🤖 AI Summary
This study addresses the challenge of spatial layout optimization for interconnected systems within non-convex design spaces by extending the SPI2 framework. It introduces, for the first time, a geometric representation based on Maximal Disjoint Ball Decomposition (MDBD) combined with differentiable inside-outside tests, enabling component placement under arbitrary non-convex boundaries. The method integrates computations of centroid and moment of inertia and establishes an end-to-end CAD workflow that supports automatic assembly reconstruction. By simultaneously satisfying geometric constraints, routing requirements, and physical performance objectives, the approach guarantees geometric feasibility within numerical precision. The efficacy and practicality of the proposed method are demonstrated through a multi-system co-layout case study of a synthetic aircraft auxiliary unit.
📝 Abstract
This paper presents a spatial optimization methodology that extends the Spatial Packaging of Interconnected Systems with Physical Interaction (SPI2) framework to support arbitrary, non-convex design boundaries. We introduce a smooth, differentiable inside-outside evaluation for components represented using the Maximal Disjoint Ball Decomposition (MDBD) method. The framework also incorporates center-of-gravity and moment-of-inertia calculations directly into the optimization, and provides an end-to-end computer-aided design (CAD) workflow for importing components and reconstructing the optimized assembly. The method is demonstrated on a fictional aircraft auxiliary unit. Results show that the optimizer can place multiple interconnected components within a custom geometry while simultaneously handling routing and physics-based objectives. The approach maintains geometric feasibility within numerical tolerance and illustrates the potential of MDBD-based SPI2 methods for practical engineering design applications.