A Geometrically Exact Curved Thin-Walled Beam Finite Element Accounting for Cross-Section Deformation

Most of the current research requiring the computational modeling of thin-walled members is shell finite element-based, even though in particular applications either Generalized Beam Theory or Finite Strips can be employed with significant advantages. However, for thin-walled members susceptible to cross-section deformation and undergoing large displacements and/or material nonlinearity, shell finite elements are usually more accurate and much more efficient from a computational point of view.

In spite of the above considerations, the so-called geometrically exact beam finite elements can also be successfully employed in the large displacement range. The geometrically exact beam concept was pioneered by Reissner (1972) and Simo (1985), owing its name to the fact that no geometric simplifications are introduced besides the assumed kinematics. The inclusion of cross-section deformation in initially straight geometrically exact thin-walled beam formulations has been presented by Goncalves et al. (2010; 2011).

In this paper, the geometrically exact thin-walled beam formulation presented by Goncalves et al. (2010) is extended to account for initial curved geometries (not a trivial task) and some computational aspects are improved - for instance the derivative of the torsional curvature, which is computationally expensive, is no longer required. As in the previous formulation, cross-section in-plane and out-of-plane deformation are included. The accuracy and efficiency of the proposed element are assessed through several illustrative numerical examples. For validation purposes, the results obtained are compared with values yielded by shell finite element models.

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