An Analytical Approach for Simulating the Bending of Nanobeams in Thermal Environments Considering the Flexomagnetic Effect

This research utilizes analytical solutions to investigate the issue of nonlinear static bending in nanobeams affected by the flexomagnetic effect. The nanobeams are exposed to mechanical loads and put in a temperature environment. The equilibrium equation of the beam is formulated based on the newly developed higher-order shear deformation theory. The flexomagnetic effect is explained by the presence of the strain gradient component, which also takes into consideration the impact of small-size effects. This study has used a flexible transformation to derive the equilibrium equation for a single variable, which significantly simplifies the process of determining the precise solution to the bending issue. This highlights the originality and significance of the present study, which is based on a newly developed shear deformation theory to clarify the distinctions between the nonlinear and linear problems. This study also presents the findings of numerical simulations that investigate the impact of various geometric, material, and temperature parameters on the nonlinear behavior of nanobeams. These discoveries are significant for designers to develop nanobeams that can function efficiently in many physical conditions, including mechanical, thermal, and magnetic mediums.