Assessment of CUF-Based Variable-Section 1D Finite Elements for the Nonlinear Analysis of a Wingbox Structure

Assessment of CUF-Based Variable-Section 1D Finite Elements for the Nonlinear Analysis of a Wingbox Structure

Francesco Mario Antonio MITROTTA, Antonio Paolo FONTANELLA, Maria CINEFRA, Rauno CAVALLARO

Abstract. The integration of postbuckling behavior into aeroelastic optimization frameworks faces a critical barrier in the computational cost of nonlinear finite element analyses with traditional shell-based wingbox models. This study investigates whether variable-section 1D finite elements based on the Carrera Unified Formulation (CUF) can replicate the nonlinear response of wingbox structures with reduced computational cost. Nonlinear analyses of the Simple Transonic Wing benchmark are performed using MSC Nastran shell elements and two CUF models with different mesh refinements. While the CUF models achieve comparable or better computational efficiency, the approaches predict substantially different onset points for geometric nonlinearity: the Nastran model exhibits softening behavior at the linear buckling load of 133 kN, whereas the CUF models maintain nearly linear response until approximately 264–272 kN. Importantly, the close agreement between the two CUF mesh refinements demonstrates that this discrepancy cannot be attributed to insufficient CUF discretization. These findings raise a critical question about the minimum fidelity required to accurately capture global nonlinear postbuckling behavior, whose answer is essential for including nonlinear structural stability analysis in aeroelastic optimization.

Keywords
Carrera Unified Formulation, Finite Element Analysis, Nonlinear Analysis, Wingbox Structure

Published online 7/20/2026, 6 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Francesco Mario Antonio MITROTTA, Antonio Paolo FONTANELLA, Maria CINEFRA, Rauno CAVALLARO, Assessment of CUF-Based Variable-Section 1D Finite Elements for the Nonlinear Analysis of a Wingbox Structure, Materials Research Proceedings, Vol. 69, pp 1416-1421, 2026

DOI: https://doi.org/10.21741/9781644904251-248

The article was published as article 248 of the book CEAS – AIDAA Conference 2025

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] Air Transport Action Group. Waypoint 2050: Balancing growth in connectivity with a comprehensive global air transport response to the climate emergency. Technical report, Geneva, Switzerland, 2021.
[2] P. Bardon and O. Massol. Decarbonizing aviation with sustainable aviation fuels: Myths and realities of the roadmaps to net zero by 2050. Renewable and Sustainable Energy Reviews, 211:115279, 2025. https://doi.org/10.1016/j.rser.2024.115279
[3] G. Zhang, Y. Hu, B. Yan, M. Tong, and F. Wang. Buckling and post-buckling analysis of composite stiffened panels: A ten-year review (2014-2023). Thin-Walled Structures, 205:112525, 2024. https://doi.org/10.1016/j.tws.2024.112525
[4] F.M.A. Mitrotta, A. Pirrera, T. Macquart, J.E. Cooper, A. Pereira do Prado, and P. Higino Cabral. Proof of concept of a nonlinear structural stability constraint for aeroelastic optimisation. The Aeronautical Journal, 129(1335):1237-1264, 2025. https://doi.org/10.1017/aer.2024.151
[5] M. Cinefra. Non-conventional 1d and 2d finite elements based on cuf for the analysis of non-orthogonal geometries. European Journal of Mechanics – A/Solids, 88:104273, 2021. https://doi.org/10.1016/j.euromechsol.2021.104273
[6] A.C. Gray and J.R. Martins. A proposed benchmark model for practical aeroelastic optimization of aircraft wings. In AIAA SCITECH 2024 Forum. https://doi.org/10.2514/6.2024-2775
[7] F.M.A. Mitrotta, A. Pirrera, and J.E. Cooper. Preliminary aeroelastic optimization of the simple transonic wing with nonlinear structural stability constraints. In AIAA SCITECH 2025 Forum. https://doi.org/10.2514/6.2025-2811
[8] A.P. Fontanella, T. Sironi, P. Chiaia, M. Cinefra, and A. Pagani. Nonlinear post-buckling analysis of variable cross-section beams using the carrera unified formulation. In CEASAIDAA Joint Conference 2025.