Flexoelectric nanostructure design using explicit topology optimization

Flexoelectricity is the coupling between polarization and strain gradient. As the large strain gradient leads to a strong flexoelectric effect, the design of flexoelectric nano-structure via topology optimization has seen growing attentions. In the present work, an explicit topology optimization framework is proposed for flexoelectric structures design. To achieve this purpose, the Moving Morphable Void (MMV)-based approach is employed in the context of Isogeometric Analysis (IGA) combined with the Trimming Surface Analysis (TSA). Energy conversion factor and effective electric polarizability are respectively optimized to improve the flexoelectric performance of the nanostructure. Performing design under the explicit framework coupled with IGA can bring several advantages. Due to the use of NURBS basis functions of IGA, the required continuity in the approximation of the PDEs of flexoelectricity can be satisfied straightforwardly. Furthermore, with the use of the TSA technique, the occurrence of weak/gray material, which may cause numerical instability in flexoelectricity design, can be avoided. Also due to the explicit geometry description in MMV, the optimized result can be imported to the CAD system directly, which is significant for nanoscale structure from manufacturing perspective. Several representative numerical examples for topology optimization of flexoelectric structures are presented to demonstrate the effectiveness and advantages of the proposed approach.