A thin-walled beam element based on semi-analytical solution modes

Using energy principles, a thin-walled beam element is introduced for the analysis of beams with deformable cross-sections that are prone to distortion. The beam element is based on previously attained semi-analytical displacement solution modes of an advanced thin-walled beam model. The first-order beam element for linear analysis handles shear deformations related to both Timoshenko and Mindlin-Reissner type deformations, warping effects of torsion, cross-section distortion including associated warping effects, as well as the transverse displacement effect from normal stress.

The formulation can handle both open and closed cross-sections without special attention. The formulation of the displacement solution modes and the stiffness integration of the products of the advanced displacement modes using the Hadamard product are described. The paper also presents the transformations between modal degrees of freedom and element displacement degrees of freedom.

Four examples show the beam element capabilities and good agreement with results obtained using the shell and solid elements of a commercial finite element program. The kinematic assumptions that the thin-walled beam model accommodates leads to local shear stress transfer at corners. This transfer of shear stresses is not normally seen in thin-walled beam formulations or shell models.

However, the shear transfer is verified through examination of a finite element model using solid elements.