Flexoelectric nanostructure design using explicit topology optimization

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

“…The gradual decrease of the void size (from the loading point to the supported boundary) results in the gradation of the structural stiffness and thus in the high strain gradient. This result coincides with those of the theoretical analysis in Reference [26]. In the result, the value of objective functional is I = −5.19 × 10 −3 , which is 1.96 times larger than that of the initial design.…”

“…A key challenging issue in flexoelectric optimization is the singularity phenomenon caused by infinitesimal feature size as discussed in Reference [26]. Unlike Reference [26] which imposes mechanical property constraints to regularize the 2 ) , while t is a small positive number which satisfies the manufacturing requirement (such as the minimum length scale requirement in additive manufacture). With the use of the lower/upper bound constraints, the components always run through the cell.…”

“…All these processes are common treatments in flexoelectric design. 26 Finally, all optimization examples are solved with the use of MMA algorithm. 51…”

“…The first issue is the singularity phenomenon caused by infinitesimal feature size in flexoelectric design, which can produce excellent flexoelectric performance, but is often accompanied by serious manufacturing issues. It is a common treatment to introduce mechanical constraints (such as compliance constraint in Reference [26]) to regularize the solution space of the problem. However, additional mechanical constraints may seriously affect the optimality of the flexoelectric performance.…”

“…It is found that due to the complex infill microstructures, porous materials can provide much higher flexoelectric effect than pure solid materials. Unlike the aforementioned approaches which solve the flexoelectric optimization problem under the implicit framework, Zhang et al 26 recently proposed an explicit topology optimization framework for flexoelectric structure design, where moving morphable voids (MMV) approach is combined with Trimmed surface analysis (TSA) technique. In Reference [26], it is also found that material distribution in graded form can obtain excellent flexoelectric performance.…”