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Bending and buckling analyses of BiTiO3–CoFe2O4 nanoplates based on nonlocal strain gradient and modified couple stress hypotheses: rate of surface layers variations

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Abstract

In the present article, the bending and buckling analyses of a rectangular BiTiO3–CoFe2O4 nanoplate are examined based on the nonlocal strain gradient and modified couple stress hypotheses to be able to analyze the rate of surface layers variations. The BiTiO3–CoFe2O4 nanoplate is capable of converting magnetism, electricity, thermal, and elasticity energies from one form to another form. The refined plate hypothesis is utilized to develop the governing equations; subsequently, the principle of virtual work is used to derive the relevant equilibrium equations and then, an analytical solution is employed to solve those obtained equations. The present nanoplate is under diverse external in-plane loads including magnetic, electric, thermal, and mechanical forces. The proposed model is validated by those previously accessible results in the literature. One of the most significant results of the current research is that the nonlocal parameter could apply an opposite effect on the rate of surface layers variations when it compares with the strain gradient and modified couple stress parameters. Moreover, the influence of small-scale parameters on the rate of surface layers variations in the bending problem is exactly opposite to the buckling case.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Morteza Karimi

  2. Borjavaran Center of Applied Science and Technology, University of Applied Sciences and Technology, Tehran, Iran

    Mohammad Reza Farajpour

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  1. Morteza Karimi
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  2. Mohammad Reza Farajpour
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Correspondence to Morteza Karimi.

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Karimi, M., Farajpour, M.R. Bending and buckling analyses of BiTiO3–CoFe2O4 nanoplates based on nonlocal strain gradient and modified couple stress hypotheses: rate of surface layers variations. Appl. Phys. A 125, 530 (2019). https://doi.org/10.1007/s00339-019-2811-6

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