Topology Optimization of Subtractive-Additive Designs by Two Phase Minimum Length Scale Control
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Establishing minimum length scales in both the solid and the void phase is a key aspect of structural topology optimization. Beyond ensuring mesh independence and suppressing checkerboard patterns, length-scale control can substantially affect the resulting topology. The minimum length scale of the solid phase is directly related to the smallest geometric feature size, such as wall thicknesses or bar diameters. Efficient closed-walled designs can be obtained only if the prescribed minimum feature size remains sufficiently small. As the minimum feature size increases, optimal layouts tend to shift towards less filigree, truss-like topologies. For comparatively large minimum feature sizes, the available material is ultimately distributed in a predominantly compact manner, yielding less complex designs that resemble conventional engineering parts. Since manufacturing processes—ranging from casting to the various additive manufacturing technologies—impose lower bounds on producible feature sizes, enforcing a solid-phase minimum length scale is commonly done for the sake of manufacturability. The minimum length scale of the void phase is related to the smallest admissible hole size in the sense that a sphere with a diameter not exceeding this length scale can touch any point on the outer surface of the structure without collision. At least for non-enclosed voids, this provides a measure of local accessibility, which is a prerequisite for subtractive manufacturing. Accordingly, a length scale in the void phase is often used as a simplified machining constraint. Methods for enforcing minimum length scales in either the solid or the void phase have been proposed, for example in [Ref1] and [Ref2]. In many practical settings, single-phase methods are sufficient to ensure manufacturability. However, this is no longer necessarily the case for hybrid designs, where a monolithic part is intended to be produced by multiple manufacturing techniques. In this paper, we focus on hybrid subtractive–additive manufacturing and present a case study that applies a novel length scale control strategy during topology optimization to achieve adequate manufacturability. The approach is based on a reformulation of the morphological operators introduced to topology optimization in [Ref3]. The results demonstrate the effectiveness of the proposed strategy and highlight both opportunities and limitations associated with hybrid designs.
