| Summary: | The need for efficient thermally radiating structures for aerospace applications is apparent in many system designs including satellites, launch vehicles and hypersonic aircraft. While multidisciplinary structural optimization methods have been employed to design these systems, few have incorporated thermal radiation as part of their multi-physics analysis capability. Moreover, with the rapid advancement of manufacturing technologies, the ability to fabricate flight hardware with unprecedented geometric complexity has challenged the limits of human design intuition. As a result, there is a critical need for free-form design methods to harness the full potential of these new manufacturing techniques. This thesis presents a level set based topology optimization approach for designing thermally efficient radiating structures considering multiple objectives, constraints and disciplines. Level set based methods offer a key advantage of defining crisp structural boundaries while seamlessly handling complex geometric transformations. The first contribution of this thesis is deriving a shape sensitivity of the thermal heat power radiated objective function using the adjoint method. This sensitivity is a necessary ingredient for our gradient-based algorithm. The second contribution is developing a topology optimization framework capable of handling multiple objectives and constraints via the augmented Lagrangian method. Both von Mises stress and first mode frequency constraints are implemented since they are commonly found in aerospace design problems where severe structural loads can lead to catastrophic failure. The final contribution is testing several data mining techniques to identify prominent topological features of a large set of designs found using our topology optimization approach. The CUR matrix decomposition is best suited for identifying the principal designs and also aids in categorizing the solution topologies. These contributions are demonstrated on several 2D example problems where the goal is to identify thermally efficient radiating structures able to reject heat using limited material. Both von Mises stress and first mode frequency constraints are enforced to ensure that solutions are sufficiently rigid. The results indicate that many locally optimal solutions exist in the design tradespace with topologically diverse features. Additionally, we show that the thermal compliance objective function commonly used to design conductive structures is not sufficient when a radiating surface exists
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