Sizing High-Aspect-Ratio Wings with a Geometrically Nonlinear Beam Model

Abstract

This study considers the effect of geometric nonlinearity at the design concept stage of an aircraft wing. A nonlinear finite element beam model adopting the finite volumes concept with an intrinsic strain and curvature formulation is used to size a single-aisle passenger aircraft. A linearized version of this geometrically nonlinear formulation provides a linear benchmark from which the nonlinear predictions of loads, weight, and performance can be compared. A baseline study on a wing with an aspect ratio of 18 shows that geometric nonlinearity can have a significant impact on the internal loads, leading to a reduction in the wing weight. The effect of aspect ratio is also explored, yielding optimal values at which the Breguet range is maximized and showing the effect of geometric nonlinearity on that range. This is complemented by a parameter study on the effect of varying the wing span and surface area, showing that, if gate limitations in the form of span constraints are imposed on the sizing, the optimal aspect ratio is significantly reduced and geometrically nonlinear effects are mitigated. The paper demonstrates the correlation between geometric nonlinearity and the improvements in the wing mass and Breguet range as compared to a conventional linear analysis.