Abstract
In this paper, a new 2D formulation is developed for analyzing the effects of magnetic and electric fields on the static bending behavior of magneto-electro-elastic (MEE) nanobeams subjected to transverse loading conditions. The nonlocal elasticity theory is utilized to consider the small-scale effect on the behavior of nanobeams. In order to increase the accuracy of the model to obtain more realistic predictions, a general displacement field is considered, which take into account a general form for the distribution of normal and shear strains in the nanobeam and to consider a general form for the distribution of magnetic and electric fields in the MEE nanobeam. Using the principle of minimum total potential energy, the governing equations of the MEE nanobeam under external magnetic, electric, and mechanical loadings are determined. An analytical solution is developed to investigate the effects of magnetic and electric fields on the bending of the MEE nanobeam. According to the numerical results, it is shown that the present method can predict the deflection of magneto-electro-elastic nanobeams more accurately in comparison with predictions of the shear deformation theories available in the literature, due to considering all in-plane and out of plane strain components and considering a general (not predefined) form for the distribution of electric and magnetic field through the thickness of MEE nanobeam. A detailed numerical study is presented to examine the influence of the nonlocal parameter, magnetic potential, electric potential, transverse and axial loadings, and aspect ratio on the deflection of magneto-electro-elastic nanobeam. The results revealed for BaTiO3–CoFe2O4 nanobeam that the maximum deflection of MEE nanobeam increases by applying a negative external magnetic potential as well as a positive external electric potential. Due to the excellent accuracy of the presented formulation, it can be used in the analysis and design of MEE nanostructures and as a benchmark for the investigation of the accuracy of other numerical models.
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