The use of multi-axis additive manufacturing has enabled the possiblity to fabricate parts using curved layer deposition. Compared to the traditional deposition using planar layers of a fixed thickness, multiaxis additive manufacturing significantly increases the number of possible fabrication sequences. With the introduction of a time component for topology optimization in recent work, fabrication-processdependent physics can now be incorporated in the optimization process. The fabrication sequence resulting from such complex optimizations can lead to layers with large variations in thickness. For manufacturability reasons, considering multi-axis additive manufacturing, this variation should be controlled. In this thesis, we present a method to control the variation in thickness of the projected layers to improve the manufacturability. We use the continuous pseudo-time field and its gradients to track the development of the layer boundaries. To demonstrate the effectiveness of the method, we apply the thickness control method on a fabrication sequence optimization for minimizing thermal distortion. The results show that the proposed method is able to reduce the variation of thicknesses compared to the original sequence optimization without thickness control resulting in improved manufacuturability.

Additive manufacturing (AM) has revolutionized part manufacturing, offering unprecedented design freedom and the ability to fabricate intricate structures. Computational design methods like topology optimization (TO) effectively capitalize on AM's design freedom. However, manufacturability constraints must be considered to ensure reliable manufacturing. A significant constraint is local overheating, prevalent in metal additive manufacturing, leading to defects, part distortion, and diminished mechanical properties. While overhangs are commonly associated with overheating, they are not the only geometric features prone to overheating. This thesis addresses the overheating issue in topology optimization by a novel geometric approach. Specifically, we propose to estimate the local conductivity around each element by evaluating the material distribution in its vicinity. This is then used to generate a pseudo temperature field (i.e., hotspot map) to assess overheating risks. Formulated as a constraint in topology optimization, our approach creates optimized structural layouts free of local overheating during additive manufacturing. Additionally, the approach is implemented in space-time topology optimization, limiting overheating risks by simultaneous optimization of structural layout and fabrication sequence. Compared with existing overheating prevention methods, the geometry-based constraint demonstrates significant computational advantages. Transient thermal AM simulations were conducted on the final designs obtained using the physics-based method from the literature and the novel geometry-based overheating prevention method. The numerical results have shown that the proposed geometric approach is efficient and effective in controlling local overheating in topology optimization for metal additive manufacturing.

In the realm of traditional additive manufacturing, design and fabrication sequence planning have historically followed separate tracks. However, recent strides in the field, particularly in the utilization of robotic arms with multiple degrees of freedom, have brought forth a revolutionary approach known as Space-Time Topology Optimization (STTO). This groundbreaking algorithm breaks down the barriers between design and fabrication by simultaneously optimizing the structure and fabrication sequence. It achieves this feat by employing density and time fields as design variables, allowing for a holistic and integrated approach to the manufacturing process. However, within the framework of STTO, multiple iterations of finite element computations become necessary. This results in a substantial computational burden throughout the overall process. My contribution within STTO lies in its adoption of a multi-resolution strategy. This strategy enables the use of different resolutions for the design fields, enhancing computational efficiency. Coarsening, a critical component of this strategy, is implemented through a sophisticated weighted average scheme. This coarsening process facilitates the construction of stiffness matrices with significantly reduced finite element calculations, resulting in substantial time savings during the optimization process. The impact of coarsening in STTO has been rigorously studied across various levels, yielding remarkable results and advantages. In 2D scenarios, this approach has achieved an impressive 5-fold reduction in computation time, while in the more complex 3D domain, it has led to an astounding 30-fold decrease. Moreover, it's worth noting that compliance, a crucial performance metric, maintains its integrity even with coarsening, with compliance drop remaining below 5% for levels deemed acceptable. This study illuminates the profound implications of coarsening within the STTO framework, emphasizing the significant strides made in computational efficiency while ensuring structural integrity and performance.