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

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 general...

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Bibliographic Details
Published in:Computational mechanics 2017-06, Vol.59 (6), p.1031-1048
Main Authors: Pagani, A., de Miguel, A. G., Carrera, E.
Format: Article
Language:English
Subjects:
Aeronautics
Beam theory (structures)
Boundaries
Classical and Continuum Physics
Computational Science and Engineering
Computing time
Cross-sections
Curved beams
Cylindrical shells
Engineering
Finite element method
Mapping
Mathematical models
One dimensional models
Original Paper
Software development tools
Theoretical and Applied Mechanics
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Summary: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.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-017-1390-7