Heaviside-Based Morphological Filters for Topology Optimization

To ensure manufacturability and mesh independence in density-based topology optimization schemes, it is imperative to use restriction methods. This paper proposes a family of Heaviside-based morphological filters based on the morphology-based restriction schemes, namely open, close, open-close and close-open filters. In the proposed morphological filters, Heaviside projection filter plays the role of dilation filter and modified Heaviside projection filter acts as the erosion filter. They work as principle operators and then applied sequentially to form the close, open, close-open, and open-close filters. The proposed morphological filters are tested by the compliance minimization problem. Test results show that the proposed four filters are volume preserving, and the characteristics of each filter are discussed.