EXTENDING ORIGAMI TECHNIQUE TO FOLD FORMING OF SHEET METAL PRODUCTS

This dissertation presents a scientific based approach for the analysis of folded sheet metal products. Such analysis initializes the examination in terms of topological exploration using set of graph modeling and traversal algorithms. The geometrical validity and optimization are followed by utilizing boundary representation and overlapping detection during a geometrical analysis stage, in this phase the optimization metrics are established to evaluate the unfolded sheet metal design in terms of its manufacturability and cost parameters, such as nesting efficiency, total welding cost, bend lines orientation, and maximum part extent, which aides in handling purposes. The proposed approach evaluates the design in terms of the stressed-based behavior to indicate initial stress performance by utilizing a structural matrix analysis while developing modification factors for the stiffness matrix to cope with the stress-based differences of the diverse flat pattern designs. The outcome from the stressed-based ranking study is mainly the axial stresses as exerted on each element of folded geometry; this knowledge leads to initial optimizing the flat pattern in terms of its stress-based behavior. Furthermore, the sheet folding can also find application in composites manufacturing. Thus, this dissertation optimizes fiber orientation based on the elasticity theory principles, and the best fiber alignment for a flat pattern is determined under certain stresses along with the peel shear on adhesively bonded edges. This study also explores the implementation of the fold forming process within the automotive production lines. This is done using a tool that adopts Quality Function Deployment (QFD) principle and Analytical Hierarchy Process (AHP) methodology to structure the reasoning logic for design decisions. Moreover, the proposed tool accumulates all the knowledge for specific production line and parts design inside an interactive knowledge base. Thus, the system is knowledge-based oriented and exhibits the ability to address design problems as changes occur to the product or the manufacturing process options. Additionally, this technique offers two knowledge bases; the first holds the production requirements and their correlations to essential process attributes, while the second contains available manufacturing processes options and their characteristics to satisfy the needs to fabricate Body in White (BiW) panels. Lastly, the dissertation showcases the developed tools and mathematics using several case studies to verify the developed system\u27s functionality and merits. The results demonstrate the feasibility of the developed methodology in designing sheet metal products via folding

Optimal face-to-face coupling for fast self-folding kirigami

Kirigami-inspired designs can enable self-folding three-dimensional materials from flat, two-dimensional sheets. Hierarchical designs of connected levels increase the diversity of possible target structures, yet they can lead to longer folding times in the presence of fluctuations. Here, we study the effect of rotational coupling between levels on the self-folding of two-level kirigami designs driven by thermal noise in a fluid. Naturally present due to hydrodynamic resistance, we find that optimization of this coupling as control parameter can significantly improve a structure's self-folding rate and yield

APPLICATIONS OF PARAMETERIZED L-SYSTEMS FOR PRELIMINARY STRUCTURAL DESIGN AND OPTIMIZATION

Preliminary design is a complicated problem that is often solved using topology optimization. In this work, a heuristic approach to topology optimization is considered. This approach involves the coupling of a genetic optimization with a parallel rewriting system, known as an L-System. This approach encodes design variables into a string of characters that are then coupled with an interpreter to develop a structure in a given domain. By considering a heuristic bio-inspired approach over more traditional density and level set topology approaches, we are able to avoid numerical issues and rapid increasing design space dimensionality associated with complicated multi objective problems. In this work a new interpreter for L-Systems, called the Spatial Interpretation for the Design of Reconfigurable Structures (SPIDRS), is applied to several design problems. This work seeks to show SPIDRS as a powerful preliminary design tool for difficult problems that lack traditional engineering intuition. First, a morphing airfoil inspired by the rotor blade of the UH-60 is considered. SPIDRS is utilized to determine the internal structural layout as well as the placement of actuators to facilitate morphing to meet a shape objective while minimizing mass. A coupled fluid structure interaction (FSI) evaluation is performed using the finite element method (Abaqus) and vortex lattice method (XFOIL). The resulting final shape of the airfoil, as determined by the FSI evaluation, and the mass are used as objectives in a genetic optimization Second, a set of origami fold design problems are considered. SPIDRS is first validated using the well established square twist pattern and the results are compared to previous work in the literature. SPIDRS is then used with an arbitrary continuous kinematic objective to determine its ability to evolve towards an unknown solution pattern. The standard square twist pattern is also utilized to evaluate the efficacy of altering the original SPIDRS production rules for use specifically in origami

Mathematical Imaging and Surface Processing

Within the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images. This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains

Shape Design and Optimization for 3D Printing

In recent years, the 3D printing technology has become increasingly popular, with wide-spread uses in rapid prototyping, design, art, education, medical applications, food and fashion industries. It enables distributed manufacturing, allowing users to easily produce customized 3D objects in office or at home. The investment in 3D printing technology continues to drive down the cost of 3D printers, making them more affordable to consumers. As 3D printing becomes more available, it also demands better computer algorithms to assist users in quickly and easily generating 3D content for printing. Creating 3D content often requires considerably more efforts and skills than creating 2D content. In this work, I will study several aspects of 3D shape design and optimization for 3D printing. I start by discussing my work in geometric puzzle design, which is a popular application of 3D printing in recreational math and art. Given user-provided input figures, the goal is to compute the minimum (or best) set of geometric shapes that can satisfy the given constraints (such as dissection constraints). The puzzle design also has to consider feasibility, such as avoiding interlocking pieces. I present two optimization-based algorithms to automatically generate customized 3D geometric puzzles, which can be directly printed for users to enjoy. They are also great tools for geometry education. Next, I discuss shape optimization for printing functional tools and parts. Although current 3D modeling software allows a novice user to easily design 3D shapes, the resulting shapes are not guaranteed to meet required physical strength. For example, a poorly designed stool may easily collapse when a person sits on the stool; a poorly designed wrench may easily break under force. I study new algorithms to help users strengthen functional shapes in order to meet specific physical properties. The algorithm uses an optimization-based framework — it performs geometric shape deformation and structural optimization iteratively to minimize mechanical stresses in the presence of forces assuming typical use scenarios. Physically-based simulation is performed at run-time to evaluate the functional properties of the shape (e.g., mechanical stresses based on finite element methods), and the optimizer makes use of this information to improve the shape. Experimental results show that my algorithm can successfully optimize various 3D shapes, such as chairs, tables, utility tools, to withstand higher forces, while preserving the original shape as much as possible. To improve the efficiency of physics simulation for general shapes, I also introduce a novel, SPH-based sampling algorithm, which can provide better tetrahedralization for use in the physics simulator. My new modeling algorithm can greatly reduce the design time, allowing users to quickly generate functional shapes that meet required physical standards

A New Design Method Framework for Open Origami Design Problems

With the development of computer science and manufacturing techniques, modern origami is no longer just used for making artistic shapes as its traditional counterpart was many centuries ago. Instead, the outstanding lightweight and high flexibility of origami structures has expanded their engineering application in aerospace, medical devices, and architecture. In order to support the automatic design of more complex modern origami structures, several computational origami design methods have been established. However these methods still focus on the problem of determining a crease pattern to fold into an exact pre-determined shape. And these methods apply deductive logic and function for only one type of topological origami structure. In order to drop the topological constraints on the shapes, this dissertation introduces the research on the development and implementation of the abductive evolutionary design methods to open origami design problems, which is asking for their designs to achieve geometric and functional requirements instead of an exact shape. This type of open origami design problem has no formal computational solutions yet. Since the open origami design problem requires searching for solutions among arbitrary candidates without fixing to a certain topological formation, it is NP-complete in computational complexity. Therefore, this research selects the genetic algorithm (GA) and one of its variations – the computational evolutionary embryogeny (CEE) – to solve origami problems. The dissertation made two major contributions. One contribution is on creating the GA-based/abstract design method framework on open origami design problems. The other contribution is on the geometric representation of origami designs that directs the definition and mapping of their genetic representation and physical representation. This research introduced two novel geometric representations, which are the “ice-cracking” and the pixelated multicellular representation (PMR). The proposed design methods and the adapted evolutionary operators have been testified by two open origami design problems of making flat-foldable shapes with desired profile area and rigid-foldable 3D water containers with desired volume. The results have proved the proposed methods widely applicable and highly effective in solving the open origami design problems

Computational Unfolding of the Human Hippocampus

The hippocampal subfields are defined by their unique cytoarchitectures, which many recent studies have tried to map to human in-vivo MRI because of their promise to further our understanding of hippocampal function, or its dysfunction in disease. However, recent anatomical literature has highlighted broad inter-individual variability in hippocampal morphology and subfield locations, much of which can be attributed to different folding configurations within hippocampal (or archicortical) tissue. Inspired in part by analogous surface-based neocortical analysis methods, the current thesis aimed to develop a standardized coordinate framework, or surface-based method, that respects the topology of all hippocampal folding configurations. I developed such a coordinate framework in Chapter 2, which was initialized by detailed manual segmentations of hippocampal grey matter and high myelin laminae which are visible in 7-Tesla MRI and which separate different hippocampal folds. This framework was leveraged to i) computationally unfold the hippocampus which provided implicit topological inter-individual alignment, ii) delineate subfields with high reliability and validity, and iii) extract novel structural features of hippocampal grey matter. In Chapter 3, I applied this coordinate framework to the open source BigBrain 3D histology dataset. With this framework, I computationally extracted morphological and laminar features and showed that they are sufficient to derive hippocampal subfields in a data-driven manner. This underscores the sensitivity of these computational measures and the validity of the applied subfield definitions. Finally, the unfolding coordinate framework developed in Chapter 2 and extended in Chapter 3 requires manual detection of different tissue classes that separate folds in hippocampal grey matter. This is costly in the time and the expertise required. Thus, in Chapter 4, I applied state-of-the-art deep learning methods in the open source Human Connectome Project MRI dataset to automate this process. This allowed for scalable application of the methods described in Chapters 2, 3, and 4 to similar new datasets, with support for extensions to suit data of different modalities or resolutions. Overall, the projects presented here provide multifaceted evidence for the strengths of a surface-based approach to hippocampal analysis as developed in this thesis, and these methods are readily deployable in new neuroimaging work

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus