Displacement modes of a thin-walled beam model with deformable cross sections

A novel one dimensional beam model for analysis of prismatic thin-walled beams with deformable cross sections is introduced and a novel cross section mode determination procedure, which leads to the three dimensional beam displacement modes, is derived. The first order beam model for linear analysis includes: shear deformations related to both Timoshenko and Mindlin-Reissner type shear deformations, the warping effects of torsion, cross section distortion with related warping effects, as well as the Poisson effect with transverse displacements due to normal stress. The generality of the model allows it to handle open, closed and multi-cell cross sections with branched walls. The cross section analysis procedure leads to two types of beam displacement modes referred to as distortional beam modes and fundamental beam modes, with exponential and polynomial variations along the beam axis, respectively. It turns out that each of the beam deformation modes consists of a sum of one to four cross section displacement fields each with an individual axial variation. The displacement modes can facilitate the formulation of an advanced thin-walled beam element. The beam displacement modes will be illustrated for an open and a closed cross section.