On the Importance of Cross-Sectional Distortions and their Inclusion in an Efficient GBT-Formulation

Abstract

This proceeding proposes an efficient generalized beam theory formulation, which accounts for cross-sectional deformations in slender prismatic structures. It was shown by the authors in a recent publication [1] that in-plane distortional deformations and accompanied out of plane warping deformations of the cross-section influence the accuracy of results in beam dynamics especially if thin-walled cross-sections are applied. The GBT formulation proposed in [1] overcomes the inaccuracies of classical beam mechanics, however, requires a two-dimensional plane discretization of the cross-section. The computational complexity can be reduced vastly, if the thin-walled cross-sections can be discretized with one-dimensional elements. Consequently, this proceeding discusses a corresponding derivation, where the line mesh which discretizes the cross-section has six degrees of freedom at each node. The membrane part consists of mass-less micro-polar rotations (drilling rotations) and can be derived independently from the bending part, where a shear elastic formulation is selected.