Abstract
Buckling analysis of nonlocal magneto-electro-elastic nano-plate is investigated based on the higher-order shear deformation theory. The in-plane magnetic and electric fields can be ignored for magneto-electro-elastic nano-plates. According to magneto-electric boundary condition and Maxwell equation, the variation of magnetic and electric potentials along the thickness direction of the magneto-electro-elastic plate is determined. To reformulate the elastic theory of magneto-electro-elastic nano-plate, the nonlocal differential constitutive relations of Eringen is applied. Using the variational principle, the governing equations of the nonlocal theory are derived. The relations between local and nonlocal theories are studied by numerical results. Also, the effects of nonlocal parameters, in-plane load directions, and aspect ratio on buckling response are investigated. Numerical results show the effects of the electric and magnetic potentials. These numerical results can be useful in the design and analysis of advanced structures constructed from magneto-electro-elastic materials.
Highlights
In recent years, the study of smart or intelligent materials involving piezoelectric and/or piezomagnetic material structures has attracted many researchers
Composites made of piezomagnetic/ piezoelectric materials show a magnetoelectric effect that is not present in single-phase piezomagnetic or piezoelectric materials.[2]
An analytical investigation on buckling and free vibration behavior of Mindlin rectangular MEE nano-plates resting on Pasternak medium via nonlocal elasticity theory has been carried out by Li et al.[9]
Summary
The study of smart or intelligent materials involving piezoelectric and/or piezomagnetic material structures has attracted many researchers. An analytical investigation on buckling and free vibration behavior of Mindlin rectangular MEE nano-plates resting on Pasternak medium via nonlocal elasticity theory has been carried out by Li et al.[9] They showed that the normalized frequency of system decreases by increasing the value of electric potential. The buckling analysis of a MEE higher-order shear deformable nano-plate is presented in both tabular and graphical forms to investigate the influences of the various parameters. The influences of various aspect ratios, electric and magnetic potentials, and in-plane load directions on the buckling response of MEE nano-plate are investigated. ∂w(x, y, t) ∂y ð1Þ in which u0x, u0y, w, ux, and uy are the five unknown displacements of the middle surface, and C(z) denotes the shape function determining the distribution of the transverse shear stresses and strains along the thickness. For a MEE medium whose poling direction coincides with the positive z-axis, the material constant matrices C, e, f, h, g, and k have the following forms
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