This thesis concerns the approximation of optimally controlled partial differential equations for applications in optimal design and reconstruction. Such optimal control problems are often ill-posed and need to be regularized to obtain good approximations. We here use the theory of the corresponding Hamilton-Jacobi-Bellman equations to construct regularizations and derive error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method where the first, analytical, step is to regularize the Hamiltonian. Next its stationary Hamiltonian system, a nonlinear partial differential equation, is computed efficiently with the Newton method using a sparse Jacobian. An error estimate for the difference between exact and approximate objective functions is derived, depending only on the difference of the Hamiltonian and its finite dimensional regularization along the solution path and its L2 projection, i.e. not on the difference of the exact and approximate solutions to the Hamiltonian systems. In the thesis we present solutions to applications such as optimal design and reconstruction of conducting materials and elastic structures. / QC 20101110

Detta examensarbete använder ett systematiskt tillvägagångssätt för att omkonstruera ett växellådshus till ett elektriskt fordon med avsikt att förbättra prestanda med avseende på hållfasthet, livslängd och styvhet. I examensarbetet ges även en kort beskrivning av hur växellådan fungerar, vilken roll den spelar i de elektriska fordonen, samt grundläggande teori som används  vid konstruktion av liknande växellådor. Den huvudsakliga arbetsmetoden som använts för att nå målen är topologioptimering och olika lösningar har simulerats för att förenkla den framtida omkonstruktionen. Analyser av de olika resultaten har lett fram till ett grovt förslag på hur växellådshuset kan utformas. Det resultatet förkastades efter det att några extra simuleringar gjorts. Även om inget slutgiltigt förslag hittades, har detta examensarbete tagit fram en bra grund och vägvisning för att senare lyckas med uppdraget. / This thesis targets a systematic approach for redesign of the gearbox housing for an electrical vehicle, with an intention to improve its performance in terms of structural integrity, durability and compliance. Throughout the work, a brief overview of gearbox purpose, position and significance in context of electric vehicles has been presented, some theoretical background concerning design of similar gearboxes is presented and underlying theoretical fundamentals are reviewed. Topology optimization has been utilized as the main method for achieving the goals and various solving runs were performed in order to ease the subsequent redesign. Interpretations of multiple result sets led to a rough outline guess of a possible solution candidate. After supplementary studies, that solution was later discarded. In the end, although no final redesign was generated, clear and comprehensive directions for achieving the targeted goal have been formulated.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24226号 / 工博第5054号 / 新制||工||1789(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 平山 朋子, 教授 岩井 裕, 教授 松原 厚 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Topology Optimization is a lightweighting method based on finite element analysis that produces a part with optimum material distribution in the design space. Results from topology optimization often have organic shapes and curves that are difficult if not impossible to machine with traditional subtractive manufacturing methods. This paper analyzes the implementation of the Solidworks® Topology Optimization add-in into the mechanical design process and discusses required postprocessing to ensure manufacturability of the optimized part though a case study on two example parts. Results of traditional optimization, topology optimization and “selective” optimization (optimization using the results from topology optimization to selectively remove material to ensure manufacturability) were compared in terms of weight reduction and time required for optimization. In addition, simplified lightweighted parts were experimentally tested to validate the results of Solidworks® FEA and Topology Optimization to ensure physical part performance and increase confidence in future model results. Overall, it was determined that due to the large amount of time to setup and run, topology optimization may not be the most effective lightweighting method if time is a significant design constraint. However, for some specific applications where part weight is of major importance or where additive manufacturing may be a possible manufacturing process, the benefits of topology optimization’s material removal capability outweigh the required solution time.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24849号 / 工博第5166号 / 新制||工||1987(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 泉井, 一浩, 教授 松原, 厚, 教授 平山, 朋子 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This thesis evaluates an alternative method for creating vibration test fixtures. The new method is based on producing fixtures by utilizing the external forces, that a fixture is subjected to during vibration tests, instead of creating it with estimations and guess-work, as it is done today. The purpose is to be able to create fixtures that have high natural frequencies and are reliable during tests and the goal is to create a computational model that corresponds with the real test conditions. The computational model was defined by applying gravitational loads in all six directions on a static solid model and the computation was solved with topology optimization, to create a structure with the most optimal material distribution. Data was collected in quantities and a model was chosen to work further with to create the version that fulfills the requirements. The final version of the fixture was optimized to an optimal weight of $2.5\;kg$ and produced with additive manufacturing in order to test it on an electrodynamic shaker. The result was a fixture with improved characteristics and a computational model proven valid. Kongsberg Automotive can now create vibration fixtures with higher eigenfrequencies, lower mass and lower manufacturing costs, that are more reliable in vibration tests.

Chronic or degenerative diseases affecting the lumbar spine, commonly referred to as low back pain (LPB), are a major cause of dysfunction, pain, and disability worldwide. According to the Global Burden of Disease (GBD) report of 2019, LPB affects over half a billion people, severely limiting their well-being and lifestyle. Unfortunately, these numbers have been steadily increasing over the last decade, with a rise of more than 15%, mainly due to demographic aging of the population, making it a significant socioeconomic global issue. When conservative treatments such as medications, drugs, and injections fail to alleviate the symptoms, surgical interventions become necessary. Spinal surgeries have become increasingly common and account for 40% of the top ten surgical procedures in the United States alone. As a result, the global market for spinal implants and medical orthopedic devices has been growing at a compound annual growth rate (CAGR) of 5.0% in the United States. Degenerative disc diseases, herniated intervertebral discs, and spondylolisthesis are among the most common problems requiring implant surgery, with lumbar interbody fusion cages or total disc replacements being the most common options. These surgical techniques often utilize a metal endplate or hollow cage as a load-bearing structure to ensure correct load transmission and biomechanical spinal functionality. Currently, endplates for total disc replacement are produced using subtractive manufacturing techniques from bulk biomedical-graded metal alloys like Ti-6Al-4V. The endplates are inserted between two adjacent vertebral bodies, where bone ingrowth and implant fusion are necessary. However, the elastic properties of bulk metals and bone tissue do not match, resulting in stress-shielding phenomena, implant loosening, or implant subsidence. These complications frequently necessitate surgical revision of the implant, which not only impacts the daily activities of the patients but also has a relevant economic impact. Therefore, researchers are exploring alternative design and manufacturing strategies to develop next-generation prosthetic devices that overcome these challenges. Metal additive manufacturing (MAM), particularly Laser-Powder Bed Fusion (L-PBF), has revolutionized the fabrication of specialized components with complex shapes, including architected cellular materials - a novel class of engineered materials with tunable mechanical properties. The biomedical field is a prime example of where lattice application has proved beneficial. MAM provides numerous advantages, including patient-specific customization, a vast design space, and reduced stress shielding. However, issues with structural integrity, lack of AM-specific norms, and the need for fine-tuning process optimizations are still hindering MAM's widespread adoption on the international market. An essential issue that requires resolution is the impact of process-induced flaws on the fatigue behavior of components made of L-PBF lattices. Despite a growing body of scientific literature on the fatigue behavior of lattice unit cells, little attention has been given to the function of fatigue at a millimetric scale, specifically the role of sub-unital lattice elements such as struts and junctions. As fatigue is highly localized, understanding primary fatigue behavior and fracture mechanisms at a strut scale may be critical to addressing the aforementioned problems. Moreover, designing proper prosthetic devices requires fulfilling both biomechanical and biological requirements, leading to a bottleneck in component quality. Proper tuning of osteointegration often requires large porosity and small strut dimensions, approaching the limits of industrial 3D printers. This increases the likelihood of manufacturing lattices with unconnected struts, drosses, parasitic masses, and severe deviations from the nominal as-designed geometries, leading to highly susceptible components under fatigue. To address these challenges, combined approaches with bone tissue engineering may be advantageous. Biopolymers from natural sources, such as silk fibroin and collagen derivatives (i.e., gelatin), are widely used for bone-filler applications due to their exceptional biological properties. These polymers can create highly interconnected biodegradable porous 3D scaffolds suitable for cell differentiation towards an osteogenic phenotype, such as in the form of foams. These foams can be embedded into metal lattice structures, resulting in a hybrid composite device that simultaneously fulfills the load-bearing, fatigue, and osteointegrative requirements that a spinal prosthetic device necessitates. This thesis work covers a range of topics mentioned above. Firstly, an introductory theoretical background is presented in Chapter I, followed by experimental findings which are presented in three different chapters. Chapter II is dedicated to the fatigue behavior of L-PBF Ti-6Al-4V sub-unital lattice elements in the form of miniaturized dog-bone specimens that mimic struts and nodes. This chapter is divided into four sections. The first section investigates the fatigue strength of strut-like specimens based on their building orientations at four different angles with respect to the printing job plate. Morphological features of the miniaturized specimens such as average and minimum cross-section, eccentricity, waviness, and surface texture are correlated with fatigue strength. The role of inner and surface defects, such as lack-of-fusion (LoF) and gas holes, is also considered to explain the main failure mechanisms. The impact of building orientation on the printing quality of the specimens is highlighted, with an increase in surface roughness and defectiveness as the printing angle decreases, resulting in a shorter fatigue life for miniaturized struts. In the second section, the fatigue effect is studied across different fatigue regimes. The role of the mean stress effect is assessed using the Haigh diagram, which reveals an increase in fatigue life moving towards compressive loading regimes. The effect of the printing angle is also investigated, showing different trends according to the different stress ratios, suggesting different fatigue failing mechanisms. The third section introduces strut-junction miniaturized specimens and evaluates their fatigue behavior according to building orientations. Horizontal specimens show an increased fatigue life compared to their thin strut counterparts, and different morphological outcomes are highlighted, including improved surface quality even at lower angles, possibly related to the node acting as an additional supporting structure. The fourth section presents a design-led compensation strategy for sub-unital lattice specimens, aimed at reducing as-designed/as-built deviations. This systematic decrease in geometrical mismatch suggests potential new design strategies for fatigue enhancement. In Chapter III, bone tissue engineering strategies are explored for the design of foam scaffolds as bio-fillers for lattice-based design. The feasibility of the polymer-metal composite is assessed, using an N2O-based gas foaming technique to fabricate silk fibroin and silk fibroin/gelatin porous scaffolds infilled into a cubic L-PBF Ti-6Al-4V lattice structure. The adhesion at the polymer/metal interface is assessed, with simultaneous electrowetting, showing promise for better and more intimate contact on the outermost surface of the lattice struts. A statistical-based analysis of the foam porosity is then carried out, aimed at optimization towards osteointegration improvement. Selected foams are biologically evaluated, revealing good cell adhesion and differentiation towards an osteogenic phenotype. Chapter IV reports on two different strategies for the design of a Ti-6AL-4V L-PBF lattice-based endplate for total disc replacement. The first strategy focuses on homogenized-based topology optimization, designing an octet-truss prosthetic device with a graded structure and a cell size suitable for polymeric infilling. The second strategy aims at optimizing octet-truss lattice components for fatigue, evaluating the optimal building orientation for the specimens. Experimental results reveal an improvement in the fatigue life of three-point bending test specimens, suggesting the potential of the proposed model. In Chapter V, the major takeaways of this thesis work are discussed, highlighting important advancements in understanding the fatigue behavior of lattice structures and the development of novel hybrid strategies for the design of biomedical devices, with a particular focus on spinal orthopedics. Future possible directions for research are also explored.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第25013号 / 工博第5190号 / 新制||工||1991(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 泉井 一浩, 教授 小森 雅晴, 教授 井上 康博 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Switched reluctance machines (SRMs) have recently attracted more interest in many applications due to the volatile prices of rare-earth permanent magnets (PMs) used in permanent magnet synchronous machines (PMSMs). They also have rugged construction and can operate at high speeds and high temperatures. However, acoustic noise and high torque ripples, in addition to the relatively low torque density, present significant challenges. Geometry and topology optimization are applied to overcome these challenges and enable SRMs to compete with PMSMs. Key geometric design parameters are optimized to minimize various objective functions within geometry optimization. On the other hand, the material distribution in a particular design space within the machine domain may be optimized using topology optimization. We discuss how these techniques are applied to optimize the geometries and topologies of SRMs to enhance machine performance. As optimizing the machine geometry and material distribution at the design phase is of substantial significance, this work offers a comprehensive literature review on the current state of the art and the possible trends in the optimization techniques of SRMs. The thesis also reviews different configurations of SRMs and stochastic and deterministic optimization techniques utilized in optimizing different configurations of the machine. This thesis introduces a new ON/OFF optimization method based on the line search method to overcome the limitations of the conventional annealing-based ON/OFF optimization. The proposed method shows a faster convergence to optimal solutions than the conventional annealing-based ON/OFF method. The thesis also compares the performance of the generative optimization and the topology optimization of a 6/14 switched reluctance machine with the proposed method and the conventional method. The two methods are applied to two different design domains of the machine for topology and generative optimization and the results are compared to the results of the annealing-based ON/OFF method. The results show the effectiveness of the newly proposed method. A new technique has been introduced in this thesis for reducing the time of calculating stator radial force density waves of switched reluctance machines (SRMs). The method is based on the finite element (FE) simulation of a fraction of an electrical cycle. The new approach shows that a significant time reduction is achieved as compared to the time required for stator radial force density calculation based on the one mechanical cycle simulation method. As the switched reluctance motors introduce new challenges in aspects such as acoustic noise, vibrations, and torque ripples, the method introduced in this helps reduce the time of the optimization process of switched reluctance machines in the design stage to improve the machine performance. The proposed method is applied to radial flux switched reluctance machines. Three different SRMs configurations were used to show the effectiveness of this technique in different force components with minimal error as compared to the benchmark method based on the FE simulation of one mechanical cycle. / Dissertation / Doctor of Philosophy (PhD)

The aim of this work is to model, manufacture, and test an optimized Messerschmitt-BölkowBlohm beam using additive manufacturing. The implemented method is the Solid Isotropic Material with Penalization of a minimum compliance design. The Taubin smoothing technique was used to attenuate geometric noise and minimize the formation of overhanging angles and residual stresses due to the thermal activity of the selective laser melting process. The optimized model required examination and repair of local errors such as surface gaps, non-manifold vertices, and intersecting facets. A comparison between experimental and numerical results of the linear elastic regimes showed that the additively manufactured structure was less stiff than predicted. Potential contributors are discussed, including the formation of an anisotropic microstructure throughout the layer-by-layer melting process. In addition, the effect of selective laser melting process on the mechanical properties of stainless steel 316l-0407 and its influence on structural performance was described.