To Refine or Not to Refine: Topology Optimization of Adaptively Refined Infill Structures for Additive Manufacturing
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We present a novel method for optimizing structures by adaptively refining the structural details. The adaptively refined structures topologically resemble the graph composed of edges in the quadtree mesh. However, while adaptive mesh refinement is employed in numerical analysis for reducing computational complexity, in this work we interpret the edges as structural elements carrying mechanical loads. The adaptivity and full coverage over the design domain make adaptively refined structures well-suited as infill for 3D printed parts, where uniform infill structures have been typically used in practice. The topology optimization of adaptively refined structures is realized based on two novel ideas. First, we relax the binary design variables (i.e., to refine or not to refine) by using continuous variables, giving rise to sensitivity analysis for an efficient gradient-based optimization. Second, we propose a refinement filter to encode the dependence of design variables among multiple levels in the structural hierarchy. The refinement filter thus enables considering the design variables on all levels simultaneously in the optimization. Our numerical results demonstrate optimized structures spanning multiple levels in the quadtree, with cell sizes smoothly varying in the closed-walled design domain.
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