The deflection platform phenomenon of functionally graded flexoelectric simply supported nanobeam

Direct flexoelectricity appears in dielectrics as a kind of coupling effect of electric field and elastic strain gradient. Its strong size dependence makes it effective in nanostructures. In this paper, based on the flexoelectric theory and mixed finite element method (FEM), the mechanical properties of the two-dimensional functionally graded (FG) flexoelectric nanobeam are studied, and the phenomenon of the deflection platform is found. By applying various types of loads to FG nanobeams, the influence of geometric parameters, length scale, and material distribution on the phenomenon of the deflection platform is discussed. According to the simulation results, it is found that the aspect ratio and the length scale of the beam will change the shape of the deflection platform, making it change regularly among various shapes. The geometric size will greatly increase the height of the platform, but it has little effect on the dimensionless deflection. Reasonable material distribution can enhance the internal coupling effect, increase the height of the platform and reduce the required load. Our results suggest that when studying nano-scale flexoelectric models, the deflection platforms or similar phenomena should be considered.