The robust topology optimization formulation that introduces the eroded and dilated versions of the design has gained increasing popularity in recent years, mainly because of its ability to produce designs satisfying a minimum length scale. Despite its success in various topology optimization fields, the robust formulation presents some drawbacks. This paper addresses one in particular, which concerns the imposition of the minimum length scale. In the density framework, the minimum size of the solid and void phases must be imposed implicitly through the parameters that define the density filter and the smoothed Heaviside projection. Finding these parameters can be time consuming and cumbersome, hindering a general code implementation of the robust formulation. Motivated by this issue, in this article we provide analytical expressions that explicitly relate the minimum length scale and the parameters that define it. The expressions are validated on a density-based framework. To facilitate the reproduction of results, MATLAB codes are provided. As a side finding, this paper shows that to obtain simultaneous control over the minimum size of the solid and void phases, it is necessary to involve the 3 fields (eroded, intermediate and dilated) in the topology optimization problem. Therefore, for the compliance minimization problem subject to a volume restriction, the intermediate and dilated designs can be excluded from the objective function, but the volume restriction has to be applied to the dilated design in order to involve all 3 designs in the formulation.
翻译:引进受侵蚀和膨胀设计版本的坚固的表层优化配方近年来越来越受欢迎,这主要是因为它有能力制作符合最短规模的设计,尽管在各种表层优化领域取得了成功,但稳健的配方有一些缺点。本文件特别述及一个问题,即最小长度尺度的强制;在密度框架内,固态和真空阶段的最小尺寸必须隐含地通过界定密度过滤器和平滑的 Heaviside预测参数的参数来实施。发现这些参数可能耗时繁琐,妨碍稳健的配方的一般代码的实施。受这一问题的驱动,我们在本条中提供的分析表达方式明确涉及最低长度尺度和界定其定义的参数。这些表达方式在基于密度的框架中得到验证。为了便于复制结果,提供了MATLAB代码。作为附加结论,该文件表明,要同时控制固态和真空阶段的最小尺寸,就必须将3个领域(有色、中间和三角)纳入表层优化问题。因此,为了在最大程度设计中,在最大程度设计中,可将最大限度应用到最大程度设计中,在最大程度设计中,要将最大限制到最大程度设计中。