High-Fidelity Gradient-Based Wing Structural Optimization Including Geometrically Nonlinear Flutter Constraint

Abstract

Lightweight high-aspect-ratio wings make aircraft more energy efficient thanks to their lower induced drag. Because such wings exhibit large deflections, design optimization based on linear flutter analysis of the wing undeformed shape is inadequate. To address this issue, we develop a framework for integrating a geometrically nonlinear flutter constraint, which considers in-flight deflections, into a high-fidelity gradient-based structural optimization. The wing mass and stress constraints are evaluated on a linear built-up (detailed) finite element model to capture realistic structural features. The geometrically nonlinear flutter constraint is based on a condensed low-order beam representation of the built-up finite element model, which captures the impact of in-flight deflections with tractable computational effort for optimization. The flutter constraint is differentiated with respect to the detailed structural model sizing variables using the adjoint method to enable large-scale optimizations. The framework is demonstrated by minimizing the mass of a wingbox model subject to the geometrically nonlinear flutter constraint along with stress and adjacency constraints. The geometrically nonlinear flutter constraint adds a penalty of up to 60% of the baseline mass due to the impact of in-flight deflections on the flutter onset speed and its mechanism. In contrast, a linear flutter constraint evaluated on the undeformed wing adds a mass penalty of only 10%. This methodology can help design energy-efficient aircraft with high-aspect-ratio wings, which require geometrically nonlinear flutter analyses early in the design cycle.