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Machine Learning to Improve Buckling Predictions for Structural Optimization of Stiffened Structures.

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Bibliographic Details
Title:	Machine Learning to Improve Buckling Predictions for Structural Optimization of Stiffened Structures.
Authors:	Engelstad, Sean P.¹, Burke, Brian J.¹, Kennedy, Graeme J.²
Source:	AIAA Journal. Mar2026, Vol. 64 Issue 3, p1713-1728. 16p.
Abstract:	Buckling is a key failure mode in aircraft structural design. Full wingbox buckling analyses are expensive to include in structural optimizations, so closed-form buckling predictions at the panel level are often used. However, these closed-form solutions are limited to special cases that are analytic, such as simply supported boundary conditions, thin-walled panels, and high aspect ratios for shear buckling. To improve buckling predictions while maintaining computational efficiency for structural optimization, the authors propose the use of machine learning to augment closed-form solutions. Their machine learning models are trained on finite element datasets of stiffened panel buckling with nondimensional parameters informed by closed-form solutions. The authors identify a log transform linear asymptote property from the closed-form buckling solutions. This property is included in the Gaussian process (GP) models to improve model extrapolation for low-aspect-ratio and highly stiffened designs. The custom GP model achieves a 99% R² value for extrapolated data as compared to the closed form and provides accurate buckling predictions on a finite element dataset of mixed simply supported to clamped panels. With the mixed boundary condition dataset, potential weight savings are demonstrated of 3.12 and 11.7% on a subsonic wingbox and a supersonic wingbox, respectively. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	Buckling is a key failure mode in aircraft structural design. Full wingbox buckling analyses are expensive to include in structural optimizations, so closed-form buckling predictions at the panel level are often used. However, these closed-form solutions are limited to special cases that are analytic, such as simply supported boundary conditions, thin-walled panels, and high aspect ratios for shear buckling. To improve buckling predictions while maintaining computational efficiency for structural optimization, the authors propose the use of machine learning to augment closed-form solutions. Their machine learning models are trained on finite element datasets of stiffened panel buckling with nondimensional parameters informed by closed-form solutions. The authors identify a log transform linear asymptote property from the closed-form buckling solutions. This property is included in the Gaussian process (GP) models to improve model extrapolation for low-aspect-ratio and highly stiffened designs. The custom GP model achieves a 99% R² value for extrapolated data as compared to the closed form and provides accurate buckling predictions on a finite element dataset of mixed simply supported to clamped panels. With the mixed boundary condition dataset, potential weight savings are demonstrated of 3.12 and 11.7% on a subsonic wingbox and a supersonic wingbox, respectively. [ABSTRACT FROM AUTHOR]
ISSN:	00011452
DOI:	10.2514/1.J065925