Verification of the Thin-walled Beam Theory with Application of FEM and Shell Modelling

This article presents the results of a systematic comparison of predictions of the thin-walled beam theory and shell theory in the context of bending of elastic thin-walled beams with an open or closed cross-section. The results for shell theory were obtained using FEM and the ABAQUS/Standard program. The bending task of the thin-walled beam was decomposed into the task with a symmetrical and anti-symmetrical loading, so that the bending and torsion of the thin-walled element would be better visible. In order to objectify the comparison, two coefficients characterizing the mutual similarity of functions were introduced: root mean square deviation coefficient determined for the selected cross-section (in relation to the entire contour) and a coefficient determining the maximum relative difference of a given quantity. The comparison was made for both the stress and the displacement state.