The effective elastic-piezoelectric properties of nanostructures have been shown to be strongly size-dependent. In this paper, a nonlocal second-order shear deformation formulation is presented to study the size-dependent thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core. Temperature is considered as uniform and nonlinear distributions across plate’s thickness direction. Based on the developed nonlocal second-order shear deformation theory, the size-dependent equations of motion are derived. The nonlocal thermal buckling responses of simply supported nanoplates are solved via Navier method. The reliability of present approach is verified by comparing the existing results provided in the open literature. The influences of nonlocal parameter, gradient index, electric voltage, and Winkler–Pasternak parameters on the thermal buckling characteristics of functionally graded nanoplates are examined.
HuangX-LShenH-S. Nonlinear vibration and dynamic response of functionally graded plates in thermal environments. Int J Solids Struct2004; 41: 2403–2427.
BouderbaBHouariMSATounsiA. Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations. Steel Compos Struct2013; 14: 85–104.
4.
ZidiMTounsiAHouariMSAet al.Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory. Aerosp Sci Technol2014; 34: 24–34.
5.
HamidiAHouariMSAMahmoudSet al.A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates. Steel Compos Struct2015; 18: 235–253.
6.
BousahlaAABenyoucefSTounsiAet al.On thermal stability of plates with functionally graded coefficient of thermal expansion. Struct Eng Mech2016; 60: 313–335.
7.
BouderbaBHouariMSATounsiAet al.Thermal stability of functionally graded sandwich plates using a simple shear deformation theory. Struct Eng Mech2016; 58: 397–422.
8.
MenasriaABouhadraATounsiAet al.A new and simple HSDT for thermal stability analysis of FG sandwich plates. Steel Compos Struct2017; 25: 157–175.
9.
ParkJ-SKimJ-H. Thermal postbuckling and vibration analyses of functionally graded plates. J Sound Vib2006; 289: 77–93.
10.
MatsunagaH. Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory. Compos Struct2009; 90: 76–86.
11.
ZenkourASobhyM. Thermal buckling of various types of FGM sandwich plates. Compos Struct2010; 93: 93–102.
12.
BeldjeliliYTounsiAMahmoudS. Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory. Smart Struct Syst2016; 18: 755–786.
13.
ShahsavariDShahsavariMLiLet al.A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation. Aerosp Sci Technol2018; 72: 134–149.
14.
LiLLiXHuY. Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int J Eng Sci2016; 102: 77–92.
15.
ChahtFLKaciAHouariMSAet al.Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect. Steel Compos Struct2015; 18: 425–442.
16.
KaramiBJanghorbanM. Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory. Mod Phys Lett B2016; 30: 1650421–1650421.
17.
AhouelMHouariMSABediaEet al.Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept. Steel Compos Struct2016; 20: 963–981.
18.
BounouaraFBenrahouKHBelkorissatIet al.A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation. Steel Compos Struct2016; 20: 227–249.
19.
KaramiBJanghorbanMTounsiA. Effects of triaxial magnetic field on the anisotropic nanoplates. Steel Compos Struct2017; 25: 361–374.
20.
EbrahimiFBaratiMR. Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium. J Brazil Soc Mech Sci Eng2017; 39: 937–952.
21.
KaramiBShahsavariDLiL. Temperature-dependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field. J Therm Stress2017, pp. 1–17.
22.
EbrahimiFBaratiMRZenkourAM. A new nonlocal elasticity theory with graded nonlocality for thermo-mechanical vibration of FG nanobeams via a nonlocal third-order shear deformation theory. Mech Adv Mater Struct2017, pp. 1–11.
23.
KaramiBShahsavariDJanghorbanM. Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory. Mech Adv Mater Struct2017, pp. 1–11.
24.
KaramiBShahsavariDLiL. Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory. Phys E: Low-dimens Syst Nanostruct2018; 97: 317–327.
25.
ShahsavariDKaramiBMansouriS. Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories. Eur J Mech-A/Solids2018; 67: 200–214.
26.
KaramiBShahsavariDJanghorbanMet al.Wave dispersion of mounted graphene with initial stress. Thin-Walled Struct2018; 122: 102–111.
27.
LiLHuY. Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects. Int J Mech Sci2017; 120: 159–170.
28.
LiLHuY. Torsional vibration of bi-directional functionally graded nanotubes based on nonlocal elasticity theory. Compos Struct2017; 172: 242–250.
29.
ZhuXLiL. Twisting statics of functionally graded nanotubes using Eringen’s nonlocal integral model. Compos Struct2017; 178: 87–96.
30.
EringenACEdelenD. On nonlocal elasticity. Int J Eng Sci1972; 10: 233–248.
31.
ZhuXLiL. Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity. Int J Mech Sci2017; 133: 639–650.
32.
ZhuXLiL. On longitudinal dynamics of nanorods. Int J Eng Sci2017; 120: 129–145.
33.
BesseghierAHouariMSATounsiAet al.Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory. Smart Struct Syst2017; 19: 601–614.
34.
ZemriAHouariMSABousahlaAAet al.A mechanical response of functionally graded nanoscale beam: An assessment of a refined nonlocal shear deformation theory beam theory. Struct Eng Mech2015; 54: 693–710.
35.
MouffokiAAdda BediaEAHouariMSAet al.Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory. Smart Struct Syst2017; 20: 369–383.
36.
KhetirHBouiadjraMBHouariMSAet al.A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates. Struct Eng Mech2017; 64: 391–402.
37.
BouafiaKKaciAHouariMSAet al.A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams. Smart Struct Syst2017; 19: 115–126.
38.
PradhanSPhadikarJ. Nonlocal elasticity theory for vibration of nanoplates. J Sound Vib2009; 325: 206–223.
39.
AksencerTAydogduM. Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory. Phys E: Low-dimens Syst Nanostruct2011; 43: 954–959.
40.
ShahsavariDJanghorbanM. Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load. J Brazil Soc Mech Sci Eng2017; 39: 3849–3861.
41.
ShahsavariDKaramiBJanghorbanMet al.Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment. Mater Res Express2017; 4: 085013–085013.
42.
BaratiMRZenkourAMShahverdiH. Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory. Compos Struct2016; 141: 203–212.
43.
NamiMRJanghorbanMDamadamM. Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third-order shear deformation theory. Aerosp Sci Technol2015; 41: 7–15.
44.
Hanifi Hachemi AmarLKaciATounsiA. On the size-dependent behavior of functionally graded micro-beams with porosities. Struct Eng Mech2017; 64: 527–541.
45.
KaramiBJanghorbanMLiL. On guided wave propagation in fully clamped porous functionally graded nanoplates. Acta Astronaut2017.
46.
BelkorissatIHouariMSATounsiAet al.On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model. Steel Compos Struct2015; 18: 1063–1081.
47.
MitchellJReddyJ. A refined hybrid plate theory for composite laminates with piezoelectric laminae. Int J Solids Struct1995; 32: 2345–2367.
48.
ShiyekarSKantT. An electromechanical higher order model for piezoelectric functionally graded plates. Int J Mech Mater Des2010; 6: 163–174.
49.
RouzegarJAbadF. Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory. Thin-Walled Struct2015; 89: 76–83.
50.
AraniAGJamaliMMosayyebiMet al.Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory. Compos Part B: Eng2016; 95: 209–224.
51.
ArefiMZamaniMKianiM. Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation. J Intell Mater Syst Struct2017. DOI: 1045389X17721039
52.
ChenCShiYZhangYSet al.Size dependence of Young’s modulus in ZnO nanowires. Phys Rev Lett2006; 96: 075505–075505.
53.
StanGCiobanuCParthangalPMet al.Diameter-dependent radial and tangential elastic moduli of ZnO nanowires. Nano Lett2007; 7: 3691–3697.
54.
ArefiMZenkourAM. Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers. Acta Mech2017; 228: 475–493.
55.
EbrahimiFBaratiMR. Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory. Smart Mater Struct2016; 25: 105014–105014.
56.
JandaghianARahmaniO. Vibration analysis of functionally graded piezoelectric nanoscale plates by nonlocal elasticity theory: An analytical solution. Superlatt Microstruct2016; 100: 57–75.
57.
EbrahimiFDabbaghA. Nonlocal strain gradient based wave dispersion behavior of smart rotating magneto-electro-elastic nanoplates. Mater Res Express2017; 4: 025003–025003.
58.
Ghorbanpour AraniAZamaniM. Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation. J Sandwich Struct Mater2017. DOI: 1099636217721405
59.
AraniAGJafariGSKolahchiR. Vibration analysis of nanocomposite microplates integrated with sensor and actuator layers using surface SSDPT. Polym Compos2016.
60.
PradhanSMurmuT. Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever. Phys E: Low-dimens Syst Nanostruct2010; 42: 1944–1949.
61.
Suresh S and Mortensen A. Fundamentals of functionally graded materials. The Institute of Materials, 1998.
62.
PraveenGReddyJ. Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int J Solids Struct1998; 35: 4457–4476.
63.
LiXLiLHuYet al.Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory. Compos Struct2017; 165: 250–265.
64.
LiewKYangJKitipornchaiS. Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading. Int J Solids Struct2003; 40: 3869–3892.
65.
MirzavandBEslamiM. A closed-form solution for thermal buckling of piezoelectric FGM rectangular plates with temperature-dependent properties. Acta Mech2011; 218: 87–101.
66.
ReddyJN. Mechanics of laminated composite plates and shells: Theory and analysis, Boca Raton, FL: CRC Press, 2004.
67.
NoorAKBurtonWS. Three-dimensional solutions for thermal buckling of multilayered anisotropic plates. J Eng Mech1992; 118: 683–701.
68.
ShenH-SWilliamsF. Thermal postbuckling analysis of imperfect laminated plates on softening non-linear elastic foundations. Compos Sci Technol1997; 57: 719–728.
69.
ShenH-S. Thermal postbuckling analysis of imperfect Reissner-Mindlin plates on softening nonlinear elastic foundations. J Eng Math1998; 33: 259–270.
70.
JavaheriREslamiM. Thermal buckling of functionally graded plates based on higher order theory. J Therm Stress2002; 25: 603–625.
71.
LiewKMHeXKitipornchaiS. Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix. Acta Mater2006; 54: 4229–4236.
