Novel Curvilinear 2|3D Unified Finite Element Formulations for the Analysis of Complex Shell Structures
Piero CHIAIA, Maria CINEFRA, Erasmo CARRERA
Abstract. In this paper, a detailed locking analysis of novel curvilinear finite element models for the analysis of shells is proposed. In the introduced methodology, novel higher-order shell models are proposed in a non-orthogonal reference frame, recovering the classical Cartesian description via a consistent transformation law. The shell models are defined within the well-established Carrera Unified Formulation (CUF) framework, by which Lagrange-based theory of structures are merged with classical finite element interpolation of the reference mid-surface, obtaining novel shell elements with enhanced three-dimensional geometrical modeling capabilities. By exploiting the computational efficiency of 2D models, these novel 2|3D elements are now being adopted in locking investigations to assess the accuracy and capabilities of the proposed approach when complex structural problems are addressed. The methodology is validated by analyzing classical numerical benchmarks and patch tests proposed in the literature.
Keywords
Curvilinear Models, Shell Models, Variable Thickness, Variable Curvature
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: Piero CHIAIA, Maria CINEFRA, Erasmo CARRERA, Novel Curvilinear 2|3D Unified Finite Element Formulations for the Analysis of Complex Shell Structures, Materials Research Proceedings, Vol. 69, pp 1304-1309, 2026
DOI: https://doi.org/10.21741/9781644904251-226
The article was published as article 226 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] R J. N. Reddy. “Finite Element and Finite Volume Methods for Heat Transfer and Fluid Dynamics”. Cambridge University Press, 2022
[2] Addessi D., Di Re P., and Cimarello G. “Enriched beam finite element models with torsion and shear warping for the analysis of thin-walled structures”. Thin-Walled Structures, 159:107259, 2021. https://doi.org/10.1016/j.tws.2020.107259
[3] Patni M., Minera S., Weaver P.M., and Pirrera A. “Efficient modelling of beam-like structures with general non-prismatic, curved geometry”. Computers & Structures, 240:106339, 2020, https://doi.org/10.1016/j.compstruc.2020.106339
[4] Cinefra M. and Rubino A. “Assessment of New Adaptive Finite Elements Based on Carrera Unified Formulation for Meshes with Arbitrary Polygons”. Aerotecnica Missili & Spazio, Vol. 102, 279–292 (2023).. https://doi.org/10.1007/s42496-023-00165-6
[5] Carrera E., Cinefra M., Zappino E., and Petrolo M. “Finite Element Analysis of Structures Through Unified Formulation”. Wiley, Chichester, West Sussex, UK, jul 2014.
[6] Li G., Carrera E., Cinefra M., de Miguel A.G., Pagani A., and Zappino E. “An adaptable refinement approach for shell finite element models based on node-dependent kinematics”. Composite Structures, 210:1–813 19, February 2019. https://doi.org/10.1016/j.compstruct.2018.10.111
[7] Cinefra M. Formulation of 3D finite elements using curvilinear coordinates. Mechanics of Advanced Materials and Structures, 29(6):879–888, July 2020. https://doi.org/10.1080/15376494.2020.1799122
[8] Chiaia P., Cinefra M. and Carrera E. “Curvilinear 2|3D finite elements for the analysis of shells with arbitrary curvature and variable thickness”, Computers & Structures, Vol 317, October 2025, 107911. https://doi.org/10.1016/j.compstruc.2025.107911
[9] Cinefra M., Chinosi C. and Della Croce L. “MITC9 Shell Elements Based on Refined Theories for the Analysis of Isotropic Cylindrical Structures”. Mechanics of Advanced Materials and Structures, 20:2, 91-100. https://doi.org/10.1080/15376494.2011.581417
[10] Cinefra M. 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, July 2021. https://doi.org/10.1016/j.euromechsol.2021.104273
[11] Moruzzi M.C., Cinefra M., and Bagassi S. Free vibration of variable-thickness plates via adaptive finite elements. Journal of Sound and Vibration, 577:118336, May 2024. https://doi.org/10.1016/j.jsv.2024.118336
[12] Bathe K.J. and Ho L.W. “A simple and effective element for the analysis of general shell structures”. Computers & Structures, Vol. 13, pp. 673-681, 1981. https://doi.org/10.1016/0045-7949(81)90029-8
