An explicit formulation for minimum length scale control in density-based topology optimization

Abstract

Topology optimization is widely applied in various engineering areas for obtaining innovative designs. However, the optimized results often contain many small features that cannot satisfy the manufacturable requirements. It is important to develop an effective minimum length scale control method which can be easily implemented and control the length scale accurately in topology optimization. In this work, an explicit and general mathematical formulation of the minimum length scale constraint in the density-based topology optimization framework is proposed. Compared to the existing implicit method, such as robust formulation, the proposed method can give accurate length-scale control for arbitrary problems. In addition, the proposed formulation has remarkable advantages in terms of implementation simplicity and parameter insensitivity. Only computing the average density of elements in a small circular region is needed, similar to the typical filtering technique. Aggregation functions are used to gather all the local constraints into a single constraint, and the sensitivity analysis of the constraint function is derived. Some representative numerical examples are presented to verify the effectiveness of the proposed algorithm.