We present a novel method for optimizing structures by adaptively refiningthe structural details. The adaptively refined structures topologicallyresemble the graph composed of edges in the quadtree mesh. However, whileadaptive mesh refinement is employed in numerical analysis for reducingcomputational complexity, in this work we interpret the edges as structuralelements carrying mechanical loads. The adaptivity and full coverage over thedesign domain make adaptively refined structures well-suited as infill for 3Dprinted parts, where uniform infill structures have been typically used inpractice. The topology optimization of adaptively refined structures is realized basedon two novel ideas. First, we relax the binary design variables (i.e., torefine or not to refine) by using continuous variables, giving rise tosensitivity analysis for an efficient gradient-based optimization. Second, wepropose a refinement filter to encode the dependence of design variables amongmultiple levels in the structural hierarchy. The refinement filter thus enablesconsidering the design variables on all levels simultaneously in theoptimization. Our numerical results demonstrate optimized structures spanningmultiple levels in the quadtree, with cell sizes smoothly varying in theclosed-walled design domain.
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