This work presents a numerical study on the use of multi-resolution strategies for the computationally challenging problem of optimal design of high-resolution nonlinear electro-active shell-type devices using Topology Optimization methods. This paper puts forward the following novelties. First, it presents a tailor-made in-plane multi-resolution technique where a higher level of resolution for the density field is permitted within the in-plane surface of the electro-active material. Second, a numerical study is carried out to elucidate the lower bound for the critical ratio between the density resolution level (or the number of density voxels within every element of the coarse analysis mesh) and the filtering length that can be used to avoid the presence of QR-patterns in the unexplored scenario of nonlinear electromechanics, without compromising the computational efficiency of the multi-resolution scheme. The numerical experiments illustrate the benefits of the proposed methodology to obtain high-resolution designs with a reasonable computational cost and reveal the possibility for more flexible bounds for the critical ratio as those reported in linear elasticity.

这项工作提出了关于使用多分辨率策略解决使用拓扑优化方法优化设计高分辨率非线性电活性壳型设备的计算挑战性问题的数值研究。本文提出以下创新点。首先，它提出了一种量身定制的面内多分辨率技术，其中在电活性材料的面内允许更高水平的密度场分辨率。其次，进行数值研究以阐明密度分辨率水平（或粗分析网格的每个元素内的密度体素的数量）与可用于避免存在的过滤长度之间的临界比率的下限非线性机电未探索场景中的二维码模式，在不影响多分辨率方案的计算效率的情况下。数值实验说明了所提出的方法以合理的计算成本获得高分辨率设计的好处，并揭示了临界比的更灵活界限的可能性，如线性弹性中报告的那样。