Feature-driven topology optimization method with signed distance function
Feature-driven topology optimization method with signed distance function
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DOI：
10.1016/j.cma.2016.06.027
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发表时间：
2016-10
影响因子：
7.2
通讯作者：
Ying Zhou;Weihong Zhang;Jihong Zhu;Zhao Xu
中科院分区：
文献类型：
--
作者：
Ying Zhou;Weihong Zhang;Jihong Zhu;Zhao Xu
本文提出了一种特征驱动的拓扑优化方法。这是首次利用水平集函数(LSF)和布尔运算对多个工程特征进行布局设计的研究。这项工作的新颖性有三个方面。首先，将任意形状的多个工程特征作为基本设计基元，通过特征的布局和形状优化实现拓扑变化。LSF采用布尔运算构造的Kreisselmeier-Steinhauser(KS)函数，通过隐函数保证基本特征和整体结构的光滑描述和拓扑变化。其次，利用修正的Heaviside函数在固定的计算网格上对孔洞-固体材料的过渡过程进行光顺处理，建立了用于灵敏度分析的窄带区域积分格式。第三，分析了特征连接处的灰度分布区域，其根本原因是特定特征的水平集轮廓分布不等距。为了避免出现灰度区域，提出了一种近似符号距离函数来正则化LSF和KS函数。指出了KS函数的有界正规化性质，因为它是用符号距离函数或归一化一阶近似来构造的。最后通过算例验证了特征驱动拓扑优化方法在复杂设计问题中的有效性和优越性。
In this paper, a feature-driven topology optimization method is developed. This is the first study on layout design of multiple engineering features using level-set functions (LSFs) and Boolean operations. The novelty of this work is threefold. First, multiple engineering features of arbitrary shape are considered as basic design primitives and topology variation is achieved via the layout and shape optimization of the features. Kreisselmeier–Steinhauser (KS) function constructed by means of Boolean operations is adopted as the LSF, which uses an implicit function to ensure a smooth description and topological changes of basic features and the whole structure. Second, using a modified Heaviside function to smooth the void–solid material transition over a fixed computing mesh, a narrow-band domain integral scheme is developed for the efficient sensitivity analysis. Third, the gray material distribution regions at the feature-connecting portions are analyzed and the underlying reason for that is traced to the non-equidistant distribution of level-set contours of specific features. To avoid the gray regions, an approximated signed distance function is proposed to regularize the LSF and KS function. The bounded normalization property of the KS function is highlighted for its construction with the signed distance functions or normalized first-order approximations. Numerical examples are finally tested to demonstrate the validity and merits of the proposed feature-driven topology optimization for complicated design problems.