Variable thickness sheet and homogenization-based topology optimization often result in spread-out, non-well-defined solutions that are difficult to interpret or de-homogenize to sensible final designs. By extensive numerical investigations, we demonstrate that such solutions are due to non-uniqueness of solutions or at least very flat minima. Much clearer and better-defined solutions may be obtained by adding a measure of non-void space to the objective function with little if any increase in structural compliance. We discuss various alternatives for cleaning up solutions and propose two efficient approaches which both introduce an auxiliary field to control non-void space: one approach based on a cut element based auxiliary field (hybrid approach) and another approach based on an auxiliary element based field (density approach). At the end, we demonstrate significant qualitative and quantitative improvements in variable thickness sheet and de-homogenization designs resulting from the proposed cleaning schemes.

可变厚度薄板和基于均质化的拓扑优化通常会导致展开，定义不明确的解决方案，这些解决方案难以解释或去均质化为合理的最终设计。通过广泛的数值研究，我们证明了这样的解决方案是由于解决方案的不唯一性或至少非常平坦的极小值。通过在目标函数中添加非空隙空间的量度，而在结构顺应性上几乎没有增加的情况下，可以获得更清晰，定义更好的解决方案。我们讨论了用于清理解决方案的各种替代方法，并提出了两种有效的方法，它们都引入了控制非空隙空间的辅助场：一种基于基于切割元素的辅助场的方法（混合方法），另一种基于基于辅助元素的场的方法。 （密度法）。在最后，