Polyhedral Voronoi diagrams for additive manufacturing

International audienceA critical advantage of additive manufacturing is its ability to fabricate complex small-scale structures. These microstructures can be understood as a metamaterial: they exist at a much smaller scale than the volume they fill, and are collectively responsible for an average elastic behavior different from that of the base printing material making the fabricated object lighter and/or flexible along specific directions. In addition, the average behavior can be graded spatially by progressively modifying the microstructure geometry.The definition of a microstructure is a careful trade-off between the geometric requirements of manufacturing and the properties one seeks to obtain within a shape: in our case a wide range of elastic behaviors. Most existing microstructures are designed for stereolithography (SLA) and laser sintering (SLS) processes. The requirements are however different than those of continuous deposition systems such as fused filament fabrication (FFF), for which there is currently a lack of microstructures enabling graded elastic behaviors.In this work we introduce a novel type of microstructures that strictly enforce all the requirements of FFF-like processes: continuity, self-support and overhang angles. They offer a range of orthotropic elastic responses that can be graded spatially. This allows to fabricate parts usually reserved to the most advanced technologies on widely available inexpensive printers that also benefit from a continuously expanding range of materials

PIVOT: A Framework for Minimizing Stress Deviations in Structural Form

Design of efficient structural members is certainly an intricate process that requires a sound explanation, an exact fit of art and science perhaps, to harness the ever-increasing range of solutions assisted by computational advancements and manufacturing innovations. Many frameworks have been introduced previously to optimize the structural form, however, obtaining a uniform stress distribution has been neglected in favor of determining the least volume satisfying the objective function. Inadvertently, in the process of changing the volume, there are changes to the underlying geometry as well. Since there have been recent studies documenting the impact of geometry on the mechanical performance, it is crucial to obtain reliable knowledge regarding the impact it can have on strategic redistribution of stresses while keeping the volume constant. This investigation proposed the use of Voronoi tessellation, a bioinspired mathematical approach, to determine the positioning of void spaces. Stress-weighted centroids of Voronoi cells were utilized for selecting Voronoi sites based on two different weights. This technique was tested against the Lloyd’s algorithm that utilizes geometric centroids to select Voronoi sites. The results demonstrate a statistically significant difference between the Lloyd’s algorithm and PIVOT. The proposed approach, with weights inversely proportional to the stresses, showed affirmative signs of convergence while reducing the standard deviation of stress, mean stress and lowering the maximum stress value without making any changes to the volume

Fabrication-Aware Design with Performative Criteria

Artists and architects often need to handle multiple constraints during design of physical constructions. We define a performative constraint as any constraint on design that is tied to the performance of the model--either during fabrication, construction, daily use, or destruction. Even for small to medium scale models, there are functional criteria such as the ease of fabrication and the assembly process, or even the interplay of light with the material. Computational tools can greatly aid in this process, assisting with the lower-level performative constraints, while the designer handles the high-level artistic decisions. Additionally, using new fabrication methods, our tools can aid in lowering the difficulty of building complex constructions, making them accessible to hobbyists. In this thesis, we present three computational methods for designing with different approaches, each with a different material, fabrication method, and use case. The first method is a construction with intersecting planar pieces that can be laser cut or milled. These 3D forms are assembled by sliding pieces into each other along straight slits, and do not require other support such as glue or screws. We present a mathematical abstraction that formalizes the constraints between pieces as a graph, including fabrication and assembly constraints, and ensure global rigidity of the sculpture. We also propose an optimization algorithm to guide the user using automatic constraint satisfaction based on analysis of the constraint relation graph. We demonstrate our approach by creating several small- to medium-scale examples including functional furniture. The second method presents a solution to building a 3D sculpture out of existing building blocks that can be found in many homes. Starting from the voxelization of a 3D mesh we merge voxels to form larger bricks, and then analyze and repair structural problems based on a graph representation of the block connections. We then output layer-by-layer building instructions to allow a user to quickly and easily build the model. We also present extensions such as hollowing the models to use less bricks, limiting the number of bricks of each size, and including color constraints. We present both real and virtual brick constructions and associated timings, showing improvements over previous work. The final case presented tackles the inverse design problem of finding a surface to produce a target caustic on a receiver plane when light is refracted or reflected. This is an example where the performative constraint is the principal driver of the design. We introduce an optimal transport formulation to find a correspondence between the incoming light and the output target light distribution. We then show a 3D optimization that finds the surface that transports light based on the correspondence map. Our approach supports piecewise smooth surfaces that are as smooth as possible but allow for creases, to greatly reduce the amount of artifacts while allowing light to be completely diverted producing completely black regions. We show how this leads to a very large space of high-contrast, high-resolution caustic images, including point and line singularities of infinite light density as well as photo-realistic images. Our approach leads to surfaces that can be milled using standard CNC milling. We demonstrate the approach showing both simulated and fabricated examples

Framework for The Generation and Design of Naturally Functionally Graded Lattice Structures

Functionally Graded Lattice (FGL) Structures have shown improved performance over uniform lattice structures in different fields. Another form of functional grading can be seen in materials in nature, where the cellular structure can vary in both cell porosity and size. To distinguish between lattice structures that vary in porosity only and lattice structures that vary in both, we will refer to the latter in this research as Naturally Functionally Graded Lattice (NFGL) structures. Research into NFGL structures' performance against FGL structures in the literature is lacking. Furthermore, the current methods in the literature to generate these structures are severely limited and suffer from multiple drawbacks. This research aims to develop a framework, namely the NFGL Framework, to generate NFGL structures without the drawbacks that exist in current methods and to improve the performance of the generated structures using the NFGL Framework against existing FGL structures. The NFGL Framework uses a novel method to generate nodes for NFGL structures from using a developed simplified sphere packing algorithm to generate conformal NFGL structures in a deterministic and computationally efficient manner. Furthermore, the NFGL Framework can perform a similarity analysis using a modified Mean Structural Similarity (MSSIM) index to improve the performance of the generated NFGL structure. The generated structures using the NFGL Framework were tested against the existing methods and showed to overcome the drawbacks of these methods with improved performance and computational time. Furthermore, the generated NFGL structures were tested against FGL structures and the results showed a performance gain from the use of NFGL structures over FGL structures with a reduced computational cost.Ph.D

Genetic-algorithm based framework for lattice support structure optimization in additive manufacturing

The emergence and improvement of Additive Manufacturing technologies allow the fabrication of complex shapes so far inconceivable. However, to produce those intricate geometries, support structures are required. Besides wasting unnecessary material, these structures are consuming valuable production and post-processing times. This paper proposes a new framework to optimize the geometry and topology of inner and outer support structures. Starting from a uniform lattice structure filling both the inner and outer areas to be supported, the approach removes a maximum number of beams so as to minimize the volume of the support. The most suited geometry for the initial lattice structure is defined at the beginning considering the possibilities of the manufacturing technologies. Then, the pruning of the structure is performed through a genetic algorithm, for which the control parameters values have been tuned through a design of experiments. The proposed approach is validated on several test cases of various geometries, containing both inner and outer areas to be supported. The generated support structures are compared to the ones obtained by several state-of-the-art support structure strategies and are proved to have lower material consumption

A review of geometry representation and processing methods for cartesian and multiaxial robot-based additive manufacturing

Nowadays, robot-based additive manufacturing (RBAM) is emerging as a potential solution to increase manufacturing flexibility. Such technology allows to change the orientation of the material deposition unit during printing, making it possible to fabricate complex parts with optimized material distribution. In this context, the representation of parts geometries and their subsequent processing become aspects of primary importance. In particular, part orientation, multiaxial deposition, slicing, and infill strategies must be properly evaluated so as to obtain satisfactory outputs and avoid printing failures. Some advanced features can be found in commercial slicing software (e.g., adaptive slicing, advanced path strategies, and non-planar slicing), although the procedure may result excessively constrained due to the limited number of available options. Several approaches and algorithms have been proposed for each phase and their combination must be determined accurately to achieve the best results. This paper reviews the state-of-the-art works addressing the primary methods for the representation of geometries and the subsequent geometry processing for RBAM. For each category, tools and software found in the literature and commercially available are discussed. Comparison tables are then reported to assist in the selection of the most appropriate approaches. The presented review can be helpful for designers, researchers and practitioners to identify possible future directions and open issues