Buckling of flexoelectric semiconductor beams

We study the buckling of flexoelectric semiconductor beams using one-dimensional equations based on the macroscopic theory of flexoelectric semiconductors. Simple solutions for a beam with sliding ends and a simply supported beam with hinged ends are obtained. Results show that when buckling occurs, the mobile charges in the beams redistribute themselves driven by the electric polarization or field accompanying buckling through flexoelectricity. The buckling load increases due to flexoelectric coupling which may be called flexoelectric stiffening. The mobile charges redistribute themselves to screen the polarization or electric field and thus weaken the flexoelectric stiffening.