The mechanical response of nanobeams considering the flexoelectric phenomenon in the temperature environment

This article employs the novel shear strain theory for the first time to investigate the static bending and static buckling responses of nanobeams affected by the flexoelectric effect in a temperature environment. Consideration is given to the effect of applied voltage and rotation on the beam's fixed axis. The calculation formulas are based on the finite element method; the equilibrium equation is derived from Hamilton's principle, where charge polarization is considered via the strain gradient; and the voltage applied to the beam makes the electric field calculation expression significantly more complex than previously reported. This increases the realism of the research results. This study also investigated the effect of a series of rotational parameters, applied voltage, temperature, and boundary conditions on the nanobeams' mechanical response. The paper demonstrates through calculation results that the influence of the applied voltage increases the beam's load capacity. This parameter can be used to adjust the beam's bending response, which is the foundation of practical application.