Abstract
Due to their excellent mechanical and electrical behaviors, graphene sheets (GSs) are supposed to be a base material for nanoelectromechanical systems (NEMS). In the present study, we carry out the shape optimization design of GSs to enhance their vibration behavior. At first, according to the Tersoff-Brenner force field theory and a link between molecular mechanics and solid mechanics of C-C bond, we model GSs as continuum frame structures. Then, we optimize the shape of the atomistic finite element model based on a free-form optimization method for frame structures. In the shape optimization process, we use the fundamental natural frequency as objective function and maximize it under the volume constraint and encountering repeated eigenvalue problem. We assume each equivalent continuum beam to vary in the off-axis direction to the centroidal axis and derive the shape gradient function for determination of the optimal design velocity field. Hence, the shape optimum design of GSs can be carried out without shape parametrization using the derived optimal design velocity field. The results show that, the fundamental natural frequency of GSs can be significantly enhanced after shape optimum design, which will be helpful for applying GSs in NEMS.
