Multidisciplinary design optimization is playing an increasingly important role in the design of engineering systems. One example is the design of a CubeSat. Multidisciplinary optimization provides a way to evaluate complex tradeoffs involving tight power and mass budgets. However, existing methods are not able to consider swarms of CubeSats, which are becoming increasingly common. This thesis presents a new multidisciplinary optimization and modeling method for CubeSat swarms operation, including the multiple disciplines of orbita mechanics, attitude control, propulsion, and communication. The approach efficiently handles thousands of variables and successfully achieves high-fidelity optimization with respect to strict CubeSats alignment and separation constraints, and limited propellant and power. In terms of optimization results, the CubeSat swarm increases the total data download of chief communication spacecraft by 52.9% compared to the original design, yielding improvements of around 15%. improvements in the delta-v and succeeding in controlling the alignment of three CubeSats within a 300mm threshold during scientific observation phase.

Multidisciplinary design optimization (MDO) is an approach that usesoptimization methods to design complex engineering systems involving multiple disciplines simultaneously. The coupled nature of multidisciplinary systems and the large number of design variables involved in complex systems present unique challenges to solving MDO problems. One of these challenges is the implementation of software necessary to evaluate multidisciplinary models within an optimization framework. When gradient-based optimization approaches are used, efficient and accurate derivatives must be computed for each model evaluation. This dissertation presents an approach that significantly reduces the manual effort required to implement computational models for use within a gradient-based MDO framework, especially in large-scale problems. This dissertation introduces a novel approach to address these challenges and automate the process, enabling accurate and efficient adjoint-based sensitivity analysis for gradient-based MDO in particular. To address these challenges, a three-stage compiler methodology is proposed. The methodology centers around a graph representation that provides a foundation for automating sensitivity analysis in MDO. In addition, the Computational System Design Language (CSDL) is introduced, which allows for a concise description of the physical system. The adoption of CSDL demonstrates a twofold reduction in code complexity for engineering models, significantly reducing the barrier to entry for MDO practitioners. The three-stage compiler also provdes users of CSDL with the ability to measure the effect of the model structure on run-time performance and memory complexity using the graph representation. Finally, the methodology developed in this dissertation is applied to the design of a space-based virtual telescope comprised of two spacecraft flying in formation. A reformulation of the orbit dynamics of the spacecraft is found to avoid the introduction of truncation errors due to tight formation constraints that render solving the optimization problem impossible. A sequential approach to applying MDO to the design of a space-based virtual telescope is also found to be more robust than solving the MDO problem where all disicplines are considered simultaneously.

Many design optimization problems, including the optimal layout of wind turbines within a wind farm, enforce constraints to prevent the design from crossing the boundary of the feasible space. When applying gradient-based optimization to such problems, the models must provide an accurate representation of the feasible space and be continuous, smooth, amenable to differentiation, and fast-to-evaluate. This thesis presents the work from two intertwined topics involved in modeling geometric non-interference constraints and wind farm optimization. First, we formulate a new method that uses B-splines to generate an efficient-to-evaluate level set function that approximates the signed distance function for boundary constraint enforcement. Adapting ideas from the field of surface reconstruction, we formulate an energy minimization problem to calculate the B-spline control point values. Unlike previous constraint formulations, the new method requires an initial setup, but results in a more efficient and scalable representation of the geometric non-interference constraint. We present the results of accuracy and scaling studies performed on our formulation. Second, we perform optimization studies to the design of a wind farm. Utilizing the aforementioned constraint method, we perform a layout, yaw misalignment, and hub height optimizations to improve the annual energy production of a wind farm. These models used are verified and compared to industry-leading frameworks that conduct similar optimization studies. Overall, the new constraint method provides an effective way to conduct optimization studies, such as the one conducted in this thesis, with high computational efficiency, and shows promise as a tool for many more design optimization problems.

In aircraft design, unconventional configurations have gained significant recent interest due to increasing demands for greater efficiency as well as emerging applications such as urban air mobility. Since traditional empirical models are not applicable for unconventional aircraft, high-fidelity computational design methods like large-scale design optimization can be employed. However, building up models for such unconventional aircraft is time-consuming and requires a large amount of manual work during the iterative design process. Generating a mesh of a structure with complicated geometry is one of the difficult steps. We present a fully automatic approach for constructing quadrilateral meshes for shell-element analysis of aircraft structures. The method is designed to produce highly isotropic meshes while guaranteeing the coincidence of the nodes of the meshes of internal members and the structural skin. This paper also presents the applications of the algorithm on the OWN-06c Transonic Airliner from OpenVSP and the eVTOL eCRM-002 from Uber. The results show that our algorithm is simple, efficient, and versatile, which basically fulfills all the requirements of generating shell element meshes for aircraft.

Aerospace vehicle design is a complex process involving multiple engineering disciplines such as aerodynamics, structures, propulsion, and controls. This complexity led to the emergence of multidisciplinary design optimization (MDO), a field that employs numerical optimization methods to improve the designs of engineering systems while simultaneously considering multiple disciplines. Integrating all disciplines significantly increases the problem's complexity, which motivates the use of gradient-based optimization methods with analytical computation of the derivatives. This approach has demonstrated considerable success in tackling practical large-scale MDO problems with hundreds of design variables. Recent applications can be found in the conceptual design of electrified aircraft, unmanned aerial vehicles, and launch vehicles. Presently, most MDO applications formulate and solve deterministic optimization problems in which the objective and constraint functions do not consider randomness. However, real-world scenarios introduce uncertainties arising from factors like variations in operating conditions, parameter fluctuations, and manufacturing discrepancies. Incorporating these uncertainties into MDO problems transforms them into MDO under uncertainty (MDOUU) problems. Addressing well-defined MDOUU problems can enhance the robustness and reliability of MDO-optimized designs in real-world scenarios. This dissertation presents a suite of graph-accelerated uncertainty propagation methods, designed to tackle various forward uncertainty quantification (UQ) and MDOUU problems. At the core of these methods lies a new computational graph transformation method called Accelerated Model Evaluations on Tensor Grids using Computational Graph Transformations (AMTC). AMTC leverages the sparsity in the computational graphs of multidisciplinary systems to accelerate tensor-grid evaluations. This approach has been effectively combined with the non-intrusive polynomial chaos method to tackle UQ and MDOUU problems, with several extensions devised to address higher-dimensional problems within this framework. Towards the end, this dissertation also includes a case study on a laser-beam-powered aircraft design problem. This study offers a comparative analysis between the results of MDO and MDOUU, while also demonstrating the efficacy of graph-accelerated uncertainty propagation methods in addressing large-scale MDOUU problems.

Reconciling optimized designs with the original model can be a time-consuming process. This thesis presents a process for gradient-based optimization using CAD-based parameterization that avoids the reconciliation process by directly altering CAD parameters and automatically updating the design. However, the complexities surrounding most commercial CAD tools make analytically obtaining design sensitivities necessary for gradient-based optimization virtually impossible. The value of this process lies in its ability to numerically compute design sensitivities.

This is done with the use of an intermediary surface discretization of the model called the master-mesh. The master-mesh maintains continuity as CAD parameters change through the use of a mesh smoothing process consisting of two optimizations. This smoothing process ensures that the master-mesh deforms smoothly with the design. Other meshes can be derived from the master-mesh, and therefore, can also deform smoothly with the design. This allows for the finite-difference method to be used to calculate their gradients.

This master-mesh is demonstrated with three distinct applications. The first application consists of an aerodynamic optimization of a wing designed with a custom geometry engine. The second application consists of an aerodynamic shape optimization of a jet plug nozzle designed in CATIA V5. The third application consists of an aerostructural optimization of a wing designed in FreeCAD.