Abstract
The present paper presents a Bernoulli–Euler flexomagnetic (FM) nanobeam model, which considers the effects of flexomagneticity, piezomagneticity, and the surface elasticity. Differential control equations and corresponding magnetic boundary conditions are derived to investigate the influences of direct and converse FM couplings over the magnetic-elastic response. Size-dependent theoretical solutions for the static bending deformation of the cantilever, simply supported, and clamped nanobeams subjected to concentrated or uniformly distributed load are derived. Numerical simulations demonstrate that the flexomagneticity effect plays the role of the scale-dependent enhancement of the bending rigidity, which is independent of boundary conditions. But for the residual surface stresses, softening or stiffening the beam depends on boundary conditions.
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