Feature-driven topology optimization method with signed distance function

Abstract

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.