Porous structures such as trabecular bone are widely seen in nature. These structures are lightweight and exhibit strong mechanical properties. In this paper, we present a method to generate bone-like porous structures as lightweight infill for additive manufacturing. Our method builds upon and extends voxel-wise topology optimization. In particular, for the purpose of generating sparse yet stable structures distributed in the interior of a given shape, we propose upper bounds on the localized material volume in the proximity of each voxel in the design domain. We then aggregate the local per-voxel constraints by their p -norm into an equivalent global constraint, in order to facilitate an efficient optimization process. Implemented on a high-resolution topology optimization framework, our results demonstrate mechanically optimized, detailed porous structures which mimic those found in nature. We further show variants of the optimized structures subject to different design specifications, and we analyze the optimality and robustness of the obtained structures.
With the ever-increasing popularity of consumer 3D printers, much research has been devoted to address geometric and physical modeling problems for computational fabrication, including the toolpath generation @cite_10 . In this section, we review techniques related to the optimization of mechanical properties. For an overview of geometric and physical modeling for 3D printing, let us refer to a recent survey article @cite_40 and a tutorial @cite_26 .
@cite_40 @cite_26 @cite_10
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Additive manufacturing (AM) is poised to bring about a revolution in the way products are designed, manufactured, and distributed to end users. This technology has gained significant academic as well as industry interest due to its ability to create complex geometries with customizable material properties. AM has also inspired the development of the maker movement by democratizing design and manufacturing. Due to the rapid proliferation of a wide variety of technologies associated with AM, there is a lack of a comprehensive set of design principles, manufacturing guidelines, and standardization of best practices. These challenges are compounded by the fact that advancements in multiple technologies (for example materials processing, topology optimization) generate a "positive feedback loop" effect in advancing AM. In order to advance research interest and investment in AM technologies, some fundamental questions and trends about the dependencies existing in these avenues need highlighting. The goal of our review paper is to organize this body of knowledge surrounding AM, and present current barriers, findings, and future trends significantly to the researchers. We also discuss fundamental attributes of AM processes, evolution of the AM industry, and the affordances enabled by the emergence of AM in a variety of areas such as geometry processing, material design, and education. We conclude our paper by pointing out future directions such as the "print-it-all" paradigm, that have the potential to re-imagine current research and spawn completely new avenues for exploration. The fundamental attributes and challenges barriers of Additive Manufacturing (AM).The evolution of research on AM with a focus on engineering capabilities.The affordances enabled by AM such as geometry, material and tools design.The developments in industry, intellectual property, and education-related aspects.The important future trends of AM technologies. We develop a new kind of "space-filling" curves, connected Fermat spirals, and show their compelling properties as a tool path fill pattern for layered fabrication. Unlike classical space-filling curves such as the Peano or Hilbert curves, which constantly wind and bind to preserve locality, connected Fermat spirals are formed mostly by long, low-curvature paths. This geometric property, along with continuity, influences the quality and efficiency of layered fabrication. Given a connected 2D region, we first decompose it into a set of sub-regions, each of which can be filled with a single continuous Fermat spiral. We show that it is always possible to start and end a Fermat spiral fill at approximately the same location on the outer boundary of the filled region. This special property allows the Fermat spiral fills to be joined systematically along a graph traversal of the decomposed sub-regions. The result is a globally continuous curve. We demonstrate that printing 2D layers following tool paths as connected Fermat spirals leads to efficient and quality fabrication, compared to conventional fill patterns.