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.
To assist users in the design of 3D printed shapes, Stave Stava et al @cite_27 presented a system to detect structural deficiencies by finite element analysis. A set of correction operations including hollowing, thickening, and strut insertion, are proposed to improve the structural soundness. Targeting specifically for reducing the material usage inside a 3D model, @cite_5 introduced skin-frame structures as a composition of the shape interior, and optimized the layout and size of frames. @cite_18 proposed honeycomb-like Voronoi structures to hollow the interior volume, and optimized the distribution and size of Voronoi cells. In early work by @cite_52 , the layout of truss structures is optimized for designing bridges and towers. Manufacturing constraints regarding the avoidance of overhang surfaces and small geometric feature size, have been addressed by @cite_44 via self-supporting rhombic structures for infill optimization. Manufacturable micro-structures have been investigated in graphics @cite_36 @cite_31 @cite_32 and in mechanical topology optimization approaches (e.g., @cite_11 @cite_47 , among others). Our work is inspired by these works , but and builds upon topology optimization which doesn't prescribe the structural composition and thus does not limit the design space.
@cite_18 @cite_47 @cite_36 @cite_52 @cite_32 @cite_44 @cite_27 @cite_5 @cite_31 @cite_11
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The emergence of low-cost 3D printers steers the investigation of new geometric problems that control the quality of the fabricated object. In this paper, we present a method to reduce the material cost and weight of a given object while providing a durable printed model that is resistant to impact and external forces. We introduce a hollowing optimization algorithm based on the concept of honeycomb-cells structure. Honeycombs structures are known to be of minimal material cost while providing strength in tension. We utilize the Voronoi diagram to compute irregular honeycomb-like volume tessellations which define the inner structure. We formulate our problem as a strength--to--weight optimization and cast it as mutually finding an optimal interior tessellation and its maximal hollowing subject to relieve the interior stress. Thus, our system allows to build-to-last 3D printed objects with large control over their strength-to-weight ratio and easily model various interior structures. We demonstrate our method on a collection of 3D objects from different categories. Furthermore, we evaluate our method by printing our hollowed models and measure their stress and weights. Abstract Recent work has demonstrated that the interior material layout of a 3D model can be designed to make a fabricated replica satisfy application-specific demands on its physical properties, such as resistance to external loads. A widely used practice to fabricate such models is by layer-based additive manufacturing (AM), which however suffers from the problem of adding and removing interior supporting structures. In this paper, we present a novel method for generating application-specific infill structures on rhombic cells so that the resultant structures can automatically satisfy manufacturing requirements on overhang-angle and wall-thickness. Additional supporting structures can be avoided entirely in our framework. To achieve this, we introduce the usage of an adaptive rhombic grid, which is built from an input surface model. Starting from the initial sparse set of rhombic cells, via numerical optimization techniques an objective function can be improved by adaptively subdividing the rhombic grid and thus adding more walls in cells. We demonstrate the effectiveness of our method for generating interior designs in the applications of improving mechanical stiffness and static stability. Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however, so far only with flat hyper-surfaces as cell-cell contact borders. In order to reproduce the experimentally observed piecewise spherical boundary shapes, we develop a consistent theoretical framework of multiplicatively weighted distance functions, defining generalized finite Voronoi neighborhoods around cell bodies of varying radius, which serve as heterogeneous generators of the resulting model tissue. The interactions between cells are represented by adhesive and repelling force densities on the cell contact borders. In addition, protrusive locomotion forces are implemented along the cell boundaries at the tissue margin, and stochastic perturbations allow for non-deterministic motility effects. Simulations of the emerging system of stochastic differential equations for position and velocity of cell centers show the feasibility of this Voronoi method generating realistic cell shapes. In the limiting case of a single cell pair in brief contact, the dynamical nonlinear Ornstein–Uhlenbeck process is analytically investigated. In general, topologically distinct tissue conformations are observed, exhibiting stability on different time scales, and tissue coherence is quantified by suitable characteristics. Finally, an argument is derived pointing to a tradeoff in natural tissues between cell size heterogeneity and the extension of cellular lamellae. In this paper, we present a novel method, the first to date to our knowledge, which is capable of directly and automatically producing a concise and idealized 3D representation from unstructured point data of complex cluttered real-world scenes, with a high level of noise and a significant proportion of outliers, such as those obtained from passive stereo. Our algorithm can digest millions of input points into an optimized lightweight watertight polygonal mesh free of self-intersection, that preserves the structural components of the scene at a user-defined scale, and completes missing scene parts in a plausible manner. To achieve this, our algorithm incorporates priors on urban and architectural scenes, notably the prevalence of vertical structures and orthogonal intersections. A major contribution of our work is an adaptive decomposition of 3D space induced by planar primitives, namely a polyhedral cell complex. We experimentally validate our approach on several challenging noisy point clouds of urban and architectural scenes.