Computational Modeling of Flutter Constraint for High-Fidelity Aerostructural Optimization

Abstract

High fidelity computational modeling and optimization of aircraft has the potential to allow engineers to produce more efficient designs, requiring fewer unforeseen design modifications late in the design process. In order for the optimization algorithm to generate a useful design, all the relevant physics must be considered, including flutter. This is especially important for the high-fidelity aerostructural optimization of commercial aircraft, which is likely to result in wing designs that are prone to flutter. To address this issue, we develop a flutter constraint formulation suitable for gradient-based optimization. This paper investigates the feasibility of using a Doublet-Lattice Method (DLM) based flutter constraint for high-fidelity aerostructural optimization. An efficient non-iterative root finding method is developed to compute the flutter eigenvalues from a generalized eigenvalue problem, based on the p-k flutter equation. A mode tracking scheme is implemented at two levels that successfully tracks the mode migration. An effective constraint curve is then developed to define the flutter free flight envelope, in addition to preventing discontinuities in the flutter constraint. This method allows for minimum flutter velocity to be specified implicitly. The Kreisselmeier-Steinhauser (KS) function is used to aggregate the difference of the flutter damping eigenvalues and the constraint curve into a single value that is then used in an optimization. We compute accurate and efficient derivatives of the constraint value with respect to structural sizing variables, as well as wing planform variables. Derivatives are computed using a combination of analytic and automatic differentiation methods in reverse (adjoint) and validated using the complex-step method. To study the behavior of the flutter constraint using this method, we perform a design space analysis and optimize an idealized wing (flat plate) of a rectangular planform.

Structural damping models for passive aeroelastic control

“…[26,27]. The method is chosen for the studies of this paper due to its proven robustness and because it is not subject to the convergence issues experienced by iterative approaches [28]. The method solves the flutter equation using a p-k approach for a set of reduced frequencies and uses an inner-loop mode-tracking [29] and a linear interpolation for finding the solutions that verify the condition…”

Using Graph Coloring To Compute Total Derivatives More Efficiently in OpenMDAO

“…Not all optimization problems naturally have a small number of constraints, which would seem to limit the applicability of the adjoint method. However, constraint aggregation techniques [4][5][6][7] offer a way to manipulate the problem definition into a form more suitable to apply the adjoint method. Though constraint aggregation has been widely and successfully employed in a huge range of different cases, it is not universally applicable.…”

Parametric Modeling of a Long-Range Aircraft under Consideration of Engine-Wing Integration

“…Jonsson et al [11] developed and implemented a flutter constraint formulation suitable for gradient-based optimization processes for a wing-alone configuration. They performed a design space analysis and optimized the planform of an idealized wing using a multidisciplinary objective.…”