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Our analysis incorporates the geometrically nonlinear bending of the Euler-Bernoulli ferromagnetic nanobeam accounting for a size-dependent model through assuming surface effects. In the framework of the flexomagnetic phenomenon, the large deflections are investigated referring to von-Kármán nonlinearity. Employing the nonlocal effects of stress coupled to the gradient of strain generates a scale-dependent Hookean stress–strain scheme related to the small scale. Taking into account the supports of the nanobeam in two cases, that is, totally fixed and hinged, the deformations are predicted. A constant static lateral load is postulated uniformly along the length of the beam, which forces the deformation. As the analysis is based on the one-dimensional media, the electrodes are embedded so that they give off a transverse magnetic field creating a longitudinal force. The newly developed mathematical model is computed by means of the differential quadrature method together with the Newton-Raphson technique. The computational section discusses and reveals the numerical results in detail for the characteristics and parameters involved in the design of beam-like magnetic nanosensors. As shown later, the conducted research presents that there is a strong linkage between the surface effect and the flexomagneticity behavior of the bulk. [ABSTRACT FROM AUTHOR]

In this paper, the equation governing the buckling of a magnetic composite nanoplate under the influence of an in-plane one-dimensional magnetic field, assuming the concept of flexomagnetic and considering the resulting flexural force and moment, is investigated for the first time by different analytical boundary conditions. To determine the equation governing the stability of the nanoplate, the nonlocal strain gradient theory has been used by taking into account the classical plate theory. The axial magnetic force, which is originated from the magnetic field, is investigated. After extracting the governing differential equation, the critical buckling load is obtained for different support conditions. The effect of nonlocal parameter, sheet aspect ratio and the effect of one-dimensional magnetic field on critical load are discussed. It was earned that if the nanoplate is rectangular so that the value of aspect ratio is less than one, the flexomagnetic response will be more noticeable. [ABSTRACT FROM AUTHOR]