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An extended Generalized beam theory formulation for large deformation analyses of perforated Thin-Walled members
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DOI：10.1016/j.compstruc.2025.108052.png)
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Abstract
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This paper presents a geometrically exact beam finite element based on the classic Generalized Beam Theory (GBT) for large-deformation analyses of perforated thin-walled sections. The proposed formulation enables the beam to undergo arbitrary cross-sectional deformations, such as in-plane distortion, out-of-plane warping, transverse bending, and extension of the cross-sectional walls. The key novelty of the proposed approach lies in the extension/improvement of a previous GBT formulation for handling linear buckling analyses of perforated thin-section beams, proposed by the authors Duan et al. (2022), to the realm of large-deformation analysis. The geometrically exact kinematic description is built by enriching the cross-section kinematics of a spatially rotated Euler-Bernoulli/Vlasov thin-section beam with some hierarchic deformation modes and using the enrichment functions constructed in terms of signed distance functions to approximate cross-section discontinuities caused by holes. The Neo-Hookean hyperelastic material model is imposed on the proposed beam FE formulation, where an iterative procedure is performed to ensure the plane stress assumption for the stress fields in cross-section walls. The discrete equations are obtained by using the displacement Galerkin method. Some illustrative examples are presented to demonstrate the potential of the proposed beam FE, and the results demonstrate its capability to perform the GBT modal decomposition of buckled configurations of perforated thin-section members.
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