Structural Analysis and Optimization of Aircraft Wings Through Dimensional Reduction
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Federal Aviation Regulations (FARs) are key drivers of aircraft design. Early-stage aircraft design involves a tight coupling between structural dynamics, aerodynamics, and flight mechanics, with time-dependent loads arising from the considerations of the FARs. The current state-of-the-art decouples the time-domain simulation from the stress/strain computation. Further, simplifying assumptions do not account for the intricate features of the internal structure present in an aircraft wing. Beam theory for structural analysis has been successfully applied to the design of other slender structures subjected to time-dependent loads, like rotorcraft blades. While aircraft wings can be considered slender structures, aperiodicity and inhomogeneity along the span render beam theory ineffective. The present work aims to bridge this gap by proposing a method for analyzing 3-D structures through dimensional reduction. 1-D models are computationally efficient and can be used in the time-domain to obtain the loads. The Variational Asymptotic Method (VAM) allows for the systematic reduction of 3-D structures to 1-D models and further recover 3-D stresses and strains after solving the 1-D problem. A structural optimization framework was developed for the unique analysis method presented, allowing for sizing the structure under strength considerations. Findings show that: 1) the use of VAM allows for the systematic extraction of beam properties for aircraft wings, 2) the displacement and stress response of the aircraft using beam models match reasonably well against those produced by shell-based models, 3) for dynamic simulations the derived adjoint method computes accurate gradients efficiently to be used in structural optimization, 4) sizing of aircraft wings for 14 CFR specified maneuvers using the proposed approach produces a 6\% error compared to shell-based method, but with a 7.8x speed-up. The proposed approach provides improvements on the existing literature methods- it is computationally efficient, provides reasonable accuracy for early-stage structural sizing and weight prediction, and includes dynamic effects. The computational efficiency makes it well-suited for many-query applications like optimization, uncertainty quantification, and generating data for surrogate modeling.