Effect of thermo-magneto-electro-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory

Abstract

The nonlocal thermo-magneto-electro-mechanical bending behaviors of a three-layered nanoplate are presented in this study. The three-layered nanoplate includes a nano-sheet and two piezo-magnetic face-sheets at the top and the bottom. Temperature distribution is assumed linear along the thickness of the plate. The piezo-magnetic face-sheets are subjected to three-dimensional electric and magnetic potentials. The applied electric and magnetic potentials are applied at top of the face-sheets. The constitutive thermo-electro-magneto relations are derived based on the sinusoidal shear-deformation plate theory and nonlocal electro-magneto-elasticity. Using the principle of virtual work seven equations of the equilibrium are derived. The numerical results of this research indicate that some parameters have considerable effect on the bending behavior of three-layered nanoplate. Nonlocal parameter, applied electric and magnetic potentials, and temperature distribution are important parameters in this analysis.

Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations

“…A further study of the statics and dynamics of curved single-walled carbon nanotubes was approached by Hayati et al [20], based on the nonlocal theory, whose problem was solved using Navier's method. A different approach based on the sinusoidal shear deformation theory was applied by Arefi and Zenkour [21,22] for the analysis of a sandwich microbeam and nanoplate, respectively. Some additional static and dynamic analyses of curved beams at the nano-and macro-scales were presented by Aya and Tufekci [23], as well as by Hajianmaleki and Qatu [24], respectively.…”

“…Based on the available literature on the vibration and bending response of beams and plates reinforced with GPLs at the macroscale [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], as well as on the curved beams at the macroand nano-scales [18][19][20][21][22][23][24][25][26][27], here we propose a combined study of curved nanobeams reinforced with nanoplatelets. In mechanical problems of technical interest, the elastic equilibrium is generally defined in bounded structural domains, so that suitable constitutive boundary conditions have to be prescribed to ensure the equivalence between integral and differential equations [33].…”

Analysis of functionally graded plates resting on elastic foundation and subjected to non-linear hygro-thermo-mechanical loading

“…Arefi and Rabczuk [57] addressed the electro-elastic analysis for piezoelectric a doubly curved nano-shell using higher order shear deformation theory. Arefi and Zenkour [58] used the sinusoidal shear deformation plate theory to address the nonlocal thermo-magneto-electro-mechanical bending analysis for three-layered nano-plates. Linear temperature variation is assumed across the thickness.…”

“…y), external loads. Many researchers such as Reddy[43], Arefi and Arani[51], Arefi and Zenkour[54,55], Arefi and Rabczuk[57], Arefi and Zenkour[58], Arefi et al[59], Zenkour and Radwan[60], etc. have used this principle to derive governing differential equations of the theory:…”

Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams

“…In the aforementioned studies in order to incorporate the small scales in equations of motions, various theories such as the strain gradient theory and Eringen’s differential nonlocal model were used. 31,32 Classical continuum models, 33,34 nonlocal continuum theory, 35–37 strain gradient theory, 38,39 and modified couple stress models 40–42 have been used by researchers for analysis of nano/micro systems. Generally, based on the nonlocal continuum theory, the stress at a specified point of the body depends on the strains at other near points.…”