Length scale control is imposed in topology optimization (TO) to make designs amenable to manufacturing and other functional requirements. Broadly, there are two types of length-scale control in TO: \emph {exact} and \emph {approximate}. While the former is desirable, its implementation can be difficult, and is computationally expensive. Approximate length scale control is therefore preferred, and is often sufficient for early stages of design. In this paper we propose an approximate length scale control strategy for TO, by extending a recently proposed density-based TO formulation using neural networks (TOuNN). Specifically, we enhance TOuNN with a Fourier space projection, to control the minimum and/or maximum length scales. The proposed method does not involve additional constraints, and the sensitivity computations are automated by expressing the computations in an end-end differentiable fashion using the neural net's library. The proposed method is illustrated through several numerical experiments for single and multi-material designs.
翻译:在地形优化(TO)中规定了长度控制,使设计符合制造和其他功能要求。广义而言,在to中,有两种类型的长度控制:\emph {exact}和\emph {appear}。虽然前者是可取的,但其实施可能很困难,而且计算成本很高。因此,倾向于使用近似长度控制,而且往往足以用于早期设计阶段。在本文件中,我们建议了一种大致的长度控制战略,通过将最近提议的密度用于使用神经网络(TOUNN)的配方的扩大为基于神经网络(TOUNN)的配方。具体地说,我们用四维空间投射来增强TouNN,以控制最小和/或最大长度尺度。拟议方法不涉及额外的限制,而敏感度计算是自动化的,方法是利用神经网库以最终不同的方式表达计算。拟议的方法通过对单一和多物质设计进行数项实验来说明。