Breaking the Glass Ceiling of Linear Buckling

: Development of a Nonlinear Structural Stability Constraint for Aeroelastic Optimization

Abstract

The aviation industry faces increasing pressure to reduce its environmental footprint, requiring greater efficiency in aircraft design. Traditionally, wings were designed with linear structural stability constraints sufficient for older, stiffer designs. However, modern wings have become increasingly longer and more slender, making their behavior more nonlinear and linear stability constraints less accurate. Furthermore, in traditional aeroelastic optimization frameworks, linear buckling constraints are typically conservative since stiffened panels may continue to carry load beyond their theoretical linear buckling point. Consequently, linear buckling approaches can be questioned both from accuracy and efficiency perspectives, potentially limiting the achievement of more efficient designs. This thesis hypothesizes that these linear approaches create an artificial "glass ceiling" that limits sizing loads and, consequently, structural efficiency. To test this hypothesis, this work investigates nonlinear structural stability constraints for aeroelastic optimization of aircraft wings.

Through progression from canonical one-degree-of-freedom systems to a simplified wingbox model, this work demonstrates that mass reductions can be achieved by exploiting the structure's full nonlinear elastic capacity. The work uses a simplified version of NASA's Common Research Model (CRM), termed the CRM-like Box Beam. Under concentrated tip loading, this model remains stable up to a load 1.42 times its linear buckling load before experiencing limit point bifurcation. Structural optimization studies incorporating nonlinear stability constraints achieve mass reductions of 10.9% with a single design variable and up to 30% with two design variables compared to traditional linear buckling optimization. These results are obtained through nonlinear finite element analyses monitoring tangent stiffness matrix eigenvalues.

Subsequent investigations addressing load introduction methods, skin curvature, and combined bending-torsional loading confirm the conservativeness of linearly optimized designs and the availability of mass reductions with nonlinear structural stability constraints, though the extent varies depending on the specific case considered. At increased load levels, linear buckling analysis transitions from conservative to nonconservative, potentially leading to unexpected instabilities in traditionally optimized structures. When incorporating aerodynamically generated loads, load transfer methodology becomes critical, fundamentally altering nonlinear instability mechanisms and resulting optimal designs.

This thesis demonstrates that incorporating nonlinear structural stability constraints in aeroelastic optimization can either yield substantial weight savings or reveal unexpected instabilities in linearly optimized designs. The latter finding highlights critical accuracy limitations of traditional approaches that may fail to predict actual structural behavior. Therefore, considering nonlinear structural stability effects during preliminary aircraft wing design represents a valuable research direction for more accurate structural prediction and to achieve optimal designs that maintain stability throughout their entire loading history.

Date of Award	30 Sept 2025
Original language	English
Awarding Institution	University of Bristol
Sponsors	UKRI EPSRC & Embraer S.A.
Supervisor	Alberto Pirrera (Supervisor), Jonathan E Cooper (Supervisor) & Terence Macquart (Supervisor)