Geometrical Nonlinear Analysis of Beams by Hierarchical Legendre Expansion CUF Models
Alfonso PAGANI, Piero CHIAIA, Erasmo CARRERA
Abstract. A 1D Hierarchical Legendre Expansion model is proposed for the geometrically nonlinear analysis of compact and slender, thin-walled beam structures. Developed within the Carrera Unified Formulation framework, the model employs Legendre polynomial expansions to describe higher-order cross-sectional kinematics and enable efficient p-refinement. By increasing the polynomial approximation order, the formulation improves accuracy without requiring excessive mesh refinement. The hierarchical nature of the approach allows the governing equations to be derived in a compact and theory-independent manner through CUF. This makes the method a powerful alternative for generating refined finite element beam models capable of capturing complex three-dimensional deformation effects, particularly under large displacements and rotations. The proposed methodology is validated through nonlinear benchmark problems involving cross-sectional twisting and warping.
Keywords
P-refinement, Higher-Order Beam Models, Carrera Unified Formulation, Nonlinear Analysis, Hierarchical Legendre Expansion
Published online 11/8/2026, 4 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Alfonso PAGANI, Piero CHIAIA, Erasmo CARRERA, Geometrical Nonlinear Analysis of Beams by Hierarchical Legendre Expansion CUF Models, Materials Research Proceedings, Vol. 73, pp 147-150, 2026
DOI: https://doi.org/10.21741/9781644904459-29
The article was published as article 29 of the book Mechanics of Advanced Materials and Structures
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.
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