Static stability analysis of a size-dependent magneto-electro-elastic functionally graded nanoplate has an immense contribution in identification and improvement of the performance of nano-electro-mechanical systems. A refined trigonometric plate theory is employed to formulate the magneto-electro-elastic functionally graded nanoplate for the first time. Magneto-electro-elastic properties of nanoplate change in spatial coordinate based on power-law form. Regarding the small-scale effects at nanoscales, the size-dependent nonlocal continuum theory is employed to derive governing equations of the nonclassical magneto-electro-elastic functionally graded nanoplate. Analytical solution possessing functions which satisfy different boundary conditions is adopted to solve the equations. The results illustrate the size-dependent buckling behavior of magneto-electro-elastic functionally graded nanoplate affected by magnetic potential, electric voltage, various boundary conditions, small-scale parameter, material composition, plate side-to-thickness ratio, and aspect ratio.
AnsariRGholamiR (2016) Size-dependent buckling and postbuckling analyses of first-order shear deformable magneto-electro-thermo elastic nanoplates based on the nonlocal elasticity theory. International Journal of Structural Stability and Dynamics. Epub ahead of print 8 April. DOI: 10.1142/S0219455417500146.
2.
AnsariRHasratiEGholamiR. (2015) Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto–electro–thermo elastic nanobeams. Composites Part B: Engineering83: 226–241.
3.
BaratiMRShahverdiH (2016) An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position. Mechanics of Advanced Materials and Structures. Epub ahead of print 9 June. DOI: 10.1080/15376494.2016.1196788.
4.
BaratiMRZenkourAMShahverdiH (2016) Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory. Composite Structures141: 203–212.
5.
BeniYT (2016) Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams. Journal of Intelligent Material Systems and Structures. Epub ahead of print 11 January. DOI: 10.1177/1045389X15624798.
6.
BhangaleRKGanesanN (2005) Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells. Journal of Sound and Vibration288(1): 412–422.
7.
EbrahimiFBaratiMR (2016a) A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams. Arabian Journal for Science and Engineering41(5): 1679–1690.
8.
EbrahimiFBaratiMR (2016b) An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams. Advances in Nano Research4(2): 65–84.
9.
EbrahimiFBaratiMR (2016c) Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field. Applied Physics A122(4): 1–18.
10.
EbrahimiFBaratiMR (2016d) Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment. Journal of Vibration and Control. Epub ahead of print 29 April. DOI: 10.1177/1077546316646239.
11.
EbrahimiFSalariE (2015a) Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams. Mechanics of Advanced Materials and Structures23(12): 1379–1397.
12.
EbrahimiFSalariE (2015b) Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams. Smart Materials and Structures24(12): 125007–125023.
13.
EbrahimiFSalariE (2015c) Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions. Composites Part B: Engineering78: 272–290.
14.
EringenAC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics54(9): 4703–4710.
15.
EringenACEdelenDGB (1972) On nonlocal elasticity. International Journal of Engineering Science10(3): 233–248.
16.
HuangDJDingHJChenWQ (2007) Analytical solution for functionally graded magneto-electro-elastic plane beams. International Journal of Engineering Science45(2): 467–485.
17.
JandaghianAARahmaniO (2016) Free vibration analysis of magneto-electro-thermo-elastic nanobeams resting on a Pasternak foundation. Smart Materials and Structures25(3): 35023–35038.
18.
KattimaniSCRayMC (2015) Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates. International Journal of Mechanical Sciences99: 154–167.
19.
KeLLWangYS (2014) Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory. Physica E: Low-Dimensional Systems and Nanostructures63: 52–61.
20.
KeLLWangYSYangJ. (2014) Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory. Acta Mechanica Sinica30(4): 516–525.
21.
Lezgy-NazargahMCheraghiN (2015) An exact Peano Series solution for bending analysis of imperfect layered FG neutral magneto-electro-elastic plates resting on elastic foundations. Mechanics of Advanced Materials and Structures. Epub ahead of print 2 September. DOI: 10.1080/15376494.2015.1124951.
22.
LiYSCaiZYShiSY (2014) Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory. Composite Structures111: 522–529.
23.
MahmoudSRChahtFLKaciA. (2015) Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect. Steel & Composite Structures18(2): 425–442.
24.
MantariJLBonillaEMSoaresCG (2014) A new tangential-exponential higher order shear deformation theory for advanced composite plates. Composites Part B: Engineering60: 319–328.
25.
PanE (2002) Three-dimensional Green’s functions in anisotropic magneto-electro-elastic bimaterials. Zeitschrift für angewandte Mathematik und Physik—ZAMP53(5): 815–838.
26.
PanEHanF (2005) Exact solution for functionally graded and layered magneto-electro-elastic plates. International Journal of Engineering Science43(3–4): 321–339.
27.
RamirezFHeyligerPRPanE (2006) Discrete layer solution to free vibrations of functionally graded magneto-electro-elastic plates. Mechanics of Advanced Materials and Structures13(3): 249–266.
28.
ŞimşekMYurtcuHH (2013) Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Composite Structures97: 378–386.
29.
SladekJSladekVKrahulecS. (2015) Analyses of circular magnetoelectroelastic plates with functionally graded material properties. Mechanics of Advanced Materials and Structures22(6): 479–489.
30.
SobhyM (2013) Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions. Composite Structures99: 76–87.
31.
SobhyM (2015) A comprehensive study on FGM nanoplates embedded in an elastic medium. Composite Structures134: 966–980.
32.
WuCPTsaiYH (2007) Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux. International Journal of Engineering Science45(9): 744–769.
33.
WuCPChenSJChiuKH (2010) Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method. Mechanics Research Communications37(1): 54–60.
34.
ZareMNazemnezhadRHosseini-HashemiS (2015) Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method. Meccanica50(9): 2391–2408.
35.
ZemriAHouariMSABousahlaAA. (2015) A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory. Structural Engineering and Mechanics54(4): 693–710.
