010472 Zhao, 2010, Enhanced mechanical properties of graphene-based poly(vinyl alcohol) composites, Macromolecules, 43, 2357, 10.1021/ma902862u Rahman, 2013, Molecular modeling of crosslinked graphene–epoxy nanocomposites for characterization of elastic constants and interfacial properties, Composites, Part B, Eng., 54, 353, 10.1016/j.compositesb.2013.05.034 Ji, 2010, Micromechanics prediction of the effective elastic moduli of graphene sheet-reinforced polymer nanocomposites, Model. Simul. Mater. Sci. Eng., 18, 10.1088/0965-0393/18/4/045005 Spanos, 2015, Mechanical properties of graphene nanocomposites: a multiscale finite element prediction, Compos. Struct., 132, 536, 10.1016/j.compstruct.2015.05.078 Ke, 2009, Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening, Compos. Struct., 90, 152, 10.1016/j.compstruct.2009.03.003 Tang, 2013, The effect of graphene dispersion on the mechanical properties of graphene/epoxy composites, Carbon, 60, 16, 10.1016/j.carbon.2013.03.050 Park, 2015, Epoxy toughening with low graphene loading, Adv. Funct. Mater., 25, 575, 10.1002/adfm.201402553 Shokrieh, 2014, Stiffness prediction of graphene nanoplatelet/epoxy nanocomposites by a combined molecular dynamics-micromechanics method, Comput. Mater. Sci., 92, 444, 10.1016/j.commatsci.2014.06.002 Feng, 2017, Effects of reorientation of graphene platelets (GPLs) on Young's modulus of polymer nanocomposites under uni-axial stretching, Polymers, 9, 532, 10.3390/polym9100532 Dai, 2014, Graphene reinforced nanocomposites: 3D simulation of damage and fracture, Comput. Mater. Sci., 95, 684, 10.1016/j.commatsci.2014.08.011 Cho, 2007, Mechanical characterization of graphite/epoxy nanocomposites by multi-scale analysis, Compos. Sci. Technol., 67, 2399, 10.1016/j.compscitech.2007.01.006 Sun, 2018, Tensile behavior of polymer nanocomposite reinforced with graphene containing defects, Eur. Polym. J., 98, 475, 10.1016/j.eurpolymj.2017.11.050 Feng, 2018, Effects of reorientation of graphene platelets (GPLs) on Young's modulus of polymer composites under bi-axial stretching, Nanomaterials, 8, 27, 10.3390/nano8010027 He, 2009, High dielectric permittivity and low percolation threshold in nanocomposites based on poly(vinylidene fluoride) and exfoliated graphite nanoplates, Adv. Mater., 21, 710, 10.1002/adma.200801758 Fan, 2012, Graphene/poly(vinylidene fluoride) composites with high dielectric constant and low percolation threshold, Nanotechnology, 23, 10.1088/0957-4484/23/36/365702 Xia, 2017, A frequency-dependent theory of electrical conductivity and dielectric permittivity for graphene-polymer nanocomposites, Carbon, 111, 221, 10.1016/j.carbon.2016.09.078 Ravindran, 2018, Effects of graphene nanoplatelet size and surface area on the AC electrical conductivity and dielectric constant of epoxy nanocomposites, Polymers, 10, 477, 10.3390/polym10050477 Chen, 2013, Preparation of thermostable PBO/graphene nanocomposites with high dielectric constant, Nanotechnology, 24, 10.1088/0957-4484/24/24/245702 Tong, 2015, Achieving significantly enhanced dielectric performance of reduced graphene oxide/polymer composite by covalent modification of graphene oxide surface, Carbon, 94, 590, 10.1016/j.carbon.2015.07.005 Xia, 2016, A theory of electrical conductivity, dielectric constant, and electromagnetic interference shielding for lightweight graphene composite foams, J. Appl. Phys., 120, 10.1063/1.4961401 Feng, 2017, Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs), Composites, Part B, Eng., 110, 132, 10.1016/j.compositesb.2016.11.024 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 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 Sahmani, 2017, Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams, Compos. Struct., 179, 77, 10.1016/j.compstruct.2017.07.064 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 Sahmani, 2018, Small scale effects on the large amplitude nonlinear vibrations of multilayer functionally graded composite nanobeams reinforced with graphene-nanoplatelets, Int. J. Nanosci. Nanotechnol., 14, 207 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 Thanh, 2017, Nonlinear dynamic response and vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shear deformable plates with temperature-dependent material properties and surrounded on elastic foundations, J. Therm. Stresses, 40, 1254, 10.1080/01495739.2017.1338928 Sahmani, 2018, A unified nonlocal strain gradient plate model for nonlinear axial instability of functionally graded porous micro/nano-plates reinforced with graphene platelets, Mater. Res. Express, 5, 10.1088/2053-1591/aabdbb 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 Van Do, 2017, Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory, Thin-Walled Struct., 119, 687, 10.1016/j.tws.2017.07.022 Arefi, 2018, Free vibrations of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets, Aerosp. Sci. Technol., 81, 108, 10.1016/j.ast.2018.07.036 Sahmani, 2017, Axial postbuckling analysis of multilayer functionally graded composite nanoplates reinforced with GPLs based on nonlocal strain gradient theory, Eur. Phys. J. Plus, 132, 490, 10.1140/epjp/i2017-11773-4 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 Cong, 2018, Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT, Aerosp. Sci. Technol., 77, 419, 10.1016/j.ast.2018.03.020 Reddy, 2018, Free vibration of functionally graded-GPL reinforced composite plates with different boundary conditions, Aerosp. Sci. Technol., 78, 147, 10.1016/j.ast.2018.04.019 Sahmani, 2018, Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs, Compos. Struct., 198, 51, 10.1016/j.compstruct.2018.05.031 Duc, 2018, A static buckling investigation of multi-cracked FGM plate based phase-field method coupling the new TSDT, Acta Mech. Shen, 2017, Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments, Comput. Methods Appl. Math., 319, 175 Duc, 2016, Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations, J. Therm. Stresses, 39, 278, 10.1080/01495739.2015.1125194 Duc, 2017, The dynamic response and vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) truncated conical shells resting on elastic foundations, Materials (Basel), 10, 1194, 10.3390/ma10101194 Duc, 2018, Thermal buckling analysis of FGM sandwich truncated conical shells reinforced by FGM stiffeners resting on elastic foundations using FSDT, J. Therm. Stresses, 41, 331, 10.1080/01495739.2017.1398623 Duc, 2017, Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations, Thin-Walled Struct., 115, 300, 10.1016/j.tws.2017.02.016 Sahmani, 2017, Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams, Compos. Struct., 179, 77, 10.1016/j.compstruct.2017.07.064 Wang, 2018, Buckling of graphene platelet reinforced composite cylindrical shell with cutout, Int. J. Struct. Stab. Dyn., 18, 10.1142/S0219455418500402 Vuong, 2018, Nonlinear response and buckling analysis of eccentrically stiffened FGM toroidal shell segments in thermal environment, Aerosp. Sci. Technol., 79, 383, 10.1016/j.ast.2018.05.058 Sahmani, 2017, A nonlocal strain gradient hyperbolic shear deformable shell model for radial postbuckling analysis of functionally graded multilayer GPLRC nanoshells, Compos. Struct., 178, 97, 10.1016/j.compstruct.2017.06.062 Liu, 2018, Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell, Compos. Struct., 189, 560, 10.1016/j.compstruct.2018.01.106 Thanh, 2018, Nonlinear dynamic response and vibration of FG CNTRC shear deformable circular cylindrical shell with temperature-dependent material properties and surrounded on elastic foundations, J. Sandw. Struct. Mater. Dong, 2018, Buckling of spinning functionally graded graphene reinforced porous nanocomposite cylindrical shells: analytical study, Aerosp. Sci. Technol., 82–83, 466, 10.1016/j.ast.2018.09.037 Wang, 2018, Eigenvalue buckling of functionally graded cylindrical shells reinforced with graphene platelets (GPL), Compos. Struct., 202, 38, 10.1016/j.compstruct.2017.10.005 Wang, 2019, Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets, Aerosp. Sci. Technol., 85, 359, 10.1016/j.ast.2018.12.022 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 Dong, 2018, Buckling of spinning functionally graded graphene reinforced porous nanocomposite cylindrical shells: an analytical study, Aerosp. Sci. Technol., 82, 466, 10.1016/j.ast.2018.09.037 Nguyen, 2017, New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature, Aerosp. Sci. Technol., 71, 360, 10.1016/j.ast.2017.09.031 Shen, 2018, Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments, Composites, Part B, Eng., 136, 177, 10.1016/j.compositesb.2017.10.032 Duc, 2017, Dynamic response and vibration of composite double curved shallow shells with negative Poisson's ratio in auxetic honeycombs core layer on elastic foundations subjected to blast and damping loads, Int. J. Mech. Sci., 133, 504, 10.1016/j.ijmecsci.2017.09.009 Malekzadeh, 2018, Vibration of FG-GPLs eccentric annular plates embedded in piezoelectric layers using a transformed differential quadrature method, Comput. Methods Appl. Math., 340, 451 Duc, 2014, Nonlinear response of imperfect eccentrically stiffened FGM cylindrical panels on elastic foundation subjected to mechanical loads, Eur. J. Mech. A, Solids, 46, 60, 10.1016/j.euromechsol.2014.02.005 Shen, 2018, Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical panels under axial compression in thermal environments, Int. J. Mech. Sci., 135, 398, 10.1016/j.ijmecsci.2017.11.031 Duc, 2012, Nonlinear stability analysis of double-curved shallow FGM panels on elastic foundations in thermal environments, Mech. Compos. Mater., 48, 435, 10.1007/s11029-012-9289-z Wang, 2019, Nonlinear static and dynamic responses of graphene platelets reinforced composite beam with dielectric permittivity, Appl. Math. Model., 71, 298, 10.1016/j.apm.2019.02.025 Wang, 2019, Nonlinear free vibration of graphene platelets (GPLs)/polymer dielectric beam, Smart Mater. Struct. Dubois, 2008, Voltage control of the resonance frequency of Dielectric Electroactive Polymer (DEAP) membranes, J. Microelectromech. Syst., 17, 1072, 10.1109/JMEMS.2008.927741 Popov, 1968 Weng, 2010, A dynamical theory for the Mori–Tanaka and Ponte Castañeda–Willis estimates, Mech. Mater., 42, 886, 10.1016/j.mechmat.2010.06.004 Taya, 2005 Wang, 2015, Percolation threshold and electrical conductivity of graphene-based nanocomposites with filler agglomeration and interfacial tunneling, J. Appl. Phys., 118 Dyre, 1985, A simple-model of ac hopping conductivity in disordered solids, Phys. Lett. A, 108, 457, 10.1016/0375-9601(85)90039-8 Layek, 2010, Physical and mechanical properties of poly(methyl methacrylate)-functionalized graphene/poly(vinylidine fluoride) nanocomposites piezoelectric beta polymorph formation, Polymer, 51, 5846, 10.1016/j.polymer.2010.09.067 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 Liew, 2003, Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading, Int. J. Solids Struct., 40, 3869, 10.1016/S0020-7683(03)00096-9