Graphene sheets (GSs) have been supposed to be a base material for nanoelectromechanical systems (NEMS). In this study, we carry out the shape optimization design of GSs to improve their stiffness for applications. 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 at first. Then, we optimize the shape of the atomistic finite element model based on the free-form optimization method for frame structures. In the optimization process, we use the compliance as objective function and minimize it under the volume constraint. 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 optimum shape of GSs can be determined without shape parametrization using the derived optimal design velocity field. The results show that, the compliance of GSs can be significantly reduced using the free-form optimization method, which would be helpful for designing GSs for the application in NEMS.

抄録全体を表示