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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 the present study, a single general formulation has been presented for the analysis of various shell-shaped structures. The proposed model is comprehensive and a variety of theories can be used based on it. The cross-section of the shell structure can be arbitrarily analyzed with the presented equations. In other words, various types of shell structures, including cylindrical, conical, spherical, elliptical, hyperbolic, parabolic, and any non-geometric structure with functional cross-section, can be modeled mechanically with only one partial differential equation system. The obtained equations have been solved by applying SAPM semi-analytical solution method. In order to present a comprehensive research, dynamic nonlinear analysis is considered. The variation of material properties through the thickness has been assumed as functionally graded and its effect on the strength of the shell structure with the functional cross-section has been investigated. The numerical results have been compared with available papers and also with FEM results for some structures that there is no paper available for validation. Different types of shell structures have been studied in terms of cross-sectional shape and properties. Finally, the effects of some important factors on the results such as boundary conditions, nonlinear analysis, dynamic analysis, and rotation of the structure around its central axis have been conducted thoroughly. This study and its original governing equations can be considered as a comprehensive reference for mechanical analysis of various shell structures with functional cross-sectional shape. [ABSTRACT FROM AUTHOR]