A Data-Driven Modeling Framework for Nonlinear Static Aeroelasticity

Analyzing the multiphysical coupling between a deformable structural body and the forces imposed on that body from a surrounding fluid can be a challenging and computationally expensive task, especially when the structure, fluid, or both exhibit nonlinear behavior. Consequently, there exists a need for novel reduced-order static aeroelasticity analysis techniques that make efficient use of high-fidelity computational models, especially for preliminary design of next- generation aerostructures with high-aspect ratio lifting surfaces exhibiting large deformations or in situ geometric reconfigurations driven by nonlinear mechanisms. This work presents the compositional static aeroelastic analysis method: an embarrassingly parallelizable data- driven modeling technique that seeks to construct a system-level aeroelastic surrogate model representing the function composition of high-fidelity structural and fluid models in terms of shape parameters characterizing a reduced-order geometric description of the deformed fluid-structure interface. By formulating the static aeroelasticity problem as a fixed point problem, the proposed reduced-order modeling framework removes the need for a reduced- order representation of the traction field acting on the structure, unlike previous data-driven methods that independently train separate fluid and structural surrogate models. Additionally, by replacing the iterative exchange of full-order aeroelastic coupling variables with a statistical exploration of a reduced-order shape parameter space, the minimum computational time for approximating a static aeroelastic response is equivalent to one set of high-fidelity fluid and structural model evaluations. The following work presents the theoretical development of the proposed compositional method and demonstrates its use in two case studies, one of which involves a cantilevered baffle comprised of linear and nonlinear material with large deformations exceeding 35%. Numerical results show close agreement with a conventional partitioned analysis scheme, where tip displacement error is less than 1% in both material cases. It is also demonstrated how traction field information can be reused when considering structural modifications to circumvent the need for additional computationally expensive fluid model evaluations.