UC San Diego

The design and optimization of electric vertical takeoff and landing (eVTOL) aircraft present significant research opportunities due to the vast, unexplored design space of this emerging vehicle category. Accurate performance prediction necessitates partial differential equation (PDE)-based modeling for various subsystems, including electric motors, composite shell structures, and battery packs. For system design, these models must integrate with non-PDE components, such as low- to mid-fidelity aerodynamic models, geometric design tools, and analysis of multi-body dynamics. Among these challenges, gust response—capturing the dynamic structural reaction to sudden wind changes—is critical for ensuring structural integrity and safety, serving as the focus of this dissertation. This complexity highlights the need for integrating multidisciplinary design optimization (MDO) with finite element methods (FEM) in a time-domain setting, which is essential for efficiently solving PDEs within a comprehensive design framework.

This dissertation presents a time-domain structural optimization approach for a Lift-Plus-Cruise (LPC) wing under gust loads using automated adjoint methods. Two case studies are conducted with different objectives—aggregated tip displacement and mass. Both optimizations converged within reasonable turnaround times, revealing realistic optimal thickness distributions. A key contribution is the development of an adjoint-ready shell model, available in both linear and geometrically nonlinear forms, integrated within the Finite Elements for Multidisciplinary Optimization (FEMO) framework. This integration enables effective aeroelastic coupling by linking structural and aerodynamic models to optimize the interaction between aerodynamic loads and structural deformation. FEMO incorporates PDE-based models, i.e., the structural model, into gradient-based optimization of multidisciplinary systems, achieved through the integration of FEniCSx with the Computational System Design Language (CSDL), which is a domain-specific language designed to facilitate adjoint sensitivity analysis in MDO.

Apart from the LPC wing design under gust loads, the framework’s modularity is demonstratedthrough various optimization tasks, including other eVTOL-specific applications such as electric motor shape optimization, as well as traditional PDE-constrained topology optimization and optimal control problems. The shell model has also been extended to other real-world applications, such as composite wind turbine blades incorporating geometric nonlinearity, making it a valuable tool for optimizing complex structures across multiple fields.