Topology Optimization with Local Perimeter Constraints and Non-Linear Filtering for Minimum Length and Overhang Control
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One of the major challenges facing the transport industry is the development of lightweight structural designs that reduce fuel consumption and environmental impact. Topology optimization offers an effective framework for achieving significant weight reduction while simultaneously decreasing design time and cost. However, the resulting optimized geometries are often highly complex and typically require additive manufacturing for realization. To ensure manufacturability, it is essential to integrate additive manufacturing constraints directly into the optimization process, particularly those related to minimum length scale enforcement and overhang control, in order to avoid impractical shapes and unsupported volumes. This work investigates the feasibility of incorporating such constraints within topology optimization for additive manufacturing applications. Specifically, we propose the use of non-linear filtering techniques to penalize overhangs in the 3D printing sense, while simultaneously enforcing a minimum length scale in the opposite direction. This filtering strategy is further combined with a local perimeter measure, enabling manufacturing constraints to be imposed in a spatially localized manner. As a reference result, local isoperimetric problems are solved to provide a benchmark that supports and illustrates the behavior of the proposed localized approach. Numerical results demonstrate that the method successfully eliminates small-scale bar-like features and promotes vertically aligned structural elements, thereby significantly enhancing the manufacturability of the optimized designs. In summary, we propose a unified methodology applicable to both density-based and level-set topology optimization that enforces minimum length scale and overhang constraints by relying exclusively on boundary smoothing to identify and penalize removable geometric features, without requiring additional constraints or bound formulations.
