Explicit topology optimization for graded lattice flexoelectric nanostructures via ersatz material model

This work proposes a moving morphable component (MMC)-based topology optimization approach for designing graded lattice flexoelectric nanostructures, which are generally considered to have better flexoelectric properties. To this end, the infill structure is described with the use of a set of components. A coordinate perturbation is made to the topology description functions of the components to achieve a graded distribution of the flexoelectric materials. Resorting to the explicit parameters of the components, the singular disconnected structure can be naturally controlled with the use of lower/upper bound constraints. To ensure the continuity in the approximation of the PDEs of flexoelectricity, an ersatz material model is developed by combining isogeometric analysis (IGA) with MMC. Since MMC provides definite feature sizes in the optimization result, the complicated infill lattice can be manufactured by additive manufacturing directly. The flexoelectric performances of the design results from the proposed approach are demonstrated through both numerical examples and experimental measurements. It is shown that the obtained novel infill lattice structures have better flexoelectric performance when compared with traditional structural configurations.