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Cross-sectional mapping for refined beam elements with applications to shell-like structures

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Abstract

This paper discusses the use of higher-order mapping functions for enhancing the physical representation of refined beam theories. Based on the Carrera unified formulation (CUF), advanced one-dimensional models are formulated by expressing the displacement field as a generic expansion of the generalized unknowns. According to CUF, a novel physically/geometrically consistent model is devised by employing Legendre-like polynomial sets to approximate the generalized unknowns at the cross-sectional level, whereas a local mapping technique based on the blending functions method is used to describe the exact physical boundaries of the cross-section domain. Classical and innovative finite element methods, including hierarchical p-elements and locking-free integration schemes, are utilized to solve the governing equations of the unified beam theory. Several numerical applications accounting for small displacements/rotations and strains are discussed, including beam structures with cross-sectional curved edges, cylindrical shells, and thin-walled aeronautical wing structures with reinforcements. The results from the proposed methodology are widely assessed by comparisons with solutions from the literature and commercial finite element software tools. The attention is focussed on the high computational efficiency and the marked capabilities of the present beam model, which can deal with a broad spectrum of structural problems with unveiled accuracy in terms of geometrical representation of the domain boundaries.

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Notes

  1. Note that, as in the case of this paper, the use of 3D constitutive relations does not entail Poisson locking if higher-order kinematics are employed on the cross-section, see [35, 45].

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Acknowledgements

This research has been carried out within the project FULLCOMP—FULLy analysis, design, manufacturing, and health monitoring of COMPosite structures—funded by the Marie Sklodowska-Curie actions Grant Agreement No. 642121. The H2020 European Training Networks are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    A. Pagani, A. G. de Miguel & E. Carrera

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  1. A. Pagani
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  2. A. G. de Miguel
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  3. E. Carrera
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Correspondence to E. Carrera.

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Pagani, A., de Miguel, A.G. & Carrera, E. Cross-sectional mapping for refined beam elements with applications to shell-like structures. Comput Mech 59, 1031–1048 (2017). https://doi.org/10.1007/s00466-017-1390-7

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